BeginReadingTableofContentsCopyrightPage

ForKim

1.So,WhatIsMusic,Anyway?

OnmyfirsteveningasastudentinBirminghamIwalkedintothelocalchipshopandaskedformyfavoritepost-pubdelicacy—chips,peasandgravy. The Chinese lady looked at me quizzically and asked, “What’sgravy?” Iwas totally flummoxed. Iwas used tounquestioned access togravy back in my home town, and I had no idea how to describe thestuff…“Asortofthinbrownsauce?”Fortunatelythesituationwassaved—andawholenewworldofBirminghamsophisticationwasopeneduptome—whenshesmiledandsaidthemagicwords,“Currysauce?”This story is not about the pros and cons of gravy.The point is that

sometimeswecanbefamiliarwithsomethingwereallyenjoy,buthavenoideawhatitactuallyis.Thisistherelationshipmostofushavewithmusic—pleasurewithoutunderstanding.Tomyshame,ImustadmitthatIstilldon’tknowwhatgoesintogravy,butIhavemanagedtountanglesomeoftheingredientsofmusic,andIhopeyouenjoymyexplanationofhowmusiciansmanagetomanipulateourmoodsusingonlystring,bitsofwoodandlengthsoftubing.Thisbookisnotbasedonopinionsorhopefulguesswork.Itisbasedon

realinformationabouthowmusicalnotesareproducedandwhathappenswhen they combine to form a piece of music.Many people think thatmusicisentirelybuiltonart,butthisisnottrue.Therearerulesoflogic,engineeringandphysicsunderlyingthewholecreativesideofmusic.Thedevelopmentof music andmusical instruments over the past couple ofmillenniahasdependedonacontinuousinterplayofartandscience.Youwillbegladtohearthatyouneednomusicalorscientifictraining

to understand this book, although musicians and scientistsshould findplentyofthingstheydidn’tknowbefore.Theonlymusicalskillyouneedistheabilitytohumorsingtwosongs:“BaaBaaBlackSheep”and“ForHe’sa JollyGoodFellow”—and itdoesn’tmatterhowquietlyorbadlyyou sing them, I can’thear you.As far asmath skills go, it would be

usefulifyoucanadd,subtract,multiplyanddivide,buteventheseskillsarenotessential.Also,becauseIamassumingthatyouhavenotraininginthesubject,IwillexplainthemeaningofanyspecialistwordsIuseasIgoalong.Thismaybea littleover-explanatory for themusicians andscientists among you, butI would rather be irritating to some thanbafflingtoothers.ThroughoutthebookIhaveoccasionallyprovideddetailsofpiecesof

music that might be useful to illustrate various points.Most of theseexamplescanbewatchedonYouTubeorlistenedtothroughothermedia—but they are not a necessary part of readingthe book. I put them inbecause you might enjoy them, and because this is an excellentopportunity toadvertise someofmyfavoritemusic.IfyouthinkIhaveexplainedsomethingbadlyoryouneedmoredetail,pleasecontactmebyemailonhowmusicworks@yahoo.co.ukandI’llseeifIcancomeupwithananswer. (This address can alsobeusedbywealthymusic firmswhowanttobribemewithvastsumstoincludereferencestoparticularbitsofmusicinfutureeditionsofthisbook.)Musiccoversanenormousrangeofsubjects,fromthelovelivesofthe

greatcomposerstohowtobuildaguitarorplaythetrumpet.Youcouldsaythatbooksaboutthehistoryofmusiccoverthe“when”questionsandmost other music-related booksaddress the “how to” problems. Thisbook, on the other hand, deals with someof the “what” and “why”questions about music like: what is happening to the air between theinstrumentandyourears?Andwhydosuchthingsaffectyourmood?Readon,andyouwilldiscovertheanswerstothese,andlotsofother

questions,including:

•What’sthedifferencebetweenanoteandanoise?•Whatareminorkeys,andwhydotheysoundsad?•Whydotenviolinssoundonlytwiceasloudasone?•Whydoclarinetssounddifferentfromflutes?•Why areWestern instruments all tuned to the same notes—andwhy

thosenotes,notothers?•Whatisharmonyandhowdoesitwork?

Someofthesequestionshavebeenansweredinthebooksyouwillfindinthephysics sectionof the library, filedunder “MusicalAcoustics.” Theonly problem is that the technical nature of the subject hasmeant thatthese books use lots of math and complicatedgraphs in theirexplanations.Booksfullofgraphsandmathhavealimitedreadership—and this iswhy theonlypeoplewhoseem toknowanything abouthowmusicworksareafewbadlydressedacademics(andIspeakwithsomeauthorityhere,asabadlydressedacademicmyself).When I first started to study the physics and psychology ofmusic I

thought it would be straightforward. How much can therebe tounderstand about how saxophones and harps make different sounds orwhy we use scales? Then I started reading. Some ofthe things I hadthought I understood, like loudness for example, were bizarrelycomplicatedandmuchmoreinterestingthanIthoughttheywouldbe.Toaid my own understanding I began to condense the information intosimpler explanations. EventuallyI realized thatmostof thisknowledgecouldbepresentedclearlytoanyreaderwhohasnomusicalortechnicaltrainingbutsimplylovesmusic.SoIstartedtoputtogetherthenotesthateventuallygrewintothisbook.Even some top-class musicians are not familiar with the basic

underlying facts about music—they play their instruments andproducethecorrectnotes in therightorderwithoutwonderinghoworwhytheirinstruments were designed to produce thoseparticular notes and notothers. It’s as if themusiciansareacting likewaiters—theydeliver themeal to us—and the foodis put together by chefs (composers) fromboxes of ingredients, but no one knows how or why those ingredientsbecameavailableinthefirstplace.I think it’s a shame that something as popular as music has had so

much mystery attached to it. In writing this book, I haven’tused any

math,graphsorwrittenmusic,andIhavekept thestyleconversational.By exploring the basic facts behind whatnotes are, and how they canmove you to dance, kiss or weep, you’ll discover that many of themysteriesofmusicturnouttobeperfectlyunderstandable—andyou’llbedelightedtohearthatyournewlyacquiredunderstandingwon’tstopyoufromdancing,kissingorweeping.My aim is to show you—both musicians and non-musicians—that

music can be understood on a very fundamental level. This levelofunderstandingcandeepenourenjoymentofmusic in thesamewaythatsomeknowledge of how shadows are created or howperspectiveworkscan enhance our enjoyment of a painting. Some people worry thatunderstandingmoreaboutmusicwillreducethepleasuretheygetfromit,but the reverse is true. Learning how a complicated dish is preparedmakes you appreciate it even more,and doesn’t change how good ittastes.Thoughthisisabookaboutallmusic,IhaveconcentratedonWestern

music of all types—from Frank Sinatra, U2 and Beethoven,to nurseryrhymes and film music.All these styles of music, from punk rock toopera,followthesamerulesofacousticsandmoodmanipulation.Therearecomplicated,overlappinglayersofmusicalappreciationand

understanding. At first glance you might think thatthe performingmusicianknowsmoreaboutthemusicthanalistenerwhocan’tplayaninstrument,butthisisn’tnecessarilytrue.Anon-musicianwhoisafanofthe piece being played might know a lot more about how the musicshould sound thanaperformerwho isplaying it for thefirst time.Asalistener, you understand a lot about music already, but a lot of yourknowledge is hidden on a subconscious level. This book will help toexplainandclarifyallthisstuffandIhopeitwillgiveyouafew“ah,sothat’showitworks!”moments.Butenoughofthepreamble—let’sgetonwiththeambling.

Whatismusic?

The conductor Sir Thomas Beecham was always keen on sharing hisviewsonmusic,forexample:“Brassbandsareallverywellintheirplace—outdoorsandseveralmilesaway!”This ismorethana littleharshonbrass bands, but it does show that musiccan produce strong negativefeelingsaswellaspositiveones.Whenitcomestomusic,weallhaveourfavorites and intensedislikes, so no definition of music can includewordslike“beauty”and“pleasure.”Allwecansafelysayisthatmusicissoundwhich has been organized to stimulate someone—which is a bitfeeble really. The “someone” might be the composer only,and the“stimulation” might mean anything from joy to tears. Thankfully it ismuch easier to define the individual buildingblocks of music: notes,rhythm,melody,harmony,loudnessandsoon.Wewillbeexploringallthesesubjectsduringthecourseofthebook,andwewillbeginwiththemostbasicblockofall—themusicalnote.Amusicalnoteconsistsoffourthings:aloudness,aduration,atimbre

andapitch.Oneofthesefeaturescanbesummedupinjustonesentencebuttheotherthreewillrequireawholechapterormoreeach.“Duration”istheeasyone,solet’sdoitnow:somenoteslastlongerthanothers.Themost distinctive property of amusical note is itspitch, sowe’ll

startthere.

Whatispitch?Pitch distinguishes a note from a noise. I will explain this at greaterlengthoverthenextcoupleofchapters,butfornowashortintroductionwillhelptogetusstarted.If you hum any tune you like, you will be choosing a duration, a

loudness and a pitch for each note you produce. Subtle changesinloudness and duration during a song can carry a lot of emotionalinformation—butaswe’reonlygoingtobehummingthefirstfournotesof“BaaBaaBlackSheep”wedon’tneed toworrytoomuchabout that.So,tryhummingnotesforthesefourwordsatthesameloudnesswiththe

samedurationforeachnote.Allyouarechoosingnowisthepitch.Thefirst twonotes have the samepitch; then there is a shift up in pitch to“Black”;andthen“Sheep”isthesamepitchas“Black.”Allmusicalnotesinvolveregular,repeatingvibrationsintheair.When

you were humming any single note just now, you wereproducing aregular vibration with your vocal cords that was repeating itself manytimes a second; when I hum “Baa” my vocalcords vibrate about ahundred times a second. When I hum the note for “Black” I have toproduce a higher pitch note and Ido this by increasing the number ofvibrationsIproduceeverysecond.So,whetherthenoteisproducedbyavibratingstringorthevibration

of your vocal cords, higher pitch notes involve morevibrations persecond.Everymelodyismadeupofastringofnotesofdifferentpitches.

NamingournotesThe notes on a piano or any other instrument are named after the firstsevenlettersofthealphabet;A,B,C,D,E,F,G.Betweensomeoftheseletters there isanextranote (theblacknotesonapianokeyboard).Forexample, there is an extranote betweenA and B, which can be calledeither“Asharp”(meaning“onestephigherthanA”)or“Bflat”(meaning“one steplower than B”). This fairly daft-sounding system of namingnoteshasbeenhandeddowntousoverthepastfewcenturiesandIwillexplainwhy in chapter9.For themoment all youneed toknow is thatnotesarenamedafterlettersandthelettermighthavetheword“flat”or“sharp”afterit.Intheillustrationbelow,Ihaven’tthespacetowritethewords“flat”or“sharp,”soI’veusedthetraditionalsymbols“ ”forflatand“#”forsharp.Allpianosare tuned to the samepitches. Ifyoupressapianokey in

Helsinkiandrecordthepitchofthatparticularnote,andthencompareitwithapianoinNewYork,thenoteswillbeidentical.Similarly,thenotesof clarinets or saxophonesare the same all over theworld.Youmight

thinkthisisobvious,butit’snotsolongagothatthepitchesofmusicalnotesvariedfromcountrytocountry,orevenfromcitytocity.Thenoteseveryoneisusingnowadayswerecarefullychosen—butwhochosethem?Andwhy?

Partofapianokeyboardshowingthenamesofthenotes.AswemoveupthekeyboardthenotenamesrepeatinapatternwhichgoesfromAtoGandstartsagainoneverythirteenthnote.ThereareonlysevenlettersinthealphabetbetweenAandGsoweneedextranotenames(“flat”and“sharp”) to cover all the notes. This peculiar method of naming noteswillbeexplainedinchapter9.Becausethenamesofthenotesrepeat,wealsogive themnumbers.The first threenotesareA0,B 0andB0. AfterthiswehaveC1andthenthenumbergoesupeachtimewereachanotherC.

Whydoweallusethesamenotes?If you play a stringed instrument such as a violin or guitar, you cantightenorloosenthestringstoaltertheirpitch.Atafairlyearlystageofyour training you are taught how to use this tightening process to tune

your instrument. This involvesmaking the strings produce noteswhicharethecorrectdistanceapartinpitch.Forexample,thedistanceinpitchbetweenany two adjacent violin strings is the same as the distancebetween“Baa”and“Black.”Let’s saywe are tuning a violin. The first step could be to tune our

thickeststringtothecorrectnote,G,andthentunetheotherstringsusingthe“Baa–Black”differencebetweeneachone.YouwouldgettheinitialGbymatchingyourviolinnotetoatuningfork*orthecorrectnoteona(tuned)piano.Butwhathappensifyoudon’thaveatuningforkorpianohandy?Ifyouareplayingyourinstrumentalone,youcanchooseanyoldnote

for the thickest string and then tune all the otherstrings to that one(makingsurethat thedifferencebetweenanytwostrings is thesameasthe jump in pitch between “Baa”and “Black”).All you have to do tochooseyour first pitch is tomake sure that the string is stretched tightenoughtomakeaclearnote,butnotsotightthatitsnaps.ThepitchyouinitiallychoosewillnotbeG(unlessyouhaveperfectpitch,whichIwilldescribe in a while)—in fact, it will probably be a note between twoadjacentpianokeys,maybe“Aandabit”or“abitlowerthanF.”As long as the difference between your strings is the same as “Baa–

Black,”themusicyouproducewillsoundfineandothermusicianswithstringed instruments could tune to match your notes and join in.However, if one of your friends is a fluteplayer hewill not be able toplay along. This is because the notes on a flute (or any other windinstrument) are fixed—youcan’t choose anyoldnotes on a flute.Yourflute-playingfriendcanplay,forexample,an“E”oran“F”buthecan’tchoose“Eandabit.”Let’ssaythatyouandyourstring-playingfriendsareallplayingatune

thatgoes“Eandabit—Fandabit—Candabit”—thiswillsoundjustaspleasantastheflute-playingE–F–Cbutifyoubothplayatthesametimeitwillsoundhorrible.Thereareonlytwowaystomakemusictogether:

1.Youviolinplayersmusthold thefluteplayerdownwhileoneofyousawsafewtenthsofaninchofftheendofhisflute.Thenyou’llhavetofilealltheholesuntiltheyareinsuitablepositionsforthisnew,shorterflute;or2.Youcanalltuneyourviolinstomatchtheflutenotes.Onceyouhavedonethis,anyotherinstrumentcanjoininwithyoubecauseyouarenowplayingthestandardnotes.

These standard notes are no sweeter or more musical than any othergroupofnotes.Theyareonlycorrectbecausesomeonehadtodecidehowlong flutes and other wind instruments should be. (The length of suchinstrumentsdeterminesthepitchof thenotestheyproduce.)Inthepast,thingswere very confused—flutesmade in different countrieswere allslightly differentlengths—which meant that a German flute playercouldn’t play along with an English one unless he bought an Englishflute.After a lot of argy-bargy aboutwhich lengthwas thebest, itwasdecided that a bunch of experts in badly cut suits wouldform acommitteeanddecideonceandforallonagroupofnotesthateverybodywouldusefromthenon.Afteralotofexpertdiscussion(whichsoundsalotlikeargy-bargy),theydecidedonthenotesweusetodayatameetingin London in 1939. Sonow, all over theworld, flutes and all the otherWestern instruments such as violins and clarinets, guitars, pianos andxylophoneshaveasetofstandardnotes.Nowadays, if someone says “Ihaveperfectpitch” theymean that the

pitchesofthesestandardnotesarefixedintheirlong-termmemory,andthispeculiarabilityisthesubjectofthenextchapter.

2.WhatIsPerfectPitchandDoIHaveIt?

Let’simaginethreepeoplearesingingintheshower—no,notallinthesame shower, this isn’t that sort of book. These threepeople are allsinging in their (otherwise silent) bathrooms on different floors of anapartmentbuilding.OnthesecondfloorwehaveKimNormal:shehasaginand tonic in

onehandand isbeltingout“DancingQueen”byAbbaatthe topofheruntrained voice. If we taped her song and compared it to the originalrecording,wewoulddiscovertwothings:

1.Although thenotesgoupanddown inpitchat the rightplaces, theysometimes jump a little too far and sometimes don’t jumpquite farenough.Thisishowmostofussing(whichiswhyweshouldsticktoourdayjobs).2.ThenoteshestartedonwasnotthesamenotethatAbbastartedon.Infact,thenoteshestartedondoesn’tappearanywhereonapianokeyboard(whyshould it?). It’s just somenoteshepickedfromthemiddleofhervocal range and, if you checked,youwould find that itwassomewherebetweentwoadjacentnotesonapiano.Onceagain,thisiswhatmostofusdo.

UpontheseventhfloorlivesJamesSinger:heisatrainedmemberofhislocalchurchchoirbuthedoesn’thaveperfectpitch.Fortunatelyforthisdiscussion,heisalsosinging“DancingQueen.”Ifwecomparedhistunewiththeoriginal,wewouldfindthathisvocalleapsupanddownareveryaccurate.However,asinthecaseofhisdownstairsneighbor,thenotehestartedonwasnotthesameastheAbbaoriginal—itwasoneofthose“inbetween”notesthatmostofuschoosewhenwesing.Upinabathroomonthefifteenthfloor,CeciliaPerfectisalsoreliving

the 1970s, singing (wait for it)…“DancingQueen.”Cecilia is a trained

singerwhoalsohappenstohaveperfectpitch(orabsolutepitch,as it isalsoknown).Whenwe compareher renditionwith theoriginalwewillfindthat,notonlyarehervocalleapsaccurate,butshestartedonexactlythe right note. This, of course, means that she is singing all the samenotesastheoriginalAbbasong.Cecilia’sperformanceisremarkableandquiterare(onlyaverysmall

percentageofpeoplehaveperfectpitch),but it isnotnecessarilyasignthatshehasanyspecialmusicaltalent.ItispossiblethatJamesisabettersingerandthat,ifyouwheeledapianointohisbathroomandplayedthefirst note of the song, he would be able to start from there and, likeCecilia,singexactlythesamenotesasAbba.WhatCeciliaisdemonstratingisthatshehasmemorizedallthenotes

onapiano(orflute,orsomeotherinstrument)anditisjustaboutcertainthat shemanaged this incrediblememory feat before shewas six yearsold.Young children remember things farmore effectively than anyoneelse,whichishowtheylearntotalkandacquireotherskills(oneminutethey aresitting in the garden eatingworms andgoing “ga ga googoo”and a few months later they are strolling around making sarcasticcommentsaboutthequalityofthecookies).Ifyouteachasmallchildasong,shewilllearnthetuneandthewords.

Atuneisnotmadeupofspecificnotes—tunessimplyinvolveaseriesofupward and downward jumps in pitchwith a certain rhythm. “BaaBaaBlackSheep”soundsjustasgoodwhatevernoteyoustarton—and,don’tforget,nearlyallofusstartonanotewhichisbetweentwopianonotes.Itisonlywhenthetunesareproducedonaninstrumentthatthechild

mightstarttodevelopperfectpitch.Ifoneoftheparentsplaysthesamenotes on a piano each time she sings “BaaBaaBlackSheep,” the childmaystart to remember theactualnotes involved rather than just theupanddownjumpsofthetune.Eventuallythechildcouldbuildupawholementallibraryofallthenotesonapiano.Ifthishappens,shemightalsolearnthateachofthememorizednoteshasanamesuchas“theFabovemiddleC”(middleCistheCnearthemiddleofapianokeyboard).

An interesting point here is that, although perfect pitch is rare inEuropeand theUSA, it is farmorecommon incountriessuchasChinaandVietnam,where the language involves an element of pitch control.Thesoundyoumaketoproduceawordinthesetonallanguagesisacrossbetweensingingandspeaking.Thepitchatwhichyou“sing”awordinalanguagelikeMandarinisvitaltocommunication:eachwordhasseveralunrelatedmeaningsdependingonitspitch.Theword“ma,”forexample,means“mother” if you sing/say it at a high, level pitch—but itmeans“hemp” if you start at amiddle pitch that then rises; or“horse” if youstartlowerthenfallandrise.Ifyoustarthighandletthetonefallyouaresaying“lazy.”Soaninnocentquestionsuchas“Islunchready,Mother?”could easily become “Where’s my lunch, you horse?” if you get thepitches wrong.As this sort of mistake could result in a catastrophicfailureoflunchsupply,youngchildrenlearningthesetonallanguagespaymuchcloser attention topitch thanWesternersdo—andyoungchildrenwhoconcentrateonpitchalotaremorelikelytoacquireperfectpitch.The reason why very few Westerners develop this note memory is

becauseitisn’tveryusefultous—infact,itcanbeabitofapaintohaveperfect pitch because itmakes thewhistling or singing ofmost peoplesoundterriblyoutoftune.Ifyouareanorchestralviolinist,perfectpitchcouldbehelpfulintuningyourinstrumenttothecorrectpitchinthetaxionthewaytoaconcert.Ifyouareaprofessionalsinger,youcouldalwaysbesureyouwerepracticingthecorrectnotesevenifyouwerewalkinginthe countryside—but those are about the only benefits. This lack ofusefulnessisoneofthereasonsthatmusicaltrainingneverinvolvesanyattempt at perfect pitch acquisition. The othermain reason is that it isverydifficulttoachieveaftertheageofsix.Havingsaidallthat,quiteafewmusicians(andsomerealpeople)have

partialperfectpitch.WhatImeanbythis is thattheyhaverememberedone or two notes. For example, most of the musicians in an orchestrahavetotunetheirinstrumentatthebeginningofeachconcert(unlikethesmug, perfect-pitch violinist who can do his alone in the taxi). They

always usethe note “A” for this purpose. One instrument (usually theoboe)playsan“A”andtheotherplayersadjusttheirinstrumentsso thattheir “A” sounds the same. (This produces the dreadful wailing racketyou hear just before an orchestral concert.)This repeated concentrationonthenote“A”canleadafewofthemusicianstorememberit.Other examples of partial perfect pitch are also related to repeated

exposure to a particular note or song. Sometimes non-musicianscanexperience this and remember a note or notes even though they don’tknowthenamesofthem.Tryitforyourself.Getoutoneofyourfavoritesongsandsingwhatyouthinkwillbethefirstnotetobeplayed,andkeepsinging it or humming itasyoustartyourCDplayer.Youneverknow,youjustmighthavepartialperfectpitch.Thispartialperfectpitchisnotassurprisingasitmightseematfirst.

We can all remember a note for a few seconds (try thiswith your CDplayer)andarepeatedshort-termmemorycansometimesdevelopintoalong-termmemory.By the way, your singing or humming will probably be much more

accurateifyoustickafingerinoneofyourears—whichiswhyyouwillseesomesolosingersdoingthis.Thisworksbecausewearedesignednottohearourownvoicestooloudly,incasetheydrownoutanyothernoiseswe should be paying attention to—lions, avalanches, the last-call bell,etc. Stickinga finger in yourear improves the feedback between yourmouth and brain and helps you monitor your own pitch much morecarefully. You may have noticed that your voice–ear feedback alsoimproves if you have blocked sinuses, which can be very annoying. (Ioncemade themistakeofcomplainingabout this tomygirlfriend.“Myvoicesoundsreallyloudandit’sgettingonmynerves.”Herresponsewasasingleeyebrowtwitchand,“Nowyouknowwhattherestofushavetoputupwith…”)Iwanttogobacktoourthreesingersandimaginewhat’sgoingonin

theirheadsastheysing,butfirstyouneedtoknowthatthejumpsinpitchbetweenthenotesinatunearecalledintervalsandthedifferentintervals

havenames thatdescribehowbig theyare.The smallest interval is thedistance between twoadjacent* piano keys and is called thesemitone,twice this jump is called atone (not surprisingly).You don’t need toknowthenamesofall theintervals,butyoucanfindthem—andatrickshowingyouhowtoidentifythem—in“FiddlyDetails”atthebackofthebook(seehere).Sowhatareour singers subconsciously thinkingas theystart singing

thesong?

KimNormal’sbrainissendingoutthefollowingsignals:

•singanyoldnote•downabitforthenextnote•upabitforthenextnote,etc.

JamesSinger’sbrainissendingoutthefollowingsignals:

•singanyoldnote•downawholetoneforthenextnote•upthreesemitonesforthenextnote,etc.

CeciliaPerfect’sbrainissendingoutthefollowingsignals:

•singCsharp•downtoB•uptoD,etc.

But, as I said earlier, the fact that Cecilia’s notes agree with the oneschosenbyacommittee in1939doesn’tmean thatshe is abetter singerthanJames.Beingagoodsinger isnot justamatterofhitting therightnotes—youhavetosingthemclearly,withtheappropriatestress,andyouhavetomakesurethatyoudon’trunoutofbreathbeforethefinalnoteof

aphraseends.Ontopofallthis,thequalityofyourvoiceisaffectedbytheshapeandsizeof theequipmentyouhave:yourvocalcords,mouth,throatandsoon.Almostanyoneofuscouldbetrainedtobeareasonablesinger,buttobereallygoodyouneedtrainingandthecorrectequipment.

WeirdnessandpedantryInchapter1ImentionedthatGermanflutesusedtobeadifferentlengthfrom English ones and this meant that German orchestrasand Englishorchestraswouldbeplayingdifferentnotes. In fact, every country (andevensomecities)hadtheirownnotes.Inthenineteenthcenturyan“A”inLondon would be more like an “A flat” in Milan and a “B flat” inWeimar.Weknowthis becausehistorianshaveuncoveredvarioustuningforks from these confused times andwe can also compare the notes ofchurchorgansand flutesfromdifferentplaces.Just toaddto thechaos,the localstandardnotesalsowentupanddowninpitchfromdecade todecade.Imagine the scene: it is 1803, Anton Schwarz, the famous German

singer,meets Luigi Streptococci, the famous Italian singer, in a pub inBolton:

“Hey Luigi, you’re singing every note flat—I know because I haveperfectpitch.”

“No,Anton,it’syou—you’resingingsharp.IknowbecauseI trulyhaveperfectpitch.”

“No,you’rewrong.”“No,you’rewrong.”“Flat,flat,flat.”“Sharp,sharp,sharp.”

Andsoon—untilthelandlordchucksthemoutofthepubbecauseneitherof them is singing in tune with his piano (which istuned to Bolton

standardpitchfor1803).NowonderweusedtohavesomanyEuropeanwarsinthosedays.This is aweird situation. Professionalmusicianswere (and still are)

often trained from a very early age, and some of themwould havedeveloped“perfect”pitch,whichagreedwiththepitchchosenbyalocalpianotunerororganbuilder.Assoon astheybegantotraveltheywoulddiscoverotherhighlytrainedprofessionalswithdifferent“perfect”pitch.It’s a bitlikeeveryonedeclaring that their favoriteshadeofpink is theperfect pink. All these “perfect” pitches were equally valid.To haveperfectpitchallyouneed isasetofpitchesetched intoyour long-termmemory.You don’t even need to knowwhat the notes are called—youmighthavestoredallthenotesonyourmom’spianowithouteverbeingtoldthatthisoneisBflatandthatoneisD,etc.Nowadays, people with perfect pitch have usually memorized the

standard Western pitches that were decided on in 1939 because that’showallpianos, clarinets andotherWestern instruments are tuned.Thismeans that, if you have it, your perfect pitchis the same as everyoneelse’s.Most peoplewith perfect pitchwill also know the names of thenotesinvolvedbecausetheygenerallyacquiredtheirperfectpitchduringsomesortofmusicaltrainingatanearlyage.Thehistoricalfactsmakelifedifficultforthemusicalpedantsamong

us.AtypicalpedanticviewwouldbethatweshouldplayMozart’smusicexactly as hewrote it.Another, equally understandable, pedantic viewwouldbethatweshouldplayMozart’smusicexactlyashehearditinhisheadashewroteitdown.Nowherewehaveaproblem,becausealthoughMozart had “perfect” pitch, the notes hehad memorized were not thesameasthosechosenbythecommitteein1939.Infact,thenoteweknowas “A” would be calleda “slightly out of tune B flat” byMozart (weknow this becausewe have the tuning forkMozart used). SowhenwelistentoMozart’smusicnowadays,wearehearingitallaboutasemitonehigherthanhewouldhaveintended—afactwhichisguaranteedtoannoysomemusical pedants. Some of hismost difficult, high-reaching songs

wouldactuallybemucheasier tosing ifwelowered theminpitchbyasemitone,whichisclosertohowMozartintendedthemtosound.Ontheotherhand,thiswouldinvolvewritingoutallthemusicagaininalowerkey,whichwouldirritateanentirelydifferentsetofpedants.So if you are ever discussing perfect pitch, you need to bear the

followingpointsinmind:

• Ifpeoplehaveperfectpitch, itmerelymeans that theymemorizedallthe notes on a particular instrument before they werearound six yearsold.Thesepeoplegenerallyhavehighlevelsofmusicalskill,butthishasnothing to do with their perfectpitchability (which is rather useless).They usually have excellentmusical skills simply because they startedtheirmusical trainingbeforetheyweresixyearsold.Mostmusicalskillcomesasaresultoftrainingratherthaninspiration:theearlieryoubegin,thebetteryouwillbe.

•Anytalkofsomeonehaving“perfect”pitchbefore1939doesn’ttellusanythingabout thepitchesof thenotes involved,becausetherewerenoagreed international standard notes.On the other hand anyonewhohadlocal“perfect”pitchwasprobablyaverygoodmusicianbecausehehadobviouslybegunhismusicaltrainingveryearly.

Astothequestionofwhetherornotyouhaveperfectpitch, it’seasytofind out by the method I mentioned earlier. Pickout a few of yourfavorite songs fromyourCDcollectionand try to sing the firstnoteofeach one before you play it. (Rememberto put a finger in one of yourears so you canhear yourselfmore clearly, anddon’twait for the firstwordtobesungbecausetheintroductorymusicwillwarnyouwhatnoteiscomingup.Whatyouhavetosingistheveryfirstnoteonthetrack.)

•Ifyougetallthenotesrightyouhaveperfectpitch;•ifyougetsomeofthemrightyouhavepartialperfectpitch;•ifyouthinkyougotthemright,butnooneelseintheroomagrees,you

should get some sleep and try again in the morningwhen you havesoberedup.

3.NotesandNoises

Everydayyouwillhearmillionsofsoundsandonlyafewofthemwillbemusicalnotes.Usually,musicalnotesarecreateddeliberatelyfromamusicalinstrument,buttheycanbeproducedinnonmusicalsituations—whenyou“ping”awineglassorringadoorbell,forexample.Wheneverand however they are produced,musical notes sound different from allothernoises.What’s the difference between a musical note and any other sort of

noise?Everyoneyouknowwillhavesomesortofanswertothisquestion,butmostof themwill bebasedon the idea thatmusicalnotes sound…er…musicalandothernoisesare…er…notmusical.Musicplaysuponouremotionsandcanenhanceorchangeourmood.

Agoodexampleofthisisthewaythatfilmsoundtracksgiveuscluesastohowto respondemotionally to thescenewearewatching—romance,humor and tension are all magnified bythe accompanyingmusic. Thislink between music and emotion might make us think that notesthemselves have an emotional contentand that they are in some waymysteriousandmagicalsounds.Infact,therereallyisagenuine,simpledifferencebetweenmusicalnotesandallothernoises,butithasnothingtodowithemotion—acomputercouldspotthedifferenceeverytime.

SoundIfyouthrowastoneintoaflat,calmpondyouwilldisturbthesurfaceofthe water and create ripples which travel awayfrom the initial splash.Similarly,ifyouclickyourfingersinaquietroom,youwilldisturbtheairandripplesofdisturbancewillmoveawayfromyourhand.Inthecaseofthestoneinthepond,theripplesinvolveachangeinthe

height of the water and our eyes can clearly seewhat’s going on: theheight of the water goes up–down–up–down–up–down as the ripples

travelawayfromthesplash.When you click your fingers (or make any other sound, including a

musical note), the sound ripples traveling toward your earsinvolvechangesinthepressureoftheair.Wecan’tseetheseripplesbutourearscanhearthem.Whentheripplesreachourears,theairpressuregoesup–down–up–down–up–down and this makes our eardrums go in–out–in–out–in–outatthesamerate—becauseoureardrumsareliketiny,flexibletrampolines which are easily pushed in and out by changes in the airpressure. Your brain then analyzes the in–out movement of youreardrumsanddecideswhat’sgoingon—isittimetorunawayortimetoorderdessert?

Non-musicalnoisesAswe grow upwe become very skilled at identifying and interpretingnoises—the boiling of a kettle, someone buttering toastor choppingwood, the playful click of the ATM as it eats your debit card—weaccumulateavastlibraryofsoundstohelpusworkoutwhat’shappeningaroundus.Ifwecould see thepressure ripplesof thesenon-musical sounds,we

wouldnotice that theywereverycomplicated.Theoverallripplewouldbecreatedbyallsortsofthingshappeningatthesametime:thesoundofadoorclosingmightinvolvevibrationsofthedoor,thelock,thewallandthe hinges—and each of these complicated individual vibrationswouldjoin together toproduce an even more complicated set of ripples ofpressureintheair.Let’simaginethatwecanseethepressureripplesproducedbyadoor

closing. In the left-hand part of the illustration belowIhavedrawnoutpossibleripplepatterns*forthedoor,lock,wallandhingeseparately.OntherightoftheillustrationIhavejoinedthemalltogetherintotheoverallrippleshapewhichpushesoureardrumsinandoutasthedoorcloses.

Severalpressureripplesjointogethertomakeanoise.Thesoundripplesmade by a door, lock,wall and hinge join together tomake the overallnoiseofadoorclosing.

The noise ripple shape which eventually arrives at the eardrum isextremely complicated because it is made up of a chaoticgroup ofindividualrippleswhichhavenorelationshiptoeachother.Thisistrueofallnoiseswhicharenotmusicalnotes.

MusicalnotesMusical notes are different from non-musical noises because everymusicalnoteismadeupofaripplepatternwhichrepeatsitselfoverandoveragain.Intheillustrationbelowtherearesomeexamplesoftheripplepatternsofnotesproducedbydifferentinstruments.Tobeamusicalnote,it doesn’t really matter how complicated the individual ripples are, aslongasthepatternrepeatsitself.

Musical notes are made up of ripple patterns which repeat themselves

overandoveragain.Theseripplepatternsareactualrecordingsofnotesproduced by a flute (top), a clarinet (middle) and a guitar (bottom).(Source:ExploringMusicbyC.Taylor(Taylor&Francis,1992))

Oureardrumsflex inandoutas thepressure ripplespushagainst them.However, our eardrums can’t respond properly if theripple patternrepeatsitselftooquicklyortooslowly—wecanonlyhearpatternswhichrepeat themselvesmoreoften thantwenty timesa secondbut lessoftenthan20,000timesasecond.Musicalnotesdon’tneedtobemadebymusical instruments, infact,

anything which vibrates or disturbs the air in a regularway betweentwenty and 20,000 times a second will produce a note.High-speedmotorbike engines or dentists’ drills produce notes. In the song “TheFacts of Life,” the band Talking Heads useswhat sounds like acompressed air-powered drill to produce one of the notes of thebackgroundaccompaniment.Thiscombinationofmusicandengineeringfitswellwiththelyrics,whichcomparelovetoamachine.Musical instrumentsare simplydeviceswhichhavebeendesigned to

producenotesinacontrolledway.Amusicianusesfingermovementorlungpowertostartsomethingvibratingatchosenfrequencies—andnotesareproduced.

GoodvibrationsWhenthingsvibratetheygenerallydosoinlotsofdifferentwaysatthesametime.Forexample,ifyouarechoppingatreedown,everytimetheax hits the tree, the various branches all vibrate at different rates indifferent directions. Each ofthese vibrations creates a ripple pattern intheair,buttheydonotjointogethertocreateanoverallrepeatingpattern—sowehearanoise rather thananote.Musicalnotesareonlycreatedwhen all the vibrations collaborate to produce a regularlyrepeatingripple, like the ones in the illustration above. For this to occur, the

vibratingobjectmustonlyproducerippleswhicharestronglyrelated toeachotherandcanjointogetherinanorganizedway.Thishappensmosteasilyifthevibratingobjecthasaverysimpleshape.Oneofthesimplestpossibleshapesisacolumnorrod,liketheoneshowninthedrawing.Asweshallseeshortly,columnsvibrateinexactlytherightwaytoproducemusical notes, which is why most musical instrumentsinvolve thevibration of columns of air inside tubes (flutes, clarinets, etc.), orvibrating strings (strings are just long,thin columnsmade of plastic orsteel).

A column is a simple shape which vibrates in just the right way toproduce musical notes. Most musical instruments involvevibratingcolumns of air inside tubes (such as flutes or clarinets) or vibratingstrings(whicharelong,thincolumnsofsteelorplastic).

Asfarasstringsgo, thepurest, loudestnotescomefromnewstrings,whentheirshapeisasclosetoacolumnaspossible.Aftertheyhavebeenplayed for a while they get bruised and damaged and become animperfect column shape.When this happensthe strings becomequieterandthenotestheyproducecanbecomerathervagueinpitch.Professionalmusicianschangetheirstringseveryfewweeks,butwhenIwasastudentI always used to leave mine until the strings were almost untunablebeforeIboughtanewset—becauseyoucanbuyalotofchips,peasandcurrysauceforthepriceofasetofguitarstrings.Generallyyouhavetobuyawhole set, because if you just replace a coupleof theworstonesyou’llhave two freshnewstringswhichsound louderandbrighter thantheothers.Andit’snogoodtryingtocheatbybuyingtwonewstringsandartificially agingthemwith chip fat and curry sauce—the symmetricalcolumn shape of the new string will shine through such admirableattemptsathouseholdbudgetry.We can learn a lot about musical notes by looking at how a single

string vibrates when it is plucked. When you pluck a guitarstring itmoves back and forth hundreds of times every second. Naturally, thismovement is so fast that you cannot see it—youjust see the blurredoutlineof themovingstring.Stringsvibrating in thiswayon theirownmakehardlyanynoisebecausestringsareverythinanddon’tpushmuchair about. But if you attach a string to a big hollow box (like a guitarbody),thenthevibrationisamplifiedandthenoteisheardloudandclear.Thevibrationofthestringispassedontothewoodenpanelsoftheguitarbody, which vibrate back and forth at the same rate as the string. Thevibration of thewoodcreatesmorepowerful ripples in theairpressure,whichtravelawayfromtheguitar.Whentheripplesreachyoureardrumsthey flex inandout the samenumberof timesa secondas theoriginalstring. Finally, the brain analyzes the movement ofthe eardrum andthinks,“Thatidiotnextdoorispracticinghisguitaragain.”Thenumberoftimesthestringvibratesbackandforthinonesecondis

calledthefrequencyofthenote(becausethisishowfrequentlythestringgoes back and forth). One of the first people to do serious scientificresearch on frequencies was a bushy-beardedGerman called HeinrichHertz, back in the 1880s. The scientists andmusicianswhoworked onacoustics later found that theyneededa shortwayof saying“the stringhad a vibrational frequency of 196 back and forth cycles per second.”Firstofalltheyshorteneditto“thestringhadafrequencyof196cyclesper second,”* but even bearded scientists could see that this wasn’texactlyasnappywayofsayingit.Eventually(in1930)someonecameupwiththeideaofusingthename“Hertz”todescribethenumberofcyclesper second, so nowwe say “this string has a frequencyof 196Hertz.”Usuallyweshorten“Hertz” to“Hz”whenwewrite itdown:“thestringhadafrequencyof196Hz.”(I’msurethatDr.Hertzandhisbeardwouldbothhavebeenverypleasedaboutbeinghonoredinthisway—andIwishIcouldthinkofsomethingwhichcouldbemeasuredin“Powells.”)Inchapter1Iexplainedthatthepitch(orfrequency)ofeverynotewe

use was decided by a committee in 1939. Although theydid not

specifically discuss guitars, the decisions they made applied to allinstruments,soweknow,forexample,thatthesecondthickeststringonaguitar—the “A” string—should vibrate back and forth 110 times asecond.So,JohnWilliams(theclassicalguitarist’sclassicalguitarist)hasjust

twanged the “A” string on his guitar for us—and,on a properly tunedguitar,the“A”stringhasafundamentalfrequencyof110Hz.Asimplifiedviewwouldbetosaythatthestringisnowmovingtoandfro110timeseverysecondandoureardrumsaredoingthesame.Butthisisnotthefullstory. The string is, in fact, vibrating at lots of frequenciessimultaneouslyand110timespersecond,or110Hz,isjustthelowestofthe frequencies involved. The other frequencies are multiples ofthisfundamentalfrequency,i.e.,220Hz(2x110),330Hz(3x110),440Hz(4x110),550Hz(5x110),etc.Whenthestringistwangedwehearallthesefrequencies at once—but the effect on our hearing system is that of anoverallripplepatternrepeatingitself110timeseverysecond.Sonowwehaveafewveryinterestingquestions:

1.Whydoesthestringvibrateatlotsoffrequenciesratherthanjustone?2.Whydoes the string choose to vibrate only at frequencieswhich arerelated by whole numbers to the fundamental frequency(two times,threetimes,fourtimes,etc.)?

3.Whydowehearoneoverridingfundamentalfrequencywhenalltheseotherfrequenciesarejoiningin?

Let’s lookat thesituationfromthestring’spointofview.Beforebeingtwanged, the string was in a happy, stable state,i.e., in its stretchedcondition it occupied the shortest route between two points—a straightline. The twanging involvesstretching it a bit more before letting go.Thisisextremelyannoyingforthestringanditimmediatelytriestorushbacktobeingastraightlineassoonasweletgo.Unfortunately,asitgetssomewherenearitsoriginalposition,itfindsthatitistravelingtoofastto

stop—soitovershoots,stretchingitself intheoppositedirection, thenitchangesdirectionandtriestohurrybacktowarditsstraightlineshape—andcontinuestoovershootbackandforthuntilitrunsoutofenergy.Thestringrunsoutofenergybecause,asitmovestoandfro,ithastopushairout of theway all the time, and it’s also passing its vibrational energyontothewoodenbodyoftheguitarorviolin.Youmightthinkthatthestringwouldsimplyspringfromsidetoside,

fromonesmoothcurvetoanother—asdrawnontheleftintheillustrationbelow.But it cannotdo thatbecause, if it onlywent fromonecurve toanother,thestringwouldneedtobeginitsjourneyasasmoothcurve.Infact, a plucked string begins its journey as a kinked line—two straightlineswhichmeetatyourpluckingfinger—asinthedrawingontherightoftheillustration.Onceyouletgoofit,thestringwon’thaveachancetoorganizeitselfintoanicegentlecurve—allthevariousbitsofthestringwilljustraceoffasfastastheycan.

Ifwewantedtomakeastringvibrateatonlyitsfundamentalfrequency,wewouldhavetostartitoffinthecorrectshape—asmoothcurveliketheoneinthedrawingontheleft.Infact,whenyoupluckastring,itstartsoffastwostraightlineswhichmeetatyourfinger,asinthedrawingon

theright.

Sonowourstringisinabitofaquandary.Itneedstomoveonceitisreleased, but it cannot move as a simple curved linebecause it’s notstarting off as a simple curve. The answer to this problem is that thestringstartstovibrateinseveralwaysatthesametime.This might sound odd. How can a string do several things at once?

Actually it’s not that difficult. Imagine you are sittingon one of thechildren’s swings in the park—one of those old-fashioned ones withmetal chains and a wooden seat. If you swinggently backward andforward, then each link in the chain will also move backward andforward.Theonesnear theseatmovemostandtheonesnear thebaratthetopdon’tmovemuchatall,butwecansaythatthechainasawholeisrespondingtoasingleinstruction:“Movegentlybackandforth.”Nowslapthechaininaforwarddirectionataheightlevelwithyourear.Thechain will now be wiggling quickly backward and forward as well asswinginggently in the samedirection.The chainwill be following twoinstructions:1.swingslowlytoandfro;and2.wigglequicklytoandfro.You can start to twist asyoumove, to add a third instruction, and youcouldaddothersortsofmovementifyoureallywantedtofeeldizzy.Thepointis that a chain or rope or string is capable of obeying severalinstructionsatonce.Although our obedient guitar string can follow lots of orders

simultaneously,itwiselyonlyacceptsinstructionswhichallowittokeepits ends stationary—because the ends of the strings are attached to theguitarandcannotmove.Havealookatthenextillustration.Hereyoucanseeaphotographof

myfavoriteclassicalguitar—andnexttoitaresomedrawingsofafewoftheindividualwaysthatastringcouldvibratefromsidetosidewithouttheendsmoving.

Someexamplesofwaysinwhichastringcouldvibrate:1.Thewholestringvibratesat110Hz;2.Thestringdividesitselfupintotwohalveswhichvibrateat220Hz;3.Thestringdividesitselfupintothreethirdswhichvibrateat330Hz;4.Thestringdividesitselfupintofourquarterswhichvibrateat440Hz.All these vibrations (with lots of others) happenat the same time, as acomplex dance which repeats a whole cycle at thelowest frequencyinvolved—110Hz.

Keepingtheendsofthestringsstationaryautomaticallymeansthat,tocreate the various vibration types (1 – 4 in the illustrationabove, andothers),themovementpatternmustdividethestringupintoonepartortwopartsorthreeparts—oranyotherwholenumberofparts—butnotinanymorecomplicatedways.Youcan’tdivide itup intofourandahalfparts, forexample,becausethatwouldinvolveoneoftheendswagglingabout.So,while it isvibratingtoandfro, thestringdoesnot justactasone

longstringswingingbackwardandforwardatthefundamentalfrequency.It is involved inacomplicated,wigglingdancewhichencompasses lotsofvibrationshappeningatthesametime—inthesamewaythattherapid,small wiggles of the swing chains were superimposed on the overallgentleswingingofthechain.The“wholestring”movementoftheguitarstring will be accompanied by some “half string,” “third string” and“quarterstring”vibrations(andothers).Shortstringsvibrateathigherfrequenciesthanlongstrings(iftheyare

thesametypeofstringunderthesameamountoftension).Infact,thereisadirectrelationshipbetweenthelengthofastringandthefrequencyatwhich it vibrates. Ifyouhalve the lengthofyour stringyoudouble thefrequency or, if you use a string which is one sixth as long as youroriginal,thenyoumultiplythefrequencybysix.Allthe“shorterstrings”wegetwhenthestringdividesitselfupvibrate

atfrequenciesappropriatetotheirlength—sothehalvesvibrateattwice110Hzand the thirdsvibrate at three times110Hzand soon.Althoughthe halves, thirds and quartersare all doing their own thing, likedancepartners at a formal dance, theywill all “return to base” to restart thedanceatregularintervals.Theoverallpatternofthedancewillrepeatatthesamerateasthelowestfrequencyinvolved,110Hzinthiscase.Thisis why we call the lowest frequency the fundamental frequency of thenote.Thisisthepitchoftheoverallnotewehear—whichiswhywereferonly to the lowest frequencywhenwearediscussingmusicalnotes.Alltheotherfrequenciesjoinintosupportthefundamental(ratherlikeback-upsingers),andthisproducesarichersound.Whatactuallyhappenswhenyouletgoofthestringisthatallthetypes

of vibration which involve lots of movement of thestring near thepluckingpositionbeginatonce.Forexample, ifyoupluck thestring inthemiddle,youwillgetlotsofthefundamentalfrequencyandthe“threetimes”frequencybecausebothofthesetypesofvibrationinvolvelotsofmovement in the middleof the string (as you can see in the nextillustration). You will not, however, get any of the “double” or “four

times” frequenciesbecause they require the stringnot to move in themiddle.

Ifyoupluckthestringinthemiddle,allthevibrationswhichinvolvethestring moving in the middle can join in the movement.But vibrationswhichinvolvethestringnotmovinginthemiddlewillnottakepart.Hereyoucanseethestring(ontheleft)isbeingpluckedinthemiddle—soonlyvibration patterns which allow movement in the middle of the string(ticked)areallowedtojoininwhenthestringbeginstovibrate.

Asanotherexample, ifyoupluckthestringonethirdof its lengthfromoneend,youwillgetlotsofthefundamental,the“double”andthe“fourtimes”frequencies,butnoneofthe“threetimes”frequency,becausethe“threetimes”frequencycan’tjoininifthestringismovingatthatpoint,asyoucanseeinthisnextdrawing.

In thiscase,weareplucking thestringone thirdof its length fromoneend.Onceagain,thevibrationtypeswhichinvolvemovementatthispoint(ticked)areallowedtojoinin,buttheoneswhichrequirethestringtobestationaryatthispositionwillnottakepart.

Now we get the radiant light of enlightenment shining down upon us.Pluckingthestringmeanswearegoingtogetlotsofdifferentvibrationsatonce,andwherewepluckitinfluencesthevariousproportionsofthesevibrationsinthemix.Thisexplainswhyguitarstringssounddifferentifyoupluckthemnearthemiddleorclosetooneend.Whereveryoupluckthestring,thefundamentalfrequencywillremainthesame,butitwillbesupported by different proportions of the other vibrations.We havechanged the pattern of the formal dancewithout affecting how often itcompletesafullcycleofmovement.Togetanewnote,youmusteitherchooseanotherstring,orshortentheoneyouareonbyusingthefrets*ontheguitarneck.Thenyougetadifferentfundamental,withitsowngroupofrelatedfrequencies.There is, of course, one group ofmusical instrumentswhose sounds

don’t involve collaborative harmonic mixtures—they producenoisesrather thannotes.Theseare theuntunedpercussion instrumentssuchascymbals, gongs and bass drums. They are amongthe most ancientinstrumentsofallanddateback towaybefore the introductionof tablemanners.Backinthegoodolddays,peoplewouldbangalongtothetribaldancesonanythingthatcametohand.Nowadaysthingsarealittlemoresophisticated,and using the skulls of enemies or close relatives isfrownedupon,evenamongrugbyplayers.Rock,popandjazzbandsusedrums and cymbals almost continuously to provide a rhythmicdrive tothemusicandthisisthemainreasonwhytheseinstrumentsneedtomakeanoise,notanote.Ifthedrummerbangedalongusingoneortwonotesallthetime,thosenoteswoulddominatethetuneandoccasionallyclashwiththeharmoniesofthesong.Arepeatednoise—a“thud”fromadrumor a “tschhh” from acymbal—provides rhythmic information withouthijackingthemusic.Drums are circular and rather like short columns, so they have a

tendency to produce notes if you don’t dissuade them fromdoing so(somedrums, likeorchestral tympani,aredeliberately tuned toproducenotes).Abassdrumhastwoskins,oneateitherendofthe“column,”andthe way to prevent it producing notes is to tune the skins to differentnotes. The drummerhits one of the skins and this compresses the airinside thedrum,whichstartsbothof thedrumskinsmoving.However,becausethe two skins cannot agreeon amutually supportivepatternofmovement,thenoisehasnoidentifiablepitch.Thelackofmutualsupportisalsothereasonwhythesounddiesawayrapidly—whichisalsousefulifyouwanttoproduceclearrhythms.The reason I chose the “A” stringof aguitar for the example in this

chapter is because its fundamental frequency is 110Hz—and it’s deadeasytoseethat220Hzistwicethatnumberand330Hzisthreetimesasbig.Butthisbookisaboutallthenotesweuse,sowecan’tkeeponusingthis one example. The general rule is that any note is made up of afundamental frequencytogether with its “twice” frequency, its “three

times” frequency, its “four times” frequency, and so on. All thesefrequenciesare called theharmonics of the note. The fundamentalfrequency is the first harmonic, the “twice” frequency is the secondharmonicandthe“threetimes”frequencyiscalledthethirdharmonic—andsoonforalltheothernumbers.Althoughwehaveonlydiscussedguitarstringssofar,theseprinciples

are true of all musical notes—they all involve a familyof vibrationslinked by whole number relationships—and different mixes of thesevibrationsgivetheoverallnoteadifferentcharacterwithoutchangingitsfundamentalfrequency.The principle that strings produce different harmonic mixtures

dependingonwhereyoudisturb themalsoworks for instrumentswherethe string is bowed rather than plucked, such as violins and cellos. Itprovides a very useful method of controllingthe sound of yourinstrumentifyouareplayingapiecewhichrepeatsitself(asmostpiecesdo). You can play the tune at first by plucking or bowing toward themiddleofthestring,whichwillgiveyouanicemellowtone.Whenyouare repeatingthe tune later, you can get the same notes with a muchharshertoneifyoupluckorbowclosertotheendofthestring.Thisisagoodwaytoenhancethemusicalinterestforthelistenerandtoincreaseorrelaxthetensionofthepiece.Theguitaristcanstartoffwithasoulful,comfortingtoneasthesingertellshisgirlfriendthathesensesthatsheisnotentirelyhappy.Thenlater,theguitartonecanbeadjustedtosoundadamnsight lessrelaxedabout thewhole thingwhenhe’ssinging thebitabouthowsheranoffwiththatpodiatristfromSchenectady.The pressure ripples we sawhere look rather complicated, but the

vibrational patterns of the strings you see in theillustrations above arevery simple.Youmight wonder how a collection of simple things canproduceaverycomplicatedone.Infact,anyoneoftheindividualstringvibrationpatternswouldproducesimplepressureripplesintheair(likethe oneson the left in the illustrationbelow) if theyactedalone,but inpracticetheyneverdosobecausewehearthemjoinedtogetheringroups.

Arealnotemight,forexample,involvealotofthefundamentalandthethird harmonic with smaller contributionsfrom the second, fourth andninth.Thedifferentmixturesofthesevariousingredientscangiveyouanincredibly wide rangeof combined ripple shapes. The first person torealize that you could construct almost any repeating pattern out ofcombinationsof simplewaveswas a Frenchman called Joseph Fourier,who was one of Napoleon’s top men in the three closely linkedintellectualfields of Egyptology, math and swamp drainage. Usingspoon-bendingly complicated math, he managed to produce just aboutanyrepeatingpatternyoucould imagine from these simple ingredients.Thankfully,thereisnoneedforustogointoallthathere.Itisenoughforus toknowthat ifyouputanymusicalripplepattern intoacomputer itcouldworkoutthemixinvolved:“thismuchfundamentalandthatmuchsecond harmonic—with a smidgin of seventh harmonic and a twist ofnineteenth” orwhateverwasneeded toget that particular overall rippleshape.

Thevariousrelatedripplesofanotecancombineinvariousproportionsto give different overall ripple shapes with thesame fundamentalfrequency. The proportions depend on the instrument involved or ondifferentwaysofplayingaparticularinstrument—yougetthesamenotebut a different sound (smooth, hard, etc.). The combined ripples on therightarethepatternsfortheflute,clarinetandguitarwesawearlier.

Sonowwehaveanswerstoourthreequestions:

1.A stringvibrates at lots of frequencies at the same timebecause theshape it started from allows lots of different frequenciesto join in theoveralldanceofmovement.2. The frequencies are all related by whole number ratios because thestringcanonlydivideupitslengthintowholenumberdivisionswhileitvibrates (because theendsof thestringscan’tmove).The“half-length”stringsvibrateattwicethefundamentalfrequencyandthe“thirdlength”atthreetimes,etc.3.Wehearanoverridingfundamentalfrequencybecausewearehearingthe string completing one entire cycle of its complicateddance at thisfrequency.

Ifyoubreakaplateorrustleapaperbag,youhearanoisewhichismadeup of a lot of unrelated frequencies with no repeatingpattern—but allmusicalnotesaremadeupofrepeatingpatterns.Ourbrainscanrapidlyidentifyasoundasbeingmadeupofeitherarepeatingornon-repeatingripplepatternandthatishowwedistinguishbetweennotesandnoises.We know from experience that the same notes played on different

instrumentsdon’tsoundthesame—eveniftheyarethesamefrequency.Forexample,the110Hznoteproducedwhenwetwangaguitar“A”stringsoundsdifferentfromthe110Hz“A”noteonatrombone.Thisisbecausethe trombone note has different proportions of the various harmonicsadding to the mix. These differentmixtures are responsible for thedistinctivesoundsofvarious instruments—andthis is thesubjectof thenextchapter.Aswellascontrolling thesoundsofdifferent instruments,harmonics

also influence our choices of notes which sound goodtogether inharmonies and melodies. If, for example, we hear a note with afundamental frequency of 110Hz played at the sametime as one withtwicethisfundamentalfrequency(220Hz),theysoundgreattogether.The

110Hznote ismadeupofharmonicswithfrequenciesof110,220,330,440, 550, 660Hz, etc., and the 220Hz note has harmonics of 220, 440,660, etc. The reasonthe notes sound good together is because thefrequenciesoftheirharmonicshavealotincommon—thefrequenciesoftheharmonicsofthehighernotearethesameassomeoftheharmonicsof the lower note. Notes like this—where the upper note has twicethefundamentalfrequencyofthelowerone—aresaidtobeanoctaveapart.Thisinterval,theoctave,isthecornerstoneofallmusicalsystemsandwewillbehearingalotaboutitlaterinthebook.Notesanoctaveapartaresocloselyrelated that theyaregiven thesamename.Weknowthat thenotewithafundamentalfrequencyof110Hzisan“A”butthenotewithtwice this fundamental frequency(220Hz) isalsoan“A”—and thenotewithtwicethatfundamentalfrequency(440Hz)isalsoan“A,”andsoon.Infactthereareeight“A”sonapianokeyboard—andtodistinguishthemfromeachotherwenumberthem(asyoucanseehere).Ouroldfavorite,withafundamentalfrequencyof110Hz,iscalled“A2”andthe“A”aboveit,withafundamentalfrequencyof220Hziscalled“A3.”

4.XylophonesandSaxophones:SameNotesbutDifferentSounds

Imagine,ifyouwill,thatnightmarescenario—aroomfullofmusicians.Theyareinafriskymoodastwilightapproaches,becauseitwillsoonbefeedingtime.Toamusethemselvestheyaretakingturnstoplayasimpletune—firsttheviolin,thentheflute,thenthesaxophone.Eachinstrumentplays exactly the same notes as the one before but, of course, they allsounddifferent—anylistenercouldtellwhichinstrumentiswhich.The distinctive sound of each instrument is called itstimbre

(pronounced “tarmbruh”). If we ask a sax player to play “Three BlindMice,”andthenaskaxylophoneplayertorepeatthetune(usingthesamenotes), itwillbeobvious that thedifferencebetween the timbresof theinstruments is enormous, sohow can we say that they are playing the“same”notes?Toanswerthisquestionwehavetothinkaboutwhatisimportantasfar

as our hearing is concerned. Themain job of our hearingsystem is tokeepusaliveandsothefirstthingyourbrainandearmustdowhentheyencounter a sound is to analyzewhetheror not it is a dangermessage.When analyzing a sound for its danger content, our brains concentrateprimarily on the timbreof the noise, seeking to work out whether thesoundisbeingmadebyasmallanimal(rabbitisonthemenu)oratiger(Iamonthemenu).Fortunatelyitdoesn’ttakelongforourfinelytunedintellectstoworkoutthatweareunlikelytobeeatenbyaxylophone.Thesecond most important thing to do is to work out which direction thesound is coming from. Once again the brain leaps intoaction: “Thatplinkingnoise is coming fromover there—from thegeneral vicinityofthatxylophone.”Havingworkedoutthatthesituationismusicalratherthanlethal,the

brain concentrates on the frequencies of the notesbeing produced andtheirgeneralarrangementintomelodiesandharmonies.Inthecontextof

music, the timbres of the noteshave some importance, but this issecondarytothefrequencies(orpitches).Weidentifytwonotesasbeingsimilariftheirfundamentalfrequencies

are identical, irrespective of any difference in theirtimbre. The timbreadds extra interest to the situation—in the sameway that shading addsinformation to anoutlinedrawing.Thismusical shadingcanhaveabigimpactontheemotionalfeelofthemusic,whichiswhythoseviolinistswho walk fromtable to table in Italian restaurants are unlikely to bereplacedbyxylophoneplayers.Although we are going to concentrate on the timbre of individual

instrumentsinthischapter,itisworthrememberingthat,inmanycases,theoveralltimbreofapiececomesfromthecombinationofinstrumentsinvolved.Whenwritingabigorchestralpiece,thecomposerspendsalotoftimedecidingwhichinstrument,orcombinationofinstruments,getstoplaywhichbitsofthemelodyandharmony,inordertopresentthemusicin the most effective way. It’s quite a balancing act to combine thevariousloudnessesandtimbresof theindividual instrumentstoproduceanoverall“voice,”ortimbre.Inthecaseofafour-piecerockband,thedistributionofnotesispretty

obvious,buttheinstrumentalistscanchooseawiderangeoftimbresfortheirinstruments.Theleadguitaristwillpressvariousbuttonsduringthecourse of the song tomake the soundmore or less aggressive, and thekeyboard players can do the same, or move from instrument toinstrument.Iwilldescribethisbutton-pressingmalarkeyinmoredetailattheendofchapter5inthesectiononsynthesizers,butfornow,let’slookatthetimbresofindividual,non-electronicinstruments.Here are three notes of the same frequency with different timbres.

Thesewavepatternsrepresentthevariationinairpressureexperiencedbyan ear. Imagine thesewave patterns “washing up” against the eardrumjustlikedifferenttypesofwaveswashinguponabeach.

Recorded wave patterns of three notes with the same frequency butdifferenttimbres.Notethatineverycasethereismore thanone“hump”ineachcompletecycle.(Source:MeasuredTonesbyI.Johnston(Taylor&Francis,2002)).

Inthecaseofthetopwavepattern,theeardrumwillmovebackwardandforward in an even, regular way as the air pressuregoes up and down.Thiswillresult inthebrainexperiencingaratherpuresound.Thewavepattern shown here is a trace ofa note from a flute—which soundssmoothandeventoourears.The middle and lower waves in this illustration are also repeating

patterns,but in thiscase thepressurevariations feltby theeardrumaremorecomplicatedandjerky,causingthebraintoexperiencethissoundasricherandlesssmooth.Thesenotesarethesamefundamentalfrequencyastheoneplayedbytheflute—andarethereforethesamenote—butthistimetheyareplayedonanoboeinonecaseandaviolinintheother.But why should a flute make a sound which is smoother and less

complexthanthatofaviolinoroboe?Toanswerthisquestionwehavetothink aboutmusical instruments asmachineswhich produce notes.Allthese machines are designed to produce repeatingripple patterns ofpressure in the air and they all do this in differentways. For example,playingafluteinvolvesastraightforwardmethodofsettingupvibrationsin a column of air. There are nomoving parts inside a flute, just thissimplevibratingbodyofair.Playingaviolin,ontheotherhand,involves

a rather complicatedmethod of vibrating a string by scraping itwithabundleofstickyhorsehair(moreaboutthislater).Thestringthenpassesits rather jerky vibration onto the body ofthe violin—which is anunusuallyshapedwoodenbox.Althoughtheoverallvibrationoftheboxwill repeat at the fundamentalfrequency, various parts of the boxwillvibrateindifferentdirections.So,ratherthansingingwithasinglevoice(liketheflute),aviolinismorelikeachoirofseveraldifferentvoices,allsingingthesamenote.Someofthesevoicesaregruff,somearesqueakyand, combined, they give a complicated, rich sound. The relativeimportanceofthevariouspartsofthe“choir”changesasweplayhighernotes, where, for example, the squeakier members might have moreinfluence, so the timbreof a violin differs quite a lot over its range.Askilledplayercanevenplayasinglenotewithdifferent timbres. Ifyouplay with your bow near the center of the string, you encourage themellowpartofyourchoirtocontributemoretothenote.If,ontheotherhand,youusethebowneartheendofthestring,closetothebridge,youwill get amuch harsher,moreaggressive sound.On instrumentswhichsing with far fewer “choir members”—like the flute—the range oftimbres is much morelimited, but even in these cases the timbre isdifferentbetweenhighandlownotes.So, if instrumentsdon’thaveasteady, identifiablewavepatternover

theirwhole range, how dowe recognize them so easilynomatterwhatnotes theyareplaying?Well,wemakeourdecisionaboutwhat typeofinstrumentitisfromtwomainsourcesofinformation:

1.Thesoundtheinstrumentmakeswhenthenoteisjuststarting;2.Thesoundtheinstrumentmakeswhilethenoteisplaying.

Let’slookatthesetwothingsseparately.

Differencesbetweeninstrumentswhenthenoteisjuststarting

It may sound daft, but we get a lot of our information about whichinstrument is playing from the unmusical noises the instrumentmakesjustbeforeeachnotestarts, rather thanfromthenotes themselves.Lotsof experiments have been carried out to provethis—usually byplayingrecordingsofslowmusicwiththeverybeginningofeachnoteremoved.Ifthisisdone,itisdifficulttoidentifywhattypeofinstrumentisplaying—eventhoughthemajorityofeachnoteisstillontherecording.There are lots of ways in which notes are started on different

instruments.Before thenotessoundoutproperly, thenon-musicalstart-upnoisesmadebyplucking,bowing,hitting,etc.,areeasilyidentifiedbythehumanear,evenifthenotesareveryshortandfast.Thishearingskillis undoubtedly linked to survival—after all, if you can’t recognize the“twang” of a bowandarrowveryquicklyyou’renotgoing to last long.Bytheway,thesestart-upnoisesareknownastransients.Inthecontextofmusicwealsoidentifyinstrumentsfromtheriseand

fall in the loudness of the notes during their individuallifetimes. Forexample,apianonotestartssuddenlyandthenfadesoff.Aclarinetnote,on the other hand, has a slowerbuild-up and can remain at the samevolumeforseveralseconds.Thisvolumevariationof thenote isknownasitsenvelope.

Differencesbetweeninstrumentswhenthenoteisplaying

Youwillrememberfromchapter3thatamusicalnoteismadeupoflotsoffrequenciesallsoundingatthesametime:thefundamentalfrequency,alongwithitsotherharmonics.At the risk of being accused of scrimping on the illustration budget

here, I would like to show you the final illustrationfrom the previouschapter again because it shows us the basic principle behind theproductionofdifferenttimbres.

Harmonics can join together in different mixtures—depending on theinstrumentandhowitisbeingplayed—togivedifferenttimbres.

Hereweseethefirstfiveharmonicsinvolvedinanotejoiningtogetherindifferent mixtures to produce notes with different timbres. There aremany more frequencies involved in most real notes so these ripplepatterns can become very complex. Thereason why instruments havedifferent timbres is because theyproduce noteswhich contain differentmixes of these harmonics.For example, on a violin, the mixture ofharmonicsforthenotemiddleCinvolveslotsoffundamentalfrequencybacked upby the second,fourth and eighth harmonics. On a flute,however,thesamenoteinvolvesmostlythesecondharmonicbackedupbythefundamentalandthethirdharmonic.Inbothcaseslotsoftheotherharmonicsjoinintoenrichthesound.As we saw earlier, the different mixes result in a much more

complicatedpressureripplepatternfortheviolinthanfortheflute.Asfaras the physics is concerned, the flute ripple is closer to the shape youwouldgetoffapure“fundamentalfrequencyonly”waveandsowecouldsay that the flute produces a “purer” note. The odd thing is that, aslisteners, we don’t seemto favor purity over impurity. We enjoy thecomplicatedsoundsoftheviolinandsaxophonejustasmuchasthepurertimbresof the flute, harp and xylophone. This is also true of ourappreciation of singers. We like the purity of sound we get fromCharlotteChurchsingingherversionof“SilentNight”justasmuchaswe

appreciate the whiskey and smoke sound of LouisArmstrong singing“WhataWonderfulWorld.”As I said earlier, the reason why the instruments produce different

mixesof frequencies isbecause theyaredifferent shapesandsizes,andalsobecausetheymaketheirsoundsindifferentways.Let’s takeacloser lookat theviolin.Whatevernote isbeingplayed,

the sound is being produced by a vibrating wooden boxwhich has aparticular shape and size. The size and shape of the boxmakes it veryresponsivetocertainfrequenciesandlesssotoothers.Everynoteplayedontheinstrumentismadeupoflotsofrelatedfrequenciesand,whatevernote is being played,some of the frequencies involved will be amongthose“favored”by theshapeandsizeof thebox.Asyoumightexpect,thesefavored frequencies are produced a little more loudly than theotherswhichmakeupthenote.Thetechnicalnameforthecollectionoffavoredfrequenciesofaninstrumentisitsformant.To understand what a formant is, let’s consider a couple of notes

played one after another on a pathetically bad cello.Areal cello hasaformantwhichfavorslotsofdifferentfrequencies,sothatitsoundsgoodfor a wide range of notes. But we are going toinvent a dreadfulinstrumentwhichfavorsonlyanarrowrangeoffrequencies.WewillplaythenotesAandDontheinstrumentandassumethat,althoughitvibratesatall frequencies tosomeextent, it favorsonlythefrequenciesclose to440vibrationspersecond(440Hz).WhentheAisplayed,wewillhearitsbasic,orfundamental,frequency

(110Hz), together with twice that frequency (220Hz)and three times(330Hz) and four times (440Hz), etc. On an instrument which had auniform,fairresponsetoallfrequencies,wewouldhearanevenlymixedcombinationofallthesevibrations.But,asIsay,realinstrumentsarenotfair, theyhavefavoritesandinthisdiscussionourinstrumentisentirelyunreasonable and only favors frequencies around 440Hz, so thefourthharmonic(440Hz)willhavemorethanitsfairshareinthesoundwehear.WhenwechangethenotetoD,thefrequencieswewillhearwillbethe

fundamental (146.8Hz), together with twice that frequency(293.6Hz),three times (440.4Hz), four times (587.2Hz), and so on. But theinstrument hasn’t changed: it still favors frequenciesaround440Hz.Sowhen D is played, our instrument will now favor the third harmonicfrequencyof440.4Hzandwewillhearthatcomponentofthenotemoreprominentlythanwewouldfromanunbiasedinstrument.These more prominent harmonics do not affect the fundamental

frequency of the note. They just change the mix of harmonics,whichaffects the timbre of the notewe hear—so these two noteswould havedifferent timbres. An instrument like the patheticcello I have justdescribedwould be useless, because it has only one favored frequency,which would dominate any music youplayed on it. Fortunately, realinstrumentshavelotsoffavoritefrequenciesandthisensuresthatallthenotes are producedclearly.However, each instrument type has its ownfamily of favored frequencies andthis is one of the reasons that cellossounddifferentfromviolinseveniftheyareplayingthesamenote.Itisalsointerestingtonotethat,inmanycases,theripplepatternofa

note changes during its lifetime.The illustrationbelowshows thisveryclearly—therippletracesarefromnearthebeginning,middleandendofa single note played on a harpsichord.These changes are different foreach typeof instrumentandadd toour assessmentof the timbreof theinstrumentinvolved.

These three ripple patterns show how a note changes during its ownlifetime.Herewe see traces taken fromnear the beginning,middle and

end of a single note played on a harpsichord. (Source: C. Taylor,ExploringMusic,Taylor&Francis,1992).

Now that we understand the basics of timbre, it’s a good time tocomparethewaysinwhichvariousinstrumentsproducethesounds theymake. The following chapter investigates the musical personalities ofsomeofourfavoriteinstruments,fromviolinstosynthesizers.

5.InstrumentalBreak

NoteproductionondifferenttypesofinstrumentsIt’sallwellandgoodformetospeakofflutesashaving“asimpleshape”and violin strings as having “rather jerky vibration,”but to achieve adeeper understanding about how instruments produce their varioustimbreswe need to look at a few instrumentsinmoredetail.Wedon’tneed to look at all of them because many of them share the sameprinciples. Clarinets, for example,are very similar to saxophones, andcellosareeffectivelyjustbigviolins.Ihavechosen threestringed instruments: theharp, theguitarand the

violin,becausetheyeachhavesomethingtotellusaboutthevibrationofstrings.Theharpisthesimplesttoexplainbecausethestringsaresimplyplucked.Theguitar involvesbothpluckingandshorteningthestrings toget the notes you want, and the violin introduces us to the concept ofbowingratherthanplucking.We thenmoveon to three instrumentswhichproducenotes from the

actionofwind in tubes:* the organ, the pennywhistle and the clarinet.The organ provides a good introduction to how notes are produced byindividualtubes,andthepennywhistleisusedtoexplainhowwecangetseveral notes from a tube with holes in it. The clarinet is a typicalexampleofhowreedsareusedtogetarich,complextimbrefromatubeofair.After these wind-activated instruments we move on to two tuned

percussioninstruments:theglockenspielandthepiano;andIwillfinishoff with a few notes about synthesizers. Between them all theseinstruments have a lot to tell us about timbre,but the followingdescriptions also contain a lot of other information about the basics ofnoteproduction.

Threestringedinstruments

Theharp

Aharp is basically a set of stringswhich are stretchedbetween a solidbeamofwoodandahollowwoodenbox(harpistsmightfeelalittlehurtbythiscoarsedescriptionoftheirinstrumentbut,asnoonehaseverbeenbeatentodeathbyaharpist,Ifeelboldandunafraid).AsIdescribedinchapter3,whenwepluckastringwestretchitinonedirectionandthenletitgo.Thestringthentriestoreturntoitsoriginal,straightcondition,but it keeps overshooting until after a whileit runs out of energy andbecomesstraightagain.Astretchedstringby itselfwillnotmakemuchsound, but if you attachit to a hollowwooden box (a guitar, violin orharp,etc.)thevibrationispassedontotheairmuchmoreeffectivelyandwehearaloudernote.Aharpnoteisloudatfirstandthendiesawayasthe movement of the string diminishes, which givesus that distinctive“twangedstring”soundthatwealsogetfromguitars.The way we excite the string couldn’t be much simpler, and the

soundboard is basically a flat piece ofwoodwhich forms thetopof anuncomplicated box shape. The timbre of a harp therefore tends to be avery pure, sweet note. This sweetness of naturemeans that harps arechosentodocertainmusical“jobs”intheorchestrabutnotothers.Onefamous example of harp use is the slow movement (adagietto) ofMahler’s Fifth Symphony. This piece, whichhas been used in severalfilms,consistsofabouttenminutesoflovelornstringswithaslowharpaccompaniment.Theharpdoesn’tseemtobedoingmuchbutitaddsalotofmagic to thepiece. Inparticular, the“loudat first thendyingaway”characterofeachharpnotehelpstoaddrhythmandafeelingofforwardmotiontothelongnotesplayedbythestrings.Thefundamentalfrequencyofthevibrationofthepluckedstring(and

thereforethenotewehear)isdeterminedbythreethings:

1.Howtightlythestringisstretched(atightlystretchedstringisinmuchmoreofahurrytoreturntoitsstraightconditionthanaslackerstringandtherefore moves to and fro more rapidly—which gives us a higherfrequencyandthereforeahigherpitchednote).2.Thematerialthestringismadeof(densematerialssuchassteelmovemore slowly to and fro than light materials such asnylon—so densermaterialsgivelowernotes).3. How long the string is (longer strings give lower notes becausevibration information needs to travel up and down the strings,and thejourneytakesmoretimeonlongerstrings).

Onaharp,oranyotherstringedinstrument,weneedallthestringstobepulledprettytightorwewon’tgetclearnotes(athin,slackstringcanproduce the same frequencynoteas a thicker, tautonebut the tautonewill be clearer and louder).For this reason we design our harps withstringsofdifferent lengths,madeof lightordensematerials inorder togetawiderangeofnotesfromasetoftightlystretchedstrings.Thelowernotestringsaremadeofsteelandthehighernotesaremadeofnylon.Arange of different string lengths is given automatically by the(approximately)triangularshapeoftheinstrument.Theonlyadjustmenttothetimbreofaharpcomesasaresultofwhere

youpluckthestring.Ifyoupluckthestringsomewherenearthemiddle,thenthenoteisatitsmostsimpleandyougetthesmoothesttimbreyoucanget fromanystringed instrument.Ifyouwantaharshersound, thenyouneedtopluckthestringnearoneofitsends.Whereveryoupluckthestring along itslength has an effect on the mix of the fundamentalfrequency with its various harmonics—just like the guitar string wediscussedinchapter3.

TheguitarTheguitarisanotherinstrumentwhichinvolvespluckedstringsattached

toahollowbox.Eachguitarstringisheldtightbetweenthenutattheendof the neck and thebridge, which is positioned on the body of theinstrument. When you pluck a string you get a harp-like note. Mostguitars,however,onlyhavesixstringsandobviouslyweneedmorethansixnotes—otherwiseguitaristswouldhavezerosexappeal.There are, in fact,more than forty notes available on any guitar and

these are produced by pressing the strings against theneck of theinstrument to shorten them. There are bits of wire called “frets”embeddedintheneckand,whenyoupressthestringagainsttheneck,itisheldtightbetweenthenearestfretandthebridge.Becausethestringisheld between thesehard objects it gives a clear, harp-like note whenplucked(ifyoujustheldthestringagainstaneckwithoutfretsyoursoftfingertipwouldsoonabsorbthevibration—andtheresultingnotewouldbemoreofa“thunk”thana“ding”).Becauseof thewayguitars aredesigned it is possible tohold all six

stringsdownatthesametimeandtwangthemalltogether,asyoucanseeinthepicturebelow.Thisabilitytoplaychords(severalrelatednotesatthe same time) is one of the reasonsthat guitars are popular foraccompanying songs. Expert players can play chords and tunes at thesametimeandclassicalorjazzguitaristsareoftenrequiredtoplaytwoorthreetunessimultaneously.

Shorteningaguitarstringbytheuseoffrets:thestringisheldbetweenthechosenfretatoneend,andthebridgeoftheguitarattheother.

Forobviousreasonsthetimbresoftheharpandtheguitarhavealotincommon—they both involve plucked strings. If youare familiar witheither instrument it isusuallyquiteeasy to spot thedifferencebetweentheir sounds because each cando things the other can’t—for example,only a harp can produce those “zinging” scales and only a guitar canproducerapid,scrubbedchords.

Itispossibletoshortenseveralguitarstringsatthesametimetoproducechords of related notes. Here, all six strings are being shortened toproduceacombinationofnoteswhichmakeupamajorchord.

If you were listening to one of these instruments on the radio, youwouldbeabletopickupalotoftimbreinformationfromhowthenotesend.Generally,guitarnotesendmoresuddenly thanharpnotesbecausetheguitaristoftenhastousethesamestringforthenextnoteinthetune.Harpists,ontheotherhand,haveonestringpernoteandtheirtechniqueofteninvolvesplayingthenextnotebeforethepreviousonehasfinished.Thisgivesusagentlefadingawayofoverlappingnotes.Anotherdifferencebetweenthetwoinstrumentsisthataguitaristcan

wigglehisfingeronastringtostretchitslightlytoandfrooverthefret.Thiswiggling changes the tension on the string a little, andmakes thepitch of the note go upand down a few times a second. The effect iscalledvibrato and is used to give notes (particularly long notes) a

trembling, “romantic”depth.Theeffect canbe achievedonquite afewinstruments,especiallyviolins,violasandcellos,andissometimesused(andoccasionallyoverused)bysingers.You canheardifferentdegreesoftheuseofvibratobysingersifyoulistentovariousrecordingsofthejazzsong “CryMe aRiver.”Rockandbluesguitarplayersarealsokeenonvibrato,particularlyonlongnotesinsolos.Tohearvibratoonaclassicalguitar,IrecommendJohnWilliamsorJulianBreamplayingPreludeNo.4byHeitorVilla-Lobos.

TheviolinTheviolinis,onceagain,aninstrumentwithstretchedstringsattachedtoahollowbox.Inthiscasewehaveonlyfourstringsand,asisthecasefortheguitar,differentnotesareproducedbypressingthestringsagainsttheneckoftheinstrumenttoshortenthem.Onaviolin,however,therearenofrets.AsIsaidabove,thismeansthatifyoupluckaheld-downstringyougeta “thunk” rather than a clear note. This thunking noise is calledpizzicato and it’s occasionally used by composers to get a tuneful butpercussive effect from violins and other stringed instruments—thePizzicatoPolkabyJohannStraussisagreatexampleofthis.Fortunatelyforallinvolved,violinplayersareonlyrarelycalledupon

to pluck their strings. Their usual method of supplyingthe string withenergyisrathermorecomplicatedanditallowstheinstrumenttoproduceclear,singingnotesratherthanthunks.Toproducelong,singingnotesfromaviolin(orviola,celloordouble

bass), you need a bow.A bow is basically a collection of hairs from ahorse’stailwhichareheldtautbyaspeciallyshapedstick.Thestretchedhorsehairsaremadetobeslightlysticky(butdry)byrubbingthemwithamaterialcalledrosin.Rosinisdried-outresin—thatsticky,glueystuffyou sometimesseeonpine trees.Rosinmanufacturers collect the resinfrompine trees and dry it out into little blocks to sell to violinistsandotherstringplayers.

Aclose-upphotoofaviolinbowshowingthebandofhorsehairs,whichisdrawnacrossthestringtomakeitvibrate(thehorsehairsareusuallybleachedwhite—astheyarehere).

BeforeIexplainhowthebowworks,Iwouldlikeyoutodosomethingforme:putthisbookdownandgoovertothenearestwindow,computerscreenorTV.Now lickyour fingertipand rub itbackwardand forwardacross the glass (this doesn’t workas well on plastic laptop screens).Within a couple of seconds you should be able to produce a squeakingnoise. This noiseis caused by the stick–slip motion of your fingertipacross the glass surface. Stick–slip motion is just what it sounds like:motion made up of alternately sticking in one place and then slippingforwardquicklybeforere-stickingandthenslippingagain.Thepressureofyourfingeragainsttheglasstendstoholdyourfinger

inthesameplacebuttheforwardpushingofyourarmforcesyourfingerto move—and your saliva helps to lubricate that movement. So, yourfingerstartsoffbybeingstationaryandtheforwardpushingforcebuildsup.Then,whenthepushingforceisenough,yourfingertipmovesquicklyforwardafractionofamillimeter.Thisrelaxestheforwardpushingforceand the fingertip can stop again—but then the pushing force buildsupagaintorepeatthecycle(itrepeatshundredsoftimeseverysecond).Inthiswayyourfingertipalternatelysticksandslipsasitmovesacrossthe

glass—andthisproducesthenoiseyouhear.As the stickyhorsehairsof thebowaredrawnacross aviolin string

(see the illustration opposite), they undergo this slip–stickmotion andthis continuously excites the string—as if it were experiencing a tinypluckingactionhundredsoftimeseverysecond.Inthiscase,thestringispushedtoonesidebythestickybow,butonceitispushedfarenough,itslipsbacktobeingstraightandthenovershoots(justasapluckedstringwill)before thestickinessof thebowgrabs itagainandpulls itback towhereitstartedslippingfrom.

Drawingthebowacrosstheviolinstringmakesthestringvibrate.

Thefrequencywithwhichtheslip–stickactionhappensisdeterminedbythe usual things which govern how often strings vibratebackward andforward:thetensionthestringisunder,thematerialitismadefrom,andits length. The length of the stringis changed by pressing the stringagainst the neck of the instrument.As I said earlier, plucking a stringheld in thisway(without frets)would justproduceashort“thunk,”butthe action of the bow effectively re-plucks the string every timeitvibratesbackwardandforward—andthisproducesthelongsingingnoteweassociatewithviolins.Bearinginmindthejerkywayinwhichthestringisvibratedandthe

complicatedshapeoftheviolinbody,itisnotsurprisingthatthetimbre

ofthevioliniscomplicatedandfullofcharacter.It is worth pointing out another big difference between guitars and

violinshere;aguitarplayer(playingaproperlytunedguitar)onlyhastoputhis fingertipdownbetween two frets toget a notewhich is in tunewith other instruments becausethe string lengthwill be determined bythepositionofthefretinvolved.Aviolinplayer,ontheotherhand,caneasilyputherfingerdowninthewrongplaceontheneckandproducearandomnotewhichisnotintunewithanything(Iwillbediscussingthesedifferencesinmoredetailinthesectionon“Choosinganinstrument”inchapter11).Forthisreasonittakeslongertobecomeacompetentviolinplayerthanacompetentguitarist.Thisisalsothereasonwhyonlygoodviolinistsplaymorethanonenoteatatime,whereasamerelycompetentguitarist will find theplaying of up to six notes at once quitestraightforward.“Competent”heremeanssomeonewhocanplayforfiveminutes ata wedding without having hors d’oeuvres thrown at them.Becomingagoodviolinplayerorguitaristtakesaboutthesameamountof time and effort because the demands of the two instruments differ—“good”inthiscasemeansthatpeoplewillpaymoneytohearyouplay.Musicaltrainingtogettotheexpertstageusuallytakesabouttenyears

andcontinuesforaslongasyouplaytheinstrument.Infact,afterlotsofdifferentinvestigationsintoskillacquisition,itisnowgenerallyacceptedthat it takes about 10,000hours to achieve expert level in almost anyactivity—from landscape gardening to karate. Musicianship fits thismodel—so that’sjustovertwoandahalfhoursofpracticeadayfortenyears.Ofcourse,we’retalkingaboutprofessionallevelsofskillhere;youcanachieveaverysatisfyinglevelofmusicianshipifyoujustgiveitanhouraweek.Professional-level training usually pushes you toward the limits of

what a human being can achieve on an instrument, but becauseinstruments are designed differently, the demands on the musician arealso different. I could teach you to play themelodyto “BaaBaaBlackSheep”onapianoinfifteenminutes,butifyoustudytheinstrumenttoa

“good” level it would be quitenormal to expect you to play it whileharmonizing the tune with lots of rippling accompaniment and chordsinvolvingsixnotesatatime—becauseplayingjustonenoteatatimeona piano is very easy. On other instruments such as the French horn orbassoon,itisdifficulttoproduceevenasimpletunereliably.Weshouldall be particularly grateful tomusicianswho strugglethrough the earlyyears of instruments like these, which are especially difficult forbeginners. I couldn’t do it—I found the early stages of classicalguitarquitepainfulenough….Come to thinkof it,myfamily foundmyearlyguitartwangingquitepainfulenoughtoo.

Musicfromwindintubes

Thechurchorgan

Todescribehowanentirechurchorganworkswouldtaketoomanypages—theyreallyareincrediblefeatsofengineering.AllIwanttodohereisdescribehowthesimplesttypeoforganpipeproducesanote.

Anorganpipe(closed-endtype),showingtheairflowoverthesharpedgeofthewhistle.

Thesimplestchurchorganpipeisbasicallyatubewithawhistleononeend that is closed at the other end.Awhistle is just a containerwhichforces a flow of air over a sharp edge or blade. In an organ pipe thewhistleisthebitwhichgeneratesthenoise,butthefrequencyofthenoteproduced isdeterminedbyhow long the tube is.Let’s lookathow thisworks.Firstofallweneedajetofair.Inthegoodolddays,starvingchildren

couldbehiredatveryreasonableratestooperatemechanicalbellowstoproduce the air neededby churchorgans.Nowadays,weusuallyuse anelectricaircompressor.Whenyoupressoneoftheorgankeysitopensavalvebelowoneoftheorganpipesandtheairflowsintothechamberatthebottomofthepipe.Theairthenescapesfromthischamberthroughanarrow opening, as a fast-flowing stream or jet. This air jet thenflowsdirectlyacrossthesharpedgeshowninthepreviousillustration,andthissetsupavibrationinthecolumnofairinthetube.Tounderstandhowthenoteisproducedweneedtoknowwhathappenswhenajetofairflowsacrossasharpedge.Whena jetof airhits a sharpedge it doesn’tdivide calmly into two

streams. In fact, there isquitea lotofconfusionat theedgeand theairtendstoalternatebetweenonesideoftheedgeandtheother.

Whenajetofairmeetsasharpedge,theair“takesturns,”goingmostlytoonesideandthenmostlytotheother.

Ifthis“takingturns”soundsunnaturalandunlikelytoyou,thenthinkofitthisway:imagineroadtrafficcomingtoalongislandinthemiddleofaone-waystreet.Allthedriversareinahurrysotheywilleachtaketheroutewhich looksmostempty to themas theyapproach the island.So,Fredseesthattheleft-handsideoftheislandhasfewercarsonit—andhewillgothatway.Jane,whoisdrivingthenextcar,willseethat,becauseFred’scarhasgoneleft,theright-handsideoftheroadhasfewercarsonit—so shegoes toward the right.The “bestway togo” swaps regularlyfromsidetosideandthecarstaketurnsingoingdowntheright-handorleft-handroute.Theairfromajetfindsitselfinasimilarsituationwhen

itmeetsa sharpedgeandso the streamofairtakes turnsgoing first toone side and then the other. The deciding factor for the stream is thepressureoneithersideoftheedge.Air,likeanyothergas,alwaystriestomove to areas where the pressure is low in the same way that wateralwaysflows downhill. The air approaching the edgewill “notice” thatthepressureishigherononesideoftheedgethantheotherandwillheadforthelow-pressureside,butingoingthatwayitincreasesthepressureonthatside,sothenextbitofairinthestreamchoosestheothersideoftheedge.

Traffic“takingturns”atalongtrafficislandinaone-waystreet.

Inanair-poweredmusicalinstrument,thefrequencyofthe“turn-taking”becomes linked to the length of the tube by a phenomenonknown asresonance.Resonanceisnecessaryfortheproductionofanymusicalnoteandneedssomeexplanation.

RESONANCE

Resonanceisaprocessbywhichasmallamountofeffortrepeatedatthecorrectfrequencycanproduceabigeffect.Forexample,ifyouarepushingachildonaswing,youcanmakethe

swinggoveryhighwithverylittleeffortaslongasyougiveasmallpushatexactlytherighttime—youneedtopushjustatthemomenttheswingstartstomoveawayfromyou.A swing is like a pendulum, and the only thing which changes how

quickly it can perform one complete backward and forwardcycle ofmovement is the lengthof the chainsor ropes attaching the seat to theframe. It doesn’tmatter howhard you push, howhigh they go, or howheavy the child is—one swing to andfro will always take the same

amount of time.Theonly important thing is tomatch the frequencyofyourpusheswiththenaturalrhythmoftheswingandyouwillgetabigeffectfortheminimumamountofeffort.Ifyoutryanyotherfrequencythen thingswillgowrong.Forexample,iftheswingtakesthreesecondsto go and come back, you must push at three-second intervals.If youdecidetobehot-headedandpusheverythreeandahalfseconds,thentheswingwon’tevenbenearyouduringsomeofyour“pushes”andatsomepoint in thenear futureyouwillpushwhen theswing isapproaching—andyou’ll have to spendtherestof theafternoon taking littleJasper totheemergencydentist.Ifyouwouldlikeanotherexampleofresonancewhichdoesn’tinvolve

makingafoolofyourselfinaplayground,trythis.Firstofallyouneedtohalf-fillafairlybigcontainerwithwater—youcoulduseabathorasink.Now waggle your handbackward and forward rapidly in the water,keepingyourhandflat(likeacanoepaddle),asintheillustrationbelow.Theeffectwillbethatofalittlestorm—lotsofsmalldisorganizedwaves—because you are fluttering your hand to and fro toofast to get anyresonance.Nowtrymovingyourhandveryslowlybackwardandforward.This timeyouwill justget lotsoflittle ripplesbecauseyouaremovingtoo infrequently to get any resonance. Finally, put some towels on thefloor and getsome resonancegoing.Youonlyneed tomoveyourhandthesameamountasbefore,butifyoudoitatthecorrectfrequencyyoucangetallthewatermovingbackwardandforwardinonebigwave.Toachievethis,justpushthewaterfromlefttorightatdifferentfrequenciesuntilyougetanoverallbiggishwavegoing toand fro, and then followtherhythmofthatwave.AswithyoungJasper’s swing,youcan’taffect thenatural rhythmof

thewave—youmustmatchthatrhythmifyouwanttogetthemaximumeffectfortheminimumamountofeffort.I’vejustdonethisexperimentinmybathandIfoundthat thewholebackwardandforwardcycletookaboutthreeseconds;inmysinkittakesaboutonesecond.Thisisbecausemysinkisaboutonethirdaslongasmybath,sothewaveonlytakesone

thirdofthetimetotravelfromoneendtotheother.Thisisanimportantpointaboutresonantfrequencies.Whetherwearetalkingaboutwaterinabathorairinatube(likeanorganpipe),theresonantfrequencyincreasesas thecontainergetsshorter.There isanexact relationshipbetween thetwo. If, for example,container “A” is one fifth the length of container“B,”thentheresonantfrequencyofcontainer“A”willbefivetimesthatofcontainer“B.”

Waggling your hand to and fro in a basin of water: a. too frequently(mini-storm);

b.tooslowly(ripplesonly);

c.ifyoumatchthespeedofyourhandtothespeedofabiggishwave,youwilleventuallygetonebigwavegoing,whichwillspillovertheedgeofyourbasinifyouarenotcareful.Thisisaresonanteffect,likepushingaswing.(ForthesephotosIcoloredthewatertomakeitmorevisible.)

Resonance is the reason why some singers can smash wine-glassesusingtheirvoices.Whenyoutapawineglass,thebowloftheglassbendsinward(awayfromyourfinger)andoutwardhundredsoftimesasecondinarepeatingpatternandproducesanoteofacertainpitch.Theglassisbasically throbbing and producing pressure changes in the air.You canmakethisworkbackwardifyousingthesamenotebackattheglassloudenough. Instead of the bending glass producing the note, the notecancausetheglasstobend.Glassisn’tparticularlyflexible,soifyoumakeitbendtoofarbysingingveryloudly,theglasswillbreak.Youhavetosingexactlythenotethattheglassgivesoffifyoutapitorresonancewillnothappen. The pressure waves of the note you sing will only “push theswing”attherighttimeiftheyarriveattherightfrequency.Tappingtheglass does not contribute toward breaking it—it’s just a method ofidentifyingthis resonant frequency. Professional singers are best atshattering glasses, because they have been trained to recognizeandreproducepitchesaccuratelyandtheyarealsotrainedtobeloud—whichmeansthatthepressurechangesoftheirnotesarelarge.Ifyouwanttotryyour skills at glass vandalism, you should use a large, old, thin-walledglass.The glass needstobe large so that thenote is lowenough forus

non-trained singers to reach. It needs to be thin-walled so that it’s notvery strong, and preferably old (and therefore covered in lots of littlescratches,whichwillencourageittobreak).Butperhapsweshouldleaveyourgrandfather’spricelesscollectionof

wineglassesaloneandgetbacktoourorganpipe.Eachlittlepuffofairinsidethetube,createdbytheturn-takingatthe

sharpedge, travelsalongthe tubeasawaveofpressure.It thenhits theclosedendof the tubeandbouncesback toward theareanear thesharpedge.Afterthishashappenedafewtimes,oneofthereturningwaveswillmeetanewlycreatedwaveandthetwoofthemwilljoinforcesbouncingup anddownthe tube.Thisbiggerwave thensetsupa resonanceeffectwhich controls how often the turns take place at the sharpedge. Turnswill be taken at a frequency which is determined by how quickly thepressurewavecancompletetheroundtripfromthesharpedgetotheendof the tube and back again (so—the longer the tube, the lower thefrequency).This resonanceeffectbegins tooperateafteronlya fractionofasecondandisthecauseofthenotewehearfromthepipe.Thenotecreatedby this effect will, of course, have the same frequency as thepressurewavebouncingupanddownthetube.Simple organ pipes come in two types—the ones we have just

discussed,whichareclosedatoneend,andotherswhichhavetheirendsopen.Youmightwonder how thewave can rebound off the end of thepipeifitisleftopen(IcertainlydidwhenIfirstheardaboutit).Well,theprocess is a little differentfrom straightforward bouncing off a closedend, but the result is very similar and, once again, a resonant effect isbuiltuptogiveusanote.AsIsaidearlier,withaclosed-endpipeawaveofhighpressurerushesuptotheendofthetubeandbouncesoffit.Iftheendofthetubeisopen,thehigh-pressurewaveleavesthetubeand,asitdoesso,itleavesbehindalow-pressurezoneattheendofthetube.Thisresults in a low-pressure wave which then rushes back down to thewhistleendofthetube.Allthisrushingbackwardandforwardsetsuparesonanceeffect(similartothesimplebouncingoffaclosedend)anda

noteisproduced.A typicalchurchorgan isabigcollectionof individualwhistles.The

frequency of the note produced is determined by onlytwo things: howlong the tube is, and whether or not the end is closed (a closed tubeproduces thenote anoctave lower thananopen-ended tubeof thesamelength).Thetimbreofthenotegivenoffbyawhistlecanbeaffectedbytheshapeofthetubeincrosssection(youcangetround,squareoreventriangularones),butoneofthemostimportantfactorsisthewidthofthetube.Thintubesencouragehighfrequencies—sotheywillgiveyouamixinvolving less of the low-numbered harmonicsand lots of contributionfromthehigherharmonics.Anotewithlotsofhighharmonicslikethishas a very bright—or evenshrill—sound,whereas a note from a fattertubewill concentrate on the fundamental and its close companions—togiveamoreroundedsound.Organbuilders specialize ingiving their instruments awide rangeof

timbres, so they fit them with lots of different setsof whistles. Theymight have one set of thin tubes, a set of fat tubes and severalintermediatesets.Bypullingvariousbuttons,calledstops, inorout, theorganist canchoose toplayone setor theother.And that’snot all; theorganbuilderwill also add severalsetsof tubeswhichhavecompletelydifferenttimbres,conicalonesforexample,andotherswithreeds,whichmakethemsoundlikeclarinets.Thisgivesuslotsofchoiceinthetimbre,but thegreat thing is thatgroupsof thesedifferent setsoftubes canbeplayedat thesametimetogiveyouhundredsofpossiblecombinations.Youmight,forexample,usethethinclarinet-likeonestogetherwiththefat open-ended tubes, and then change to all the conical ones together.For a big finale youmightwant all the tubeson theorgan to join in—which will require you topull out all the stops, which is where thatphrasecamefrom.Bytheway,thoselongshinytubesyouseeonbigchurchorgans?I’m

afraidtheyarejustfordecoration.Therealtubesarehiddenbehindthem.

Thepennywhistle

Unfortunately,pennywhistlesnolongerliveuptotheirname.Thelawsof economics have taken their toll over the years,and nowadays theyshouldbecalled“500penny”whistlesifyouwanttobepedanticaboutit.In spite of this inflation, theyare still the cheapest, most beginner-friendlyinstrumentsyoucangetholdof,and,inthehandsofanexpert,theysoundwonderful.Iwastryingtolearn“TheLonesomeBoatman”onmine,andIintendtogetrightbacktotheprojectassoonasmyneighborsdroptheirnoisecomplaint.Thepennywhistleissimilartoanorganpipe,inthatitisatubewitha

whistle on one end. In this case, however, thetube has several holesdrilled into it. You can change the length of the resonating tube byclosing these holes with yourfingers. With your fingers over all theholes,theresonatingpartofthetubeisaslongasthewholetubeandyouget thelowest frequencynote. If you takeone finger off, the air in thetubeonlyresonatesuptothefirstholeitcomesto(theoneyouhavejusttaken your finger off). This means that the tube is now shorter andthereforethefrequencyofthenotewillincrease.Thiseffectofshorteningthe resonating lengthof the tubeby takingyour fingersoff theholes isdemonstratedin the drawing opposite. The pressure waves bouncebackwardandforwardonlyasfarasthefirstplacetheycanescapefrom—thenearestuncoveredhole.

a.Allholesopen.

b.Allholesclosed.

c.Oneholeopen.

Playingdifferentnotesonapennywhistle

Whathappensinsideapennywhistle(theshadedareashowstheportionoftheairinthewhistlewhichisresonatingtoproduce thenote):a.withalltheholesclosed,theairresonatesasfarastheendofthetubeandthelowest note is produced (longtubes = low notes); b. if some of yourfingersare takenoff theholes, theaironlyresonatesas faras the firstopen hole (because the pressurewaves can escape at that point). This“shorter”tubegivesusahighernote.

Pennywhistlesaredesignedtoproduceonlythenotesofamajorscale.Therearesevendifferentnotesinamajorscalesoweonlyneedsixholes(wegetonenotewhennoneoftheholesisclosedandwegettheothersixbyclosingoffthesixholeswithourfingers).Oneinterestingthingaboutpennywhistles(andotherwindinstruments)isthatnotall theholesarethesamesize.Wecouldproducepennywhistleswithsixidenticallysizedholes—but they would be more difficult to play becausesome of theholeswouldbeuncomfortablyclosetogether.Toavoidthisproblem,itispossibletokeepthesamenoteandmovetheholetowardthemouthpieceaslongasyouuseasmallerhole.I said earlier that the pressure waves only bounce backward and

forwardasfarasthefirstuncoveredhole—butthisisonlytrueiftheholeisbigenough.Ifyouuseasmallerhole,thenthepressurewavescanbefooledintoactingasifthetubeisslightlylongerthanthedistancefromthemouthpiecetothehole—asshowninthenextillustration.Thesoundpressurewavescannot fullyescape fromthesmallholeandso thenext

hole along is also involved, and the resonating effect stopssomewherebetweenthetwoholes.

Iftheholeinthepennywhistleissmall,thenthepressurewavescannoteasilyescape.Inthiscasetheresonanceeffect(shaded)carriesonforafewmillimeters after the first open hole because two holes are sharingthejobofallowingthepressurewavestoescape.Thetubethereforegivesaslightlylowernotethanwouldnormallybeexpectedfromaholeinthatposition.

Thisprincipleisusedbymanufacturersofwindinstrumentstopositionholes in thebestplaces foreaseofplaying. It isalsousedbyadvancedpennywhistleplayers togetextranotes (between theones in themajorscale) by half covering holes—whichhas the effect ofmaking theholesmaller. Real experts, like the over-talented folks who play “TheLonesomeBoatman”onYouTube, canusethissmallhole/bigholethingtoslidegraduallyfromonenotetoanother.Theylifttheirfingerslowlyoff thehole so that it gradually appears to get bigger as far as the airinside is concerned—and the length of the column of airwhich isresonating slides up and down from one hole position to another. Ofcourse, I only understand this in theory—my attemptsto do it sadlyresultedinthatunfortunateincidentwiththedognextdoor.Recordersalsomakeuseofthesmallhole/bigholeeffecttoallowthe

player to get two notes from one finger position. Recordersoften havetwo small holes next to each other, as you can see in the illustrationbelow.Ifonlyoneoftheseholesisuncovered,youget the“smallhole”note, and ifbothof theseholesareuncovered,youget the“largehole”note—whichisasemitonehigher.

Doubleholes,liketheonesonthisrecorder,allowtheplayertogettwonotesfromonefingerposition—becauseyoucanhaveeitherasmallhole(whenoneisuncovered)oralargehole(whenbothareuncovered).

More complicated pressure wave resonances can be set up in tubeswithholesinthembyclosingupcombinationsofholeswithopenholesbetween them. This helps us to obtain the maximum number of notesfromalimitednumberofholes.Finally,itispossibletogetresonantfrequencieswhichareoneortwo

octaveshigherbyblowingharderintotheinstrument.The combination of all these note-producing techniques makes it

possible to produce a surprisingly large number of notes froma pennywhistlewhichhasonlysixholesdrilledintoit—butitdoesn’tstoppennywhistlesfrombeingveryveryirritatinginthewronghands.(“Thewronghands”inthiscontextmeans“anybodyelse,”ofcourse.)Concerning timbre, as I said in thediscussionof organpipes earlier,

thinpipesmakebrightnoisesbecausetheypromotethehighernumberedharmonics.Thesehigherfrequencyfamilymembersareencouragedevenfurtheriftheairspeedisincreased—asitiswhenyoublowhardertogettheupperoctaves.Thisiswhytheuppernotesonapennywhistlesoundso shrill. Sorry,I need to reword that last sentence…. This iswhy theuppernotesonapennywhistlesoundsodamnedshrill.

Theclarinet

To get amusical note out of a tubewe need to have a situationwhererepeatedpuffsofhighpressurearesentupthetube.Atfirstthepuffscanbe rather disorganized—but very rapidly a resonance is set up and thefrequencyof thepuffs becomesfixed, andanote isproduced.Wehaveseen that, in the case of an organ pipe or pennywhistle, the puffs areproduced bythe “turn-taking” of a jet of air as it passes over a sharpedge.Inthecaseofaclarinet,thejetofairisdividedupintoastreamofindividualpuffsbyareedatoneendofthetubewhichisforced,byyourbreath,toflapopenandclosedhundredsoftimeseverysecond.The next illustration shows how the reed works in the clarinet

mouthpiece.Theclarinetplayerpressesgentlyonthelowersurfaceofthereedwithher lower lip—this closes thepath for any air toget into thetube of the clarinet. The player thenblows fairly hard while slightlyreleasing the pressure on the reed. Eventually the air starts to squeezethrough the tinygapbetweenthereedandtherestofthemouthpiece.Abalance is then set up between the air forcing the reed open and thebottomlipsqueezingitshut.Thereedthenopensandcloseshundredsoftimesasecond—andastreamofpuffsofairisreleasedintothetubeoftheclarinet.As in thecaseof theorganpipeand thepennywhistle, thefrequency of the puffs quicklybecomes controlled by the distancebetween the mouthpiece and the first open hole in the tube (orcombinationofopenholes).Like the violin, the timbre of a clarinet is complex and full of

character. The reason for this is that, in both cases, theway we giveenergy to the instrument involves a frequently interrupted action.Instruments which produce a smooth timbre—likeharps, guitars andflutes—involve a vibration which swings to and fro in a regular, evenmanner.Wehaveseenthataplucked stringdoesthisandsodoesajetofair when it meets a sharp edge. A violin string, however, is draggedrelativelyslowlyinonedirectionbythebowandthenslipsrapidlybacktheotherwaybeforebeinggrabbedbythebowagain—sothevibrationisslowinonedirectionandquickintheother.

Aclarinetmouthpiece.Theclarinetist’sbottomlippushesupwardonthereed, closing the small gap. The clarinetist thenblows air through thegap.Thepressureoftheblownairopeningthegap,andthelippressureclosing it, balanceout, andthegapopensandcloseshundredsof timeseverysecondtoproducemusicalnotes.

Theunevennessof theclarinetvibrationcomesfromthefact that thereediscompletelyclosedforasmalltimeineachcycle.Duringthetimeswhenthereedisclosed,theenergybeinggiventothecolumnofairinthetube of the clarinet is turnedoff.We don’t hear these “off” momentsbecause they occur forminuscule periods of time, hundreds of times asecond.Nevertheless,theregularinterruptionofthepowersupplytotheinstrumentmeans that thepressure ripples it produceswill be farmorecomplicatedthanjustaregularupanddownpattern—andwehearthisasarichorcomplextimbre.However, don’t let all this chit-chat about “unevenness of vibration”

giveyou the impression thatclarinetsorviolinsmakean inferiorsoundto instrumentswhichhaveasmoother timbre,suchas theharpor flute.AsIsaidearlier,wefindthesecomplicatedtimbresjustasenjoyableasthestraightforwardonesandoftenpreferthem,becausetheyaddanextralayerofinteresttothemusic.Whencomposersarewritingsomethingforanorchestra toplay, they

have to bear in mind the timbres and loudnesses of theinstruments attheir disposal and then distribute the musical jobs accordingly. Thisprocess, calledorchestration, can make dull music interesting, orinterestingmusicdull,dependingonhowwell it isdone.Thebooksonthesubjectwilltellyou,forexample,thattherangeofabassooncanbedivided into three parts. Its low notes sound full and rough, itsmiddlenotessoundmournfulandtheuppernotesarepaleandsoft.Otherbitsofadvice include such snippets as the fact that the clarinet canplaymorequietlythanafluteandthatatrianglecan’tbeplayedquietlyatall.Mostof these books are, of course, measured and scholarlyin tone, but myfavorite one is almost rabid in its opinions. ProfessorFrederickCorderwrotehisTheOrchestra,andHowtoWriteforIt in1894.Let’shearhisopinionofthetrumpet:

I desire here to record my emphatic opinion that the trumpet in theorchestra is an almost unmitigated nuisance. In the smallorchestra ofHaydn andMozart it obliterates everything else, anddare only be usedhere and there in the padding; in themodern orchestra it is uselessbecauseofitslimitedscale,whileinthemusicofBachandHandelitisasourceofconstantvexationofspirit.

SorryFrederick, Iwouldn’twant tovexyourspirit. I’llput the trumpetaway.Perhapsalittleguitarmusic?

The guitar is notworthwastingwords over, as its veryweak tone anddeeppitch…

Oops!Perhapsarelaxingmelodyontheviola?

Violaplayershavealwaysbeenbothscarceandbad.

Oboe?

The tone of the oboe is thin, penetrating and exceedingly nasal. It isplaintive andpathetic or quaint and rustic accordingto thecharacterofthemusic,butshouldnotbeheardfortoolongtogether.

Pub?Yes?Hangon,I’llgetyourcoat…Oneof thefewinstrumentsProfessorGrumpyhasagoodwordfor is

the clarinet, but I dread to think what he would have saidabout thedrinking straw oboe. All you need in order to own one of thesemagnificent instruments is a drinking straw and apair of scissors. Theillustrationbelowshowsyouwhattodo.Squashtheendofthestrawflat,cutittoapointandthenputitintoyourmouth.Withthepointaboutonecentimeterinsideyourmouth,useyourlipstosquashthetubeflatwhileblowingdownit.Afteracoupleofminutes’practiceyouwillbeabletobalance the pressure from your lips closing the tubewith the blowingpressure which is trying to reopen it. (If you have a lot of troubleachievingthis,youprobablyhavethestrawendtoofarornotfarenoughintoyourmouth.)Youshouldgetanot-very-mellifluousreedinstrumentnoise.Ifyoucutthelengthofthetube,youwillgetdifferentnotesastheresonating length gets shorter.You can even cut little finger holes andplaydreadfulout-of-tunemelodies.Thelongwintereveningswilljustflyby.

Adrinkingstrawoboe.Squashoneendofadrinkingstrawflatandthencutittoapoint.Putthepointedendinyourmouthandkeepitsquashedflatwithyourlipswhileyoublowintoit.Yourlipsshouldbepositioned

approximatelywhere the“squashed flat”arrowisinthissketch.(Paperstrawsworkbetterthanplasticonesbecausetheyflattenmoreeasily.)

Tunedpercussion

Theglockenspiel

The glockenspiel is a member of the “tuned percussion” group ofinstruments: “percussion” because you hit them to make a noiseand“tuned”becausetheyproducenotesratherthantheuntunedbangsofmostotherpercussioninstrumentssuchasbassdrums.Thewordglockenspielmeans “bell play” in German—but the instrument looks rather like akeyboardmadeofmetalbarsonsupports.Thewayaglockenspielmakesitsnoteisrathersimpleandisrelatedto

how a plucked stringmoves.When you hit one of themetal bars, yousuddenlybenditalittlebitandimmediatelyreleaseit.Thebarthentriesto return to its original straightcondition but overshoots and becomesbentintheoppositedirection.Itthencontinuestoflextoandfrointhisway,losingalittleenergywitheachflex,untilthenotediesaway.Fromatimbrepointofview,themetalbarproducesaverypurenote—

which is almost entirely made up of the fundamental frequency.Itmanagestodothisbecauseofthewayitissupportedontheglockenspiel.Ifyoutakeaglockenspielbar,tieabitofthreadarounditanddangleitintheairbeforeyouhititwithastick,youwillstillgetthenote,butitwillhave amorecomplicated timbre,as themetal flexes inall thedifferentwaysitcan.Ifyoufititbackontotheglockenspielyouwillfindthatyougettheverypuretoneagain.Thisisbecauseitissupportedattheexactpositionswhichallowthebartovibrateinonlyoneway—theonewhichgivesthefundamentalfrequency.Thismeansthatallthebendingenergycangointotheproductionofthispitch—soitisproducedclearandloud.If you moved one of the supports a few millimeters toward,or awayfrom,themiddleofthebar,thenotewouldbecomemuchquieterandofa

more complex timbre.This is because the supportwould be positionedwhere thebar needs tomoveup anddownandwould interferewith itsmovement.

Thepositionofthesupportsonaglockenspielbarallowsittoflexinonlyoneway—thewaywhichproducesthefundamentalnote.Anyothertypesof flexing are suppressed because they would involve movement at thesupports.

Thepiano

Eleven-year-oldboys,andotherdiligentpeoplewholiketocollectfacts,will delight in telling you that the piano is apercussion instrument.Percussionmeansthatsomethinghitssomethingelsetomakethesound,butwhatdoesthatmeanwhenwe’redescribingapiano?Inside apiano, eachkey is attached to a set of leverswhichpushon

eachotherandeventuallyflickasmallwoodenhammer,wrappedinfelt,atoneofthestrings.Theloudnessofthenoteproducedisdeterminedbyhowfastthehammeristravelingwhenithitsthestring.Asthehammerapproaches the string, it is no longer connected to the levers and thismeans it canbounce off the string immediately—which it needs to do,otherwiseitwouldrestonthestringandstopitvibrating.*Whenpeopletalkaboutaviolinplayer’stone,theymeanhowwellhe

producesthenotes.Thisisacombinationofseveralthings:thequalityoftheinstrument,howaccuratelyheplaceshisfingersontheneck(andhowmuch he waggles the fingers to get a vibrato effect) and how well hecontrolsthemovementofthebow.Theviolinorfluteplayerhasalotof

controlovertheloudnessandtimbreofeverynoteheproducesfromitsbeginning to its end.This isnot trueofpercussion instruments like thexylophoneor thepiano.With this typeof instrument,youstart thenoteoffand let it ring—andyoucancut it short ifyouwant to.There isnocommunicationbetweenthenoteandthepianistwhilethenoteisringing.So,pianoplayershaveadifferentsortof“touch”fromviolinplayers.

Theinstrumentsareequallydifficulttoplayatahighlevel,buttheskillsaredifferent.Pianistscanonlycontrolhowloudanoteis,atwhattimeitstartsandhowlongitlasts.Ontheotherhand,shehastocontrolallthesethings forup to tennotes at a time,which is ahell of an achievement.Highlyskilledplayerscanputdownallfivedigitsofonehandtomakeachord andmanage to put downone of those fingersslightly faster thantheothersinordertomakethemelodynotelouderthantheothers.Itisinterestingtorealizethatquietpianonoteshaveadifferenttimbre

toloudones,becauseifyouhitastringharderyougetadifferentmixofharmonics. Hitting the string harder tends to encourage the highernumbered harmonics, which givesthe notes a more complex, harshersound.Thismeansthatpianistshavesometimbrecontrollinkedtotheircontrolofloudness.The control of the loudness of notes was originally the whole point

behind the invention of pianos—and the reason why theyare calledpianosinthefirstplace.Thefullnameforthepianoisthe“piano-forte,”whichmeans“quiet-loud.”Therewereseveralkeyboardprecursorstothepiano, but the only one which was loud enough to play with otherinstrumentswastheharpsichord.Theharpsichordhasasetofkeys joined tosmall spikesmadeof the

quillsof crows’ feathers,whichpluck the strings.The troublewith thissystem is that it doesn’t matter how quicklyor slowly you pluck thestring,orhowmuchforceyouuse,itmakesexactlythesamenoiseatthesame volume. On a guitaryou can make the plucked note louder bypulling the string furtherbeforeyou let it go—but in aharpsichord thestring isalwayspluckedbythesameamountsotheloudnessofthenote

cannot be changed. This inability to change the volume, andthe rathertwangy sound of the plucked strings, meant that instrument makersstartedlookingfornewwaystoexcitethestrings.Hittingthestringwithsomething fairly soft was the winning option and this led to thedevelopmentofthepiano.Thepianowas invented in1709by an Italian instrumentmakerwith

the mellifluous name of Bartolomeo Cristofori, and wascontinuouslydevelopedoverthenexthundredyearsorso.Oncetheinstrumentmakersgot the action of the levers worked out,they had an instrument whichcould play at any volume from quiet to loud. The ability to vary thevolumehastwogreatadvantages.Thefirstisthatyoucanmakethetunestandoutfromthequieteraccompaniment,andthesecondisthatyoucanvary theloudness(andthereforetimbre)wheneveryouwantto,inordertoemphasizetheemotionalclimaxesofthepiece.

Timbredesign—synthesizersIn the 1960s a new breed of musical instrument—the synthesizer—becameavailabletomusicians,androckbandssoonfoundoutthat theirkeyboardplayerswerebeginningtosquandermorethantheirfairshareofthe instrument budget.Before this pointin history, thekeyboardplayerwas theonewhosatat thebackwith thedrummeranddidn’tgetmuchpost-gig snogging. Bythemid-1970s someof themhadmoredials andswitches to play with than the average military helicopter pilot.Synthesizers allowed them to mix harmonics together in previouslyunheardofcombinationstogetmillionsofdifferenttimbres.Someofthesounds they produced were marvelous and were clearly the result ofweeksofexperimentationandplanning.Othersweren’t.Synthesizers produce musical notes synthetically—that is, there is

nothingvibratinginsidethem;thenotesarejustproducedbycombiningelectricalripplepatternswhichdrivespeakerstoproducemusicalnotes.When a natural musical note is produced,the overall ripple pattern is

made up of a mixture of harmonics—simple waves join together toproduce a complicated wave shape.Electronic engineers use the sameprincipletoproducesynthesizednotes.Insideasynthesizerthecircuitryproduces simpleripple patterns which are combined to produce muchmore complex ones—and because you can choose almost anycombination,youhaveavastnumberoftimbrestochoosefrom.Some sounds are more difficult to copy than others with this

technology. For example, it is much more difficult to mimic theunmusicalsoundswhicharemadebytraditionalinstrumentsaseachnotestarts than it is to copy the notes themselves. Also,smooth timbreinstrumentsareeasiertoimitatethancomplextimbressuchastheviolinor oboe.Another problem is the factthat ifyou setyour synthesizer toproduceacertainripplepattern,thetimbrewillremainthesameoverthewhole rangeof notes from high to low—and, as we saw earlier, realinstruments don’t do that. Because of these problems, synthesizersarenot generally used to mimic other instruments; they are used asinstrumentsintheirownright.Ifyouwantatraditionalinstrumentsoundthenyouuseeitherarealinstrumentorsamplingtechnology—whichis,effectively, a digital recording of the individual notes from a realinstrument.

SomethingveryoddindeedLook at this collection of frequencies. Together they make up our oldfriendthenoteA2,whichhasafundamentalfrequencyof110Hz:

110Hz,220Hz,330Hz,440Hz,550Hz,660Hz,770Hz,etc.

As you know, the timbre of an instrument is made up of the variousloudnesses of these ingredients within the ripple shape.Whatever themixtureofingredients,ourbrainrecognizesthisasanotewithanoverallfrequencyof110Hz.Eveniftheloudest,strongestcomponentwas330Hz,

the overall pattern would only be completing its dance 110 times asecond—sothefundamentalfrequencyis110Hz.“Yes,John,”Icanhearyousaying,“you’vealreadysaidall that.Are

youbeingpaidbythewordorsomething?”Bepatient,dear reader—it’sgoingtogetoddinaminuteortwo.Rather thanjustbeingaminorcontributor to thesound, it ispossible

thatoneoftheharmonicscouldbecompletelysilent.If,forexample,the770Hz frequency was completely absent, we would still hear theremainingharmonicsaspartofanotewhichhasafundamentalfrequencyof110Hz.Thisisbecauseonly110Hzcanbetheheadofafamilywhichincludes 110Hz, 220Hz,330Hz, etc. We could have several of theharmonicssilent—andstillthefundamentalfrequencywouldbe110Hz.Now the odd bit: we can even remove the first harmonic, the

fundamental—110 Hz—and the fundamental pitch of the note we hearwouldstillbe110Hz.Thissoundsalittleinsanebutit’sperfectlytrue.Ifyouhear thefollowingcollectionof frequencies:220Hz,330Hz,440Hz,550Hz,660Hz,770Hz,etc.youwillhearitasanotewithafundamentalfrequency of 110Hz, even though thesound does not contain thatfrequency.Although theheadof thefamily isabsent, the remainingcomponents

join together in a dancewhich repeats only 110 timesa second. So thefundamentalfrequencyis110Hz—andthat’sthat.Asaneperson’sresponseisusuallythatthisnoteshouldsurelysound

liketheAanoctaveabove110Hz,theonewithafundamental frequencyof 220Hz. But this isn’t true because the harmonics of that note are:220Hz, 440Hz, 660Hz, 880Hz, etc. This groupdoesn’t contain 330Hz,550Hzor anyof theodd-numberedharmonics of theoriginal harmonicfamily.These odd-numbered harmonics are present in our group with the

missingfundamental—sotheonlypossible“alltogethernow”optionforourgroupis110Hz.Not only is this “missing fundamental” thing weird—it’s actually

useful. Not, perhaps, as useful as a Swiss army knife, orthe Heimlichmaneuver—butforanythingthispeculiartohaveanyusefulnessatallisadmirable,don’tyouthink?Hi-fi or even lo-fi speakers have a range of frequencies over which

theyareeffectiveandthisisrelatedtotheirshape,sizeandwhattheyaremade of. In the old days a good quality speaker cabinetwould containtwoorthreedifferentspeakers:littlestiffonesforhigh-pitchednotesandbig floppy ones for low frequencies. Nowadays it is possible to getridiculouslylow frequencies out of small speakers by utilizing the“missing fundamental” idea. Let’s say your speaker won’t do much atfrequenciesoflessthan90Hz,butyouwanttohearthenoteA1clearly—andithasafrequencyof55Hz.Ifyoufeedtheharmonicsof55Hztoyourspeakerwithoutthefundamental(i.e.,110Hz,165Hz,220Hz,275Hz),youwillhear55Hzloudandcleareventhoughthelowestfrequencyatwhichyourspeakerismovingis110Hz.Impressive,eh?

Youarehearinganotewhichisnotactuallybeingproduced.

Itoldyouitwasodd.

6.HowLoudIsLoud?

Tentimesoneequalsabouttwo…Wecanalltellwhenmusicisgettingquieterorlouderbutitisextremelydifficult to say exactly how much louder one soundis compared toanother.Trying todecidewhetherone sound isexactly twiceas loudasanotherisjustasdifficultastryingtodecidewhetherornotyoufindonejokeexactlytwiceasfunnyasanother.Oneofthemainodditiesaboutloudnesshastodowiththeadditionof

sounds.Normallywhenyouaddthingstogethertheresultmakessense—ifIgiveFredoneorangeandyougivehimone,thenluckyFredhastwooranges; if Igivehimthreeandyougivehimtwothenhehasfive.Theaddition of sounds doesn’t work like this. When you listen to a soloviolinist playing a concertowith an orchestra, the number of peopleplayingcanvaryfrom1to100injustasecondorso,butwedon’tclampourhandsoverourearsandthink“Cripes!Themusicjustgotahundredtimes louder.” (The coarser individuals among you may substitute“Cripes”forevenstrongerlanguage—upto,andincluding,“Jeepers.”)Itisdifficulttogeneralizeabouthowmuchlouderthemusicgetsontheseoccasions:itdependsonwhichinstrumentsareinvolvedandwhetherornot thecomposerhasaskedeveryonetoplayloudlyorquietly.It is,forexample,possibleforthewholeorchestra(playingquietly)tomakelessnoisethanasingleinstrumentplayingloudly.Ifyouaddthenoiseoftenviolins(oranyotherinstrument)together,

youdon’t hear ten times the loudnessof one instrument on its own. Infact, it’s very difficult to estimate exactly howmany times louder thesoundis,butmostpeoplewouldagreethattenviolins(playingthesamenotewiththesameamountofeffort)soundapproximatelytwiceasloudasone.Similarly,for100instrumentstheanswerwouldbe,“Onehundredtimesone?…That’llbeaboutfour…Obviously.”

So, ten instruments sound only twice as loud as one, and 100instruments sound only four times as loud as one. These “strangebuttrue”statementsneedsomeexplanation.FortunatelyIhaveoneready….Beforewestartourdiscussion,let’ssimplifymattersbytalkingabout

onlyonekindofinstrumentatatime.We’llconcentrateonflutesforthenext bit, but the following points are also true of anymixed group ofinstruments.So, let’s imagine we’ve gathered together an orchestra of 100 flute

players.Firstofallthereissilence.Thenoneoftheflutesstartstoplayanote.Thedifferencebetweensilenceandoneflute isvery impressive—it’sratherlikesittingindarknessandthenlightingacandle.Thenanotherflutestartsplayingthesamenote.Thismakesadifference—butit’snotasbigasthedifferencebetweenthesilenceandthefirstflute.Whenthethird flute joins in (playing the same note) itonly makes a smalldifference to the volume of the sound and the fourth makes even lessdifference.Iftheyallplaythesamenote,andtheflautistskeeponjoininginoneatatime,youwillsoonfinditimpossibletotellwhenanewonejoins thegroupbecausethedifferencebetween,say,sixty-twoflutesandsixty-threeissotiny.This is all very odd because you could have asked that sixty-third

flautisttobethefirstinthegroup—andinthatcaseheorshewouldhavebeen the one who made the biggest difference. In fact, you could askeveryoneofthefluteplayerstoplayasolonoteasloudastheycanafterasilenceandtheywouldallsoundequallyloud.Therearetworeasonswhyour100fluteplayerssoundlessloud than

you would expect. One of them has to do with how sound waves addtogether,andtheotherisrelatedtohowourhearingsystemworks.Let’slookatthesethingsoneatatime.

HowsoundwavesjointogetherBynow,weareallcluedupaboutthefactthatamusicalnoteisaregular

patternofchangesinairpressurewhichmakesoureardrumsflexinandout.Thenumberoftimestheeardrumflexeseverysecondtellsthebrainthepitchofthenote—andloudernotesinvolvebiggerpressurechanges,sotheeardrumflexesmore.(Ifyouoverdoitbylisteningtoaveryloudnoiselikeanexplosion,thehighpressurewillflexyoureardrumtoofarandtearit,givingyouwhat’scalledaperforatedeardrum.)Theillustrationbelowgivesyouapictureofwhat’sgoingon.Bothof

theseripplepatternshavethesamefrequency—butoneoftheminvolvesmuchbiggerpressurechanges,soitpushesandpullsattheeardrummoreandsoundslouder.

Thepressure ripplepatternsof the samenote: playedquietly (top) andloudly (bottom). The frequency of the note has notchanged but thevariationinpressureisgreaterfortheloudernote.

Let’sgoshopping.Yougotothemusicshopandbuyapairofidenticalglockenspiels and I’ll go off and buy a sound pressuremonitor. Thisequipment contains amicrophonewhichworks just like an ear—soundpressurewavespushapartofitinandoutlikeaneardrum—andithasacomputerwhichmeasureshowpowerfulthewavesare.I’musingasoundpressure monitor because itresponds in a very straightforward way tochanges in sound pressure—if you double the sound pressure you getdoublethereadingfromthecomputer.Nowallweneedisabighotelandapairofidenticaltwins(trustme,

this iseventuallygoingtobe interesting).Westart inoneroomandgetthe first twin tohit anynoteon theglockenspielwhilewemeasure the

powerof thepressurewavesitproduces.Let’ssaythecomputertellsusthat the loudness of the note just after hitting the glockenspiel is tenpressureunits.Nowwe take the second twin to anyother room in thehotel andget

himtohitthesamenoteontheotherglockenspielwiththesameforceashisbrother.(Wepickedidenticaltwinsbecausewewantthemtohitwiththesameforceaseachother.)Asyouwouldexpect,whenwemeasurethepressureripplesthecomputersaysthattheloudnessis,onceagain,ten.Nowwegetthembothtogetherinthesameroom.Firstofalltheytake

turnshitting theirnotes—and,not surprisingly, thereisnodifference inthereadingweget;aslongastheyhitthesamenotewiththesameforce,wealwaysgetareadingoften.Finallyweget themboth tohit thenoteat the same time.Wemight

nowexpectthecomputertosaythattenplustenistwenty.Butitdoesn’t.Wecandothisafewtimesandtheaveragesoundpressuremeasuredforthecombinationof the twonoteswillbeaboutfourteen….Someofoursoundhasgonemissing.And if we went out and bought more glockenspiels and hired more

twins, we would find that, for forty instruments, insteadof getting apressurereadingof400,theresultwouldonlybesixty-three!Widespread disappointment—we have a roomful of expensive twins

and glockenspiels but a lot of the sound is simply disappearing. Let’ssend themalldown to thehotel lobby for afternoonteawhile I explainwhatishappening.Whenwehitonlyoneinstrumentwegetthebestvalueforourefforts:

wehitthebar,itwigglesupanddown,andpassesonthesewigglestotheairasripplesinairpressure.Sowegetourmoney’sworthfromthehit.Ifwehave two instruments,weonlyget double the effect if theup–

down–up–down pressure ripples from them are perfectlyin step witheachother—sotheycanacttogethertogiveanUP–DOWN–UP–DOWNpressureripple.But,whenwehitbothinstruments,youcanbetyourlifethatwedon’t

hit themexactly at the same time, so thepressure ripples from the twoinstruments won’t be in step when they reach the microphone. Thismeansthatsometimesthe“pressureup”partofoneripplewillbetryingtoraisetheairpressureasthe“pressuredown”partoftheotheristryingtolowerit.Ifthewavepatternswereperfectlyoutofstep,theup–down–up–downofoneofthemwouldbecanceledoutbythedown–up–down–upoftheother—andwewouldn’thearanoteatall.This is weird but true—it’s how some farmers protect their hearing

when they are driving noisy tractors all day. They buy“active eardefenders”whichlooklikeheadphones.Insideeachoftheearpiecesisamicrophone and a speaker connected tosome electronics. Themicrophonelistenstothesoundwhichisabouttoreachyoureardrumandmakesthespeakerproducethesamepressurewave—butoutofstepwiththeoriginalone.Theideaisthatwhenthetwopressurewavesmeet,oneof them triesto raise thepressureat thesame timeas theother tries tolower it—sonothingmuchhappensand theeardrum is left inpeace.Inpracticethesoundwavesaretoocomplicatedforthistoworkexactly,butitdoesreducemostofthenoise.Going back to our glockenspiels, the canceling out is nowhere near

perfect because itwould be too difficult to organize—the soundwavesarecoming fromdifferentplaces in the roomandalsobouncingoff thewalls, and it’s incrediblyunlikely thatyouwouldhit the instrumentsatpreciselytherighttimestogettheripplepatternsexactlyoutofstepjustat thepointwhere theymeet themicrophone.Whatactuallyhappens isthatwedogetmoresoundpressurefromtwoinstrumentsthanwewouldfromone—but there is some interference from the low-pressurebits ofonewavepatternwiththehigh-pressurebitsoftheother,sothereissomecancelingout.If more instruments are involved, the amount of canceling out gets

moreserious.Thepressureoftheairnexttothemicrophonecanonlybehigher than normal (pushing the microphone inward) or lower thannormal (pulling it outward): it can’t be bothat once.Each of our forty

glockenspielshasan“uppressure”or“downpressure”voteatanypointin time—but a lot of thesevotes cancel each other out. If a forty-firstglockenspielist joins our little party, then his note will be mostlycanceled—thoughalittlebitwillgetthroughtocontributetotheoverallloudness.Thiseffectisnottheonlyoneinvolvedinourappreciationofloudness.

Ifitwas,100instrumentswouldsoundtentimesasloudasone.But,asIsaidearlier,weperceive100instrumentsasbeingonlyfourtimesasloudas one. This extra diminutionin perceived loudness is the result of thewaywehumansaredesigned—solet’shavealookatthat.

Whyourbrainsdon’taddupsoundsproperlyWhydon’tourbrainsaddupsoundsnormally?Thesurprisingansweristhatourbrainsandearsaddupsoundsinanunusualwayinordertohelpusstayalive.Fromthetimesoftheearliestcavementothepresentday,wehaveusedour ears to helpusavoiddanger.This isoneof themainreasonswehaveearsinthefirstplace(althoughtheyarealsousefulforsupportingyoursunglasses).Tobeeffective,yourearshavetobeabletohearveryquietnoises (like the soundof someonecreepinguponyou),but alsotheymustnotgetdamagedbyloudnoises(suchas thunder). Itwouldn’t be any good if you had excellent hearing for quietnoises butyourearsstoppedworkingafterthefirstloudnoiseyouheard.Our ears are organized in such away that quiet noises can be heard

clearlybutanyincreaseinthevolumeofthenoisehasprogressivelylessand less impact.Thiseffect isalso trueofourother foursenses:smell,taste,sightandtouch.Sixsmellysocksaren’tsixtimesassmellyasoneonitsown(eventhougheachofthesocksisreleasingthesameamountofsmell)andtensaltedpeanutsinyourmoutharen’tfivetimesassaltyastwoofthem(eventhoughyounowhavefivetimesasmuchsaltonyourtongue).Ifyoulight100candlesoneatatimeinadarkroomyougetthesame effect as you gotwith the flutes—thefirst onemakes thebiggest

differenceandtheeighty-seventhmakeshardlyanydifference.Ifyouaredaft enough to stickapin inyour fingertip then itwill hurt, but if youstickasecondonein(nexttothefirstone)thepainwillnotbedoubled.Why, you may ask yourself, did I carefully point out in that last

sentence that the pins should be next to each other? Well, there is areason,anditissurprisinglyrelevanttoourdiscussionabouttheloudnessof sound. Imagine that Ihaveaccidentallytroddenona thumbtackwithmybigtoe.ObviouslyIwouldfeelquitealotofpainandwouldprobablydoafairbitofswearingaboutit.IfItrodontwothumbtackswithmybigtoe,theoverallsensationwouldonlybealittleworsethanasingletack—nothingliketwiceasbad.If,ontheotherhand,Itrodononethumbtackwith my left big toe and another with my right big toe,then the painwouldfeelmuchworsethantwotacksinonetoe(don’ttrythisathome—justtakemywordforit).Thereasonfortheincreaseinpainisthefactthat my brain would receive two distinct pain signals (one from eachfoot)ratherthana“two-tack”painsignalfromonetoe.Whathasallthisgottodowithmusic?Well…earlieronIsaidthatthe

ear/brainwouldcalculatetenflutesasbeingonlyabouttwiceasloudasoneflute.Thisisonlytrueifthetenflutesareplayingthesamenote.Ifyoudividetheflutesintotwogroupsandaskgroup1toplayanotewithamuch higher (or lower) pitch than group 2, then the two notes playedtogethersoundlouderthanwheneveryoneisplayingthesamenote.Thedifference in pitch between the two notes needs tobe bigger than thedifferencebetween“Baa”and“Black”forthiseffecttowork.Onereasonfor this apparent increase involume is the fact that the brain is nowreceivingtwodistinctsoundsignals(likethetwopainsignals).Theotherreasonis that thenotes from the two smaller groups experience less ofthe“cancelingout”effectImentionedearlier.

LoudnessandpitchThesensitivityofourhearingsystemisnot thesameatall frequencies.

Themost extreme demonstration of this is the factthat there are somesounds thatwecan’t hear at all because theyhave apitchwhich is toohigh(e.g.,thenotefromadogwhistle)ortoolow(e.g.,thesubsonicsyousometimesexperienceifalargetruckenginevibratesthewindowsofthebuildingyou are in). Both the dog whistle and the trembling windowsproduceanoteornoise—it’s just thatourearsarenotdesignedtohearthem.Evenwithintherangewhichcanbeheardbythehumanearthereare differences in sensitivity.We aremost sensitive at the rather high,squeaky frequency range covered by the top few notes on a piccolo—whichiswhyyoucanhearapiccoloclearlyabovetheotherinstrumentsof an orchestra or marching band. In fact, music textbooks advisecomposersthat the piccolo should be used only sparingly because it isdifficulttoblenditinwiththeotherinstruments.Atfrequencieshigherorlowerthanthishigh,squeakyrange,ourears

areprogressivelylesssensitive.Mostmusicalnotesarebelowthisrange.This means that if you want to get a balanced sound between a bassinstrument like a bassoon and a higherpitched instrument such as aclarinet, the bassoonistmight have to play as loud as he canwhile theclarinetist takes iteasy. Similarly, if two identical instruments areplaying together but one is playing high notes and the other is playinglownotes,thentheoneplayingthelownotesmustplayharderinordertosoundasloudastheoneplayingthehighnotes.

LoudnessandnotedurationYetanotherpeculiarityof loudness is thatofnoteduration.Thenormalloudnessofthenotecanbeheardifitisplayedforasecondorso,butifthe note is played for half a second or less, it will sound quieter. (Itshould be borne in mindthat lots of music involves notes which areshorter than half a second; for example, when we sing “have you anywool?”onlytheword“wool”islongerthanhalfasecond.)Ontheotherhand,ifanoteisplayedforseveraltensofsecondsthen

itsloudnesswillappeartodecreaseasthebrainbeginstostopnoticingitsomuch.Thiseffect,ofdiminishingintensityforacontinuousstimulus,alsohappenswithourothersenses,particularlyoursenseofsmell(whichissomethingwecanbequitegladofattimes).Thereasonwhythesoundappears to diminish after a while is that your brain is constantlymonitoringyoursensesfordangersignals.Ifasoundiscontinuous,andnothingbad ishappening,yourbrain loses interestbecause thenoise isobviously not important to your well-being.Your brain is primarilyinterestedinanysuddenchangesinthesoundsyouarehearing,whichiswhyyousitupand takenotice ifa long-lastingsoundsuddenlystops—the“deafeningsilence”effect.

MeasuringloudnessHumanbeingslikemeasuringthings—wemeasureourheight,weight,thespeedofourcarsandthesizeofourbathrooms.Measurementshelpustodiscussthingsmoreaccuratelyandclearly.Thereare,ofcourse,alotofthingswecan’tapplyaccuratemeasurementsystems to,suchaskissingability,or thesocial skillsofhamsters,butwheneverwecanwe inventand use a measurementsystem. As we shall see, the invention of ameasurementsystemfor loudnesswasnearlyas trickyasgettingonetoworkforkissing(andprobablyalotlessfun).BeforewestartthissectionIwouldliketogooveracoupleofpointsaboutmeasurementsystemsingeneral.Thereare twobasic typesofmeasurementsystems: theabsolute type

andthecomparative(orrelative)type.Ifweareusingtheabsolutetype,wewouldsay“FarmerSmithhaseightcowsandFarmerJoneshasfourcows.”Ifweuseacomparativesystem,wewouldsay“FarmerSmithhastwiceasmanycowsasFarmerJones.”Asyoucansee,bothsystemsgiveus some useful information,but the absolute system is more precise,which iswhywenormallyuse it. Insomecases,however,wecan’tusethe absolutesystemandweneedtousethecomparativeone.Yes…you

guessedit…loudnessisoneoftheseawkwardcases.Because our ears respond to pressure changes, any system for

measuring loudness should be based on the measurement of pressure.Unfortunately, however, the earliest system of loudness measurementwas adapted from a method for measuring the decrease instrength ofelectricalsignalsaftertheyhadtraveleddownamileofphonecable,soweendedupwithasystembasedonintensityratherthanpressure.Thisisratherlikemeasuringdistancesingallonsofgas(ifNewYorktoBostonusesfourteengallonsofgas,thenthedistancefromheretoPoughkeepsieissixgallons).Thenumbersareusefulandaccurateintheirway,butit’sallabitclunky.Thisenergy-intensitysystemofmeasuring the loudnessofsoundshasadvantagesanddisadvantages,asweshallsee.

MeasuringtheintensityofsoundsRememberourtwinswiththeirtrustyglockenspiels?Theywouldgetjustastiredhittingtheinstrumentsinindividualroomsastheywouldiftheywere standing next to each other. In each case they are using the sameamountofenergyand it’snot theirfault if thepressurewavesrefuse tocooperatefully.Theintensitysystemlooksathowmuchenergytheybothput intotheir bonging, rather than at howmuch sound theymake.Thissystemsays to itself:“Thebongingenergyinvolveddoesn’tchange justbecausetheybothnowsharearoom—onebongplusonebongequalstwobongs’worthofenergyintensity.”Thisconvenient ability tousesimpleaddition is the main advantage of the intensity system of loudnessmeasurement.Ifwetakeamicrophone,attachittoacomputerandaskittoconvert

thepressurereadingsithearsintoenergy-intensitymeasurements,wecanaddsoundstogetherbythenormalrulesofaddition.Acomputercanbeprogramed to recognize that theten flute players are working equallyhard toproduce ten timesasmuchsoundintensityasasingleflute.So,for example,wecouldnowsay:tenviolinsproducetentimesthesound

intensityandtwicetheloudnessofoneviolin.Let’ssaywearegoingtouseacomputerandmicrophonetomeasure

soundintensityfromtotalsilencetopainfullyear-damaging.Aftersomecareful experimentswe could find the quietest noise that a human canhear.Wecouldthensetthecomputerso thatitgavethissoundintensityavalue of “1” and call it the threshold of hearing. This noisewould be,perhaps, equivalentto someone ten yards away sighing. If ten peoplewere sighing ten yards away (let’s not go into why they are all sounhappy),thenthecomputerwouldgivethisnewsoundanintensitylevelof10(but,ofcourse,wewouldhearitasonlytwiceasloud).Movingup in loudness,wecanabandonall thosemiserablesodsand

startmeasuring the sound intensitiesofmotorbikesorbrassbands.Youmight imagine that, by the timeweget to thenoise levelswhichcausepain(e.g.,puttingyourearafewcentimetersfromaroaddrill),wewouldbe measuring sound intensities a few hundred times greater than ouroriginal sigh.Well, stand by to be flabbergasted—the sound intensitywhich causes pain is 1,000,000,000,000 times greater than that of thequietestnoiseyoucanhear—yes,thesoundintensitygeneratedbyaroaddrill is a trillion timesgreater than thatofasigh.So ifyou’reunhappywith your job as a road drill operator, and you want your sighs to benoticed,remembertoturnthedrillofffirst.Weneedaquickrealitycheckhere.AsIsaidearlier,ourearsdonot

directly measure intensity—theymonitor pressure differences.Pressuredifferences are related to intensities, but to convert the intensity topressureweneedtodoacalculation.Inthiscasethecalculationtellsusthattherangeofsoundpressuredifferencebetweennearsilenceandpainis not 1,000,000,000,000—it’sjust 1,000,000, a million. It’s still anenormousnumberbutit’snotaridiculouslyenormousnumber.Let’s re-enter the world of intensity measurement… We know that

every time we multiply the sound intensity by ten (by havingtenviolinistsplay rather thanone), then the loudnessof thesounddoubles.So—let’s put together a list of sounds startingfromthe quietest to the

loudestwecanhear.Everysoundinthis list is twiceas loudas theoneaboveit.

Alistofsoundsfromthethresholdofhearingtothethresholdofpain

Example Relativeloudness

Relative soundintensity

Almostsilence(asigh10yardsaway) 1 1

Asmallflyintheroom 2 10Alargebeeintheroom 4 100Someonenearbyhummingatune 8 1,000

Afairlyquietconversation 16 10,000Soloviolin,moderatevolume 32 100,000Abusyrestaurant(ortenviolins) 64 1,000,000

Citytraffic,rushhour 128 10,000,000Anorchestraplayingloudly 256 100,000,000Verynoisynightclub 512 1,000,000,000Closetothespeakersatarockconcert 1024 10,000,000,000

Bigfireworksexplosion 2048 100,000,000,000Pain—afewinchesfromaroaddrill 4096 1,000,000,000,000

(All my examples are, of course, just guidelines—perhaps you have

raucous, noisy bees where you live—or maybe your sisteris aspectacularlyloudhummer.)Thistableillustratessomeofthemainpointsaboutloudnessandgives

us twomethods for comparing loud and quiet noises.However, neithersystemprovidesuswithausefulnumericalscaleofloudnessbecausethenumbersareso large.Therelativesound-intensitynumberson therightsaythataflyhasavalueof10andtheviolinhasoneof100,000,whichmeansthatyouwouldneed10,000smallfliesintheroomtoproducethesamesoundintensityasaviolin.Thisisusefulstuffifyouareaviolin-playing maggot farmer, but we still need a noise levelmeasurementsystemwhichusesasmallerrangeofnumbers.

DecibelmadnessThe search for a systemwith a small range of numbers gave someone,sometime in the first half of the twentieth century, theclever idea of aloudnessmeasurement scale basedonhowmany zeros therewere afterthe“1”inthe“relativesoundintensity”columninthetableabove.Thisis the “Bel” scale and in it a sound intensity of 1,000 would have aloudness of 3 Bels and1,000,000would be 6Bels, etc. (just count thezerosineachcase).Thiswasthoughttobeabrilliantideaforaboutsevenand a half minutes until someone even cleverer pointed out that thiswould only give us twelve numbers of loudness measurementfromextremelyquiettopainfullyloudandthatthiswasn’tgoingtobeaveryusefulsystem—becausenowwedidn’thaveenoughnumbers.Finally itwasdecided that 120measuresof loudnesswouldbemore

usefuland thatcouldbeachievedbymultiplyingall thenumbers in theBel systemby ten and thusmeasuring loudness in “tenths of aBel” or“deci-Bels”(decibels).Sonowwehaveasystemwhereasoundintensityof1,000isequalto30decibelsand1,000,000is60decibels,etc.(countthe number of zeros andmultiply by ten).A rough sketch ofwhat thedecibel system means to our ears is presented in thetable below

(“decibel”isusuallyabbreviatedto“dB”).

Intensity,decibelsandloudness

Relative soundintensity Decibels

(dB) Relativeloudness

1 0 1(almostsilence—sigh)10 10 2(smallfly)100 20 4(largebee)

1,000 30 8(humming)10,000 40 16(quietconversation)100,000 50 32(soloviolin)

1,000,000 60 64(busyrestaurant)10,000,000 70 128(rushhour)100,000,000 80 256(loudorchestra)

1,000,000,000 90 512(nightclub)

10,000,000,000 100 1024 (rock concertspeakers)

100,000,000,000 110 2048(bigfireworks)1,000,000,000,000 120 4096(pain—roaddrill)

Nowwe have a system that can be used tomeasure loudness from thequietestnoise to the loudestwhichonlygoesfromzeroto120.But I’mafraidthateventhoughthenumbersarenowsimple,theuseofthisscaleiscomplicated.Thetableshowsthateachtimetheloudnessofthenoisedoubles, you add 10 decibels. This sounds simple enough until yourealizethatthismeansthatnotonlyis20dBtwiceasloudas10dB(which

seemsobvious)butalsothat90dBistwiceasloudas80dB(whichseemscrazy,butit’strue—justlookatthetable).AtthispointImustcomecleanandadmitthatIdon’tlikethedecibel

systemof loudnessmeasurement at all. It isn’t easy touse even if youhave studied math or physics up to collegelevel. Even a professionalscientistwouldneedacalculatorandafewminutestobeabletotellyouthedifferenceinloudnessbetween53decibelsand87decibels.Ihavenoproofofthis,butIthinkthedecibelwasinventedinabar,lateonenight,by a committee of drunken electrical engineers who wanted to takerevengeontheworldfortheirtotallackofdancingpartners.Apart fromthe calculation problems, the use of intensity for measuring sounds isindirectandoverlycomplicated.I started this book with the promise that there would be no

mathematical formulas and I intend to keep that promise. However,Ican’texplainhowtocalculatethedifferencebetween53and87decibelswithoutusing formulas.Anyonewhowould likeabitmore informationonusingthedecibelsystemwillfindsomeinpartBoftheFiddlyDetailssectionat theendof thisbook.Frankly,though,Ithinkweshouldleavethe horrid decibels behind us, and move on to discuss the muchmoreuser-friendlysystems developed in the 1930s by a bunch ofAmericanresearchers, led by an experimental psychologist called Stanley SmithStevens.

Betterloudnessmeasuringsystems:thephonandthesone

While the electrical engineers were giggling to themselves aboutlumbering us all with the decibel system, the sound engineers,concerthalldesignersandpsychologistsspecializinginhearingdecidedtostrikeback. Because they were dealing with loudnessmeasurements all day,thesepeopleknewthatthedecibelsystemhadtwobigflaws:

Bigflaw1.AsIsaidearlier,thehumanhearingsystemismoresensitiveatsomefrequenciesthanothers.Thismeansthata32dBhighnotefromaflutewill sound(toahuman)a lot louder thana32dB lownote fromabassguitar—so thedecibel system isanunreliablemeasureof loudnessforhumanbeings.

Bigflaw2.Beforetheadventofpocketcalculators,youhadtositupallnight with six pencils and three erasers working out stufflike, “Howmuchlouderthan49dBis83dB?”EvenaftercalculatorscamealongyouhadtobuyonewithafarcicalnumberofbuttonsonitandaninstructionbookasbigasWebster’sDictionary.

“Aha!”saidtheexperimentalpsychologists,“wecaneschewthedecibelsystem and develop one which gives a more accuratepicture of theresponse of the human ear.” (Experimental psychologists talk in thissuperior,pedanticwaywhenevertheygetthechance.)Theonlywaytodevelopasystembasedonthesubjectiveresponseof

thehumanearistocarryouttestsonlotsofpeople.Thisiswhytheworkwascarriedoutbypsychologists:theyweremeasuringpeople’sopinions,ratherthanthingswhichcanbemeasuredbyscientificequipment.Thefirstsetoftestswasdesignedtoovercomebigflaw1andinvolved

a largenumberofpeoplewhowereasked tocomparenotesofdifferentfrequencies and say when they thought they were equally loud. Thesetests were carried out over a widerange of loudnesses and frequenciesandledtothedevelopmentofaunitofloudnesscalledthephon.To explain the difference between phons and decibels, let’s imagine

thatwehaveenlistedarobottoplaythepianoforus.Firstofall,weasktherobottoproducealoudnessof50decibelsforeachnoteandplayallthenotes,oneatatime,startingfromthetopone.Becauseourearsareprogressivelylesssensitiveaswemovefromthe

highnotesonapianotothelowerones,wewouldhearthenotesgettinggradually quieter as the robotmoved down the keyboard.On the other

hand,acomputerattachedtoamicrophone,“listening”tothesamenotes,would“hear”eachoneashavingthesameenergyintensity.Now we ask the robot to do the same thing again, but this time

producing a loudness of 50 phons from each note. This timeourmechanicalpalwouldhitthenotesmoreandmoreforcefullyasitmoveddown thekeyboard.Youwouldhear all the notes asbeingequally loudbecausetherobotwouldbecompensatingforthefactthatyoucan’thearthelownotesonapianoaseasilyasthehighnotes(yourcomputerwould“hear” exactlywhat the robot is doing andwouldbe able to tell that itwasplayingthelownoteslouder).Thephonsystemisjustthedecibelsystemafterwehavecompensated

forthefactthathumanearsarelesssensitivetolownotes.HavingconqueredBigflaw1thepsychologistsmovedontoBigflaw

2.As the phon system is basically a version of the decibelsystem,westillhaveexactlythesameproblemworkingoutwhatthenumbersmean.What’s the loudness difference between 55and 19 phons? Pass me acalculatorandsomechocolatechipcookies…So the psychologists decided to drop the decibel system entirely and

find a way of using a scale based on relative loudness,much to theannoyanceoftheelectricalengineerswhodevelopedthedecibelsystem.Nopartyinvitationshavepassedbetweenthetwogroupssince1936.If you look back at thetable, then you will see that the relative

loudnessscalegoesfrom“1”(asigh)to“4096”(aroaddrill)and,aswesaw,thisinvolvestoomanybignumberstobeausefulscale.Buthangonaminute,thenumbersforloudnoisesareonlythisbigbecausewestartedwith1as thequietestnoisewecanhear.This is thesameasmeasuringthepriceofeverythinginpennies—wedon’tsay“mycarcost1,500,000pennies.”Wedon’tneedtousethesmallestpossible coinasthebasisforourmeasurementsystem.Thepsychologistsgavethissomethoughtanddecided tomove the “1” from an extremely quiet sound tosomewherenearer themiddleofourhearing range.Theymoved it to the levelofafairly quiet conversation—so now we havea new measurement range

with “1”where “16” used to be. Thismeanswe have to divide all thenumbers in our “relative loudness”columnby16and thenumbersnowonlygoupto256,asyoucanseeinthenexttable.Althoughwehavetousefractionsof1forquietnoises,thisisnotmuchofaproblembecausewedon’tneedtodiscussquietnoisesveryoften.Sonowwehaveasystemwhichreallyworksforhumans—it’scalled

thesone system, and there is no need to worry about big numbers orcomplicated math. Eight sones sounds twice as loud as 4 sonesand 5sonessoundshalfasloudas10sones.Modern loudness metersshouldmeasure different loudness levels in

sones because it’s the most sensible system for monitoring anddiscussingloudnesslevelsasfarashumansareconcerned.Forexample,if an acoustic guitar player has a loudness level of 4 sones and a rockband’slevelis40sones,itmeansthattherockbandistentimeslouderfor any human listener. Because the sone system is basedon humanhearing, sone-based loudness meters automatically make the necessarycompensations related to the frequencies ofthe sounds they aremonitoring.Meters like this are used to help the relevant engineers todevelopbetterloudspeakersandsoundinsulationmaterials.However, youmay have noticedmy use of theword “should” at the

beginning of the last paragraph. In fact, most of today’sloudnessmeasurementsarecarriedoutusingthedecibelsystem,althoughthereisusuallyanadjustmentforthehumansensitivitytodifferent frequencies.This is simply because the decibel system was the first to becomeestablishedand is theone referredto in thegovernmentdocumentsandlegislationdealingwithnoise levels and soundproofing.Sowe’re stuckwithit.

Thesonesystemofloudnessmeasurement

Example Relative loudness (aftercompensatingforfrequency) Sones

Almostsilence(asigh) 1 0.06Asmallflyintheroom 2 0.12Alargebeeintheroom 4 0.25Someonenearbyhummingatune 8 0.5

Afairlyquietconversation 16 1.0

Soloviolin,moderatevolume 32 2.0

Abusyrestaurant(ortenviolins) 64 4.0

Citytraffic,rushhour 128 8.0Anorchestraplayingloudly 256 16.0

Verynoisynightclub 512 32.0Closetothespeakersatarockconcert 1024 64.0

Bigfireworksexplosion 2048 128.0Pain—aroaddrill 4096 256.0

Butonedaywewillallriseupand,impalingourscientificcalculatorsonespecially pointy road drills, we will free ourselvesfrom the evil,oppressiveshacklesoftheridiculous,loathso—Butperhapsmycold, authorial objectivity is slipping a little here….

Let’s move on to a subject less troubled by controversy:the art andscienceofharmony.

7.HarmonyandCacophony

TunefulbabiesBabiessinglittlesongstoamusethemselves,whichoftenconsistofonenote repeated over and over again.As they get olderthey increase thenumberofnotesinvolvedbecauseone-notesongsarealittleuninspiring.Asbabiesgetmoreadventurous,theywilldiscoverthelowestandhighestnotestheycansing,andfindthattheycanproduceanynoteatallwithinthisrange.Thebaby,singingits“LaLaLa”song,willchooseanyoldnoteswithin

its range andmaywander frompitch to pitch,withouthitting the samenote twice. A “song” of this type might involve hundreds of slightlydifferentnotes—andso itcanneverberepeated.Asthechildgetsoldershe will realize that everyone else is singing songs which can bememorizedandrepeatedbecausetheyinvolvealimitednumberofnotes:“Baa Baa Black Sheep,” for example. The child will hear quite a fewpeoplesinging“BaaBaaBlackSheep”andwilleventuallyrealizethatitisn’timportantwhatnoteyoustarton—it’sthejumpsupanddowninthetunewhichmatter.Tomakeasongrecognizableallyouhavetodoissingthecorrectsizejumpswiththeappropriaterhythm.Once a child remembers a few tunes in this way shewill develop a

libraryoftunefuljumpsthatshecanuseforanysong.Forexample, thejump between “Baa” and “Black” is the same as the one between the“twinkles” in “Twinkle,TwinkleLittleStar.”The jumpbetween“have”and“you”(asin“haveyouanywool?”)is thesameastheonebetweenthefirsttwonotesof“FrèreJacques.”Thechildisnowusingscales,thatis,alimitednumberofrecognizable

jumpsinpitch.AsIsaidearlier,thesejumpsarecalledintervals.Trainedsingers and people with natural ability manage to sing these intervalsaccuratelybut the restofus justget closeenough for themelody tobe

recognizable.Thesimplesttypeofmusicinvolvesasinglevoicesingingaseriesof

intervals,oneaftertheother,toproduceamelody.Thenextobviousstepis to get several friends around to sing alongwith you—with everyonesingingthesamenotes.Thissortofmusic-makinghasbeenaroundsincewewerealllivingincaveswaitingforsomeonetoinventcentralheating.Theearliestcavemenwhosangtogetherwerequicklyfollowedbythe

secondearliestcavemenwhosangtogether—whodecidedtoliventhingsupabit.Likeallteenagerstheywantedtohavetheirownstyleofmusicanddidn’tcare for theold-fashionedrubbishtheirparentsweresinging.Theyhad a lot of successwith a new techniquewherehalf of the tribesangthesongwhiletheotherhalfsangjustonenote,calledadrone.Theynoticedthatsomeofthenotesofthesongsoundedbetterwiththedronethan others, but they didn’t give it muchthought. Eventually, aparticularly talentedcavewomancalled“Ningy, theparticularly talentedsinger” started to sing alongusing different notes from everyone else.Thismeantthatyoucouldheartwotunesandadroneat thesametime.Everyonewas delighted, and people became less fretful about the totalabsenceofweatherproofing.Ningy theparticularly talentedsingerknewshehad topickhernotes

carefullyiftheyweretosoundgoodwiththenotessungbyeveryoneelse—somecombinationssoundedgreatbutotherswereterrible.Thiscarefulchoice of noteswhich sound goodtogether gives uschords, and chordsarethebasisofharmony.WhenIsay“noteswhichsoundgoodtogether”Idon’tjustmeannice,pleasantcombinations.Asweshallsee,harmoniesarenotalwaysharmoniousanditisacomposer’sjobtobuilduptensionoccasionallyandthenrelaxit.TheAmericanrockmusicianFrankZappasummedthisupexcellentlywhenhesaidthatmusicwithoutanebbandflowoftensionwouldbelike“watchingafilmwithonlygoodguysinit.”

Whatarechordsandharmonies?

Chord:Achordisthesoundmadebythreeormorenotesplayedatthesametime.Harmony: A succession of chords produces a harmony. The

relationship between chords and harmony is therefore similar to thatbetweenwordsandsentences.When composers (and by composers I mean people who write pop

songsandadvertisingjingles,aswellasMozartandCo.)writeapieceofmusic,theyusuallyuseharmonytoprovideabackgroundtothemelody.Thisharmonycanalterthemoodofthemelodyjustasthebackgroundofa photograph can make a portrait more or less cheerful. Film musiccomposersoftenuseonlythreeorfourtunesforanentirefilm,andtheyneedtochangethefeelofthemelodytomatchthemoodsofthedifferentscenes.Techniques for altering the mood of the music include usingdifferentinstruments(ifit’sasceneinPariswewillheartheobligatoryaccordion)andplayingthemelodyfasterorslower.Butplayingthetunewith a different harmony is one of themost effective ways ofmanipulatingouremotions.Somecombinationsofnotes soundpleasantandsomesound tenseor

ugly. Composers often deliberately choose a sequence ofanxious-sounding chords to build up tension before releasing it with someharmonious combinations—composing is rather liketelling a story orjoke,inthatthecomposerneedstosetupasituationandthenresolveitinsome way. Changing the levelof tension in the harmony is one of thecomposer’s main tools for manipulating the mood of the music. Anexcellent example ofthis can be found in the opening to a track byGenesiscalled“WatcheroftheSkies,”whichbeginswithaseriesofslowchordsplayedbythekeyboardplayer.Inthefirstpartofthissolothereisnotuneorrhythmtospeakof,buttensioniscleverlybuiltupbytheuseofharmonyalone.Ifyoucaretocountthechords,youwillfindthatthethirteenthoneintroducesustoawholenewleveloftension—perfectforaccompanying the sort of teenage angst Iwas attempting to experiencewhenthisrecordingcameout.

Ifyouareinthemoodforsomereallyanxiouschords,trylisteningto“TheDevil’sStaircase,”apianopiecebythecomposerGyörgyLigeti.Itonlylastsaboutfiveminutes,butbytheendofityoudon’tknowwhetheryouwanttohaveaquietlie-downinadarkenedroomorlistentoitagain.Iusuallycan’tresistanothergobeforeIstartlookingforasoothinglavalamp.Inharmoniouschordscanalsobeusedforcomiceffect—justlistento

thepianoatthebeginningofthesong“DrivinginMyCar”byMadness.Inthefewsecondsafterthefirstfourhornbeeps,andbeforethesingingstarts, the pianist chooses alot of jangly chords to add to the generalchaos.Asforpleasantchords,therearesomanyexamplesthatit’sdifficultto

knowwheretostart.Harmoniouschordsdominatethemusicallandscape,from“MissChatelaine”byk.d.langto“AdagioforStrings”bySamuelBarber.But the subject of harmony canbeboileddown to a single question:

whydocertainnotessoundgoodtogether?Theillustrationoppositeshowsthepressurewavesofanotereaching

theear.Thisdrawingisagreatsimplificationbecauseitonlyshowsthefundamentalfrequencyofthenoteand,asIdescribedinchapter3,arealnote would be a lot more complicated.But I will use these simplifieddrawingstokeepthingsasclearaspossible.

Anote(ripplesofairpressure)travelingtowardanear.Therippleswillmaketheeardrumvibratebackwardandforwardlike amini-trampoline.The vibration repeats as a regular pattern and will therefore beexperiencedasanotebythebrain.

The illustration above shows us the fundamental wave pattern of asingle note, but if two notes are played at the same timethey jointogether tomake a combinedwave pattern like the one in the drawingbelow. If the two waves join together in aregular, orderly way, thecombinedsoundwillbesmoothandharmonious,andwecanseethatthisiswhathashappenedhere.

The combination ripple pattern of two notes one octave apart: it looksgood and sounds good because the relationship betweenthe notefrequenciesisverysimple—onenotehastwicethefrequencyoftheother.

Inthiscasethehighernotehasafrequencywhichisexactlytwicethatofthelowernote—andtheintervalbetweensuchnotesis called anoctave.Ifyouhearthesetwonotesatthesametime,theysoundsocomfortabletogetherthattheyaredifficulttodistinguish.Infact,musicpsychologistsinspotlesswhitelabcoatshavedecidedthattwonotesanoctaveapartaresocloselyrelatedthattheyarealmostidenticalasfarasthehumanbrainisconcerned.Let’slookatanexampleofhowthisworks.ThethirdGfromtheleft

onapianoiscalledG3. Ifyouplaythisnoteinfrontofachoirandaskthem to sing it, a lot of themenwith lowvoiceswill sing the note anoctavebelowyours (G2), and a lot of thewomenwithhighvoiceswillsingthenoteanoctaveabove(G4).Ifyoutellthemthattheyweresingingthewrongnotestheywillreply(huffily)thattheywerenot:youaskedforaGandthat’swhattheygaveyou.

The reason why notes an octave apart sound so similar is easy to

understandifwereferbacktothenatureofmusicalnotes.Inchapter3Iexplained that a musical note is made up of a family of vibrations: afundamental frequency togetherwith twice,threetimes,fourtimes,fivetimes,etc.,thatfrequency.Solet’slookatthefrequencieswehearifweplaythenoteA2(110Hz)

andthenoteanoctaveaboveit,A3(220Hz).

A2(110Hz)is:

110 220 330 440 550 660 770 880Hz,etc.

A3(220Hz)is:

220 440 660 880Hz,etc.

So ifwe hear the 110Hz note first and then both of them together, thebrainisnotprovidedwithanynewfrequencies—itjustgetsadoubledoseofsomeof the frequencies itheard in theoriginalnote.For this reasonthe frequency-recognizing systemof thebrainhears thecombinednotesas simply a slightly different version of the first note—which is whynotesanoctaveapartsoundsoharmonious.Thisverystrongfamilyrelationshipisthereasonwhynotesanoctave

apartareevengiventhesamename(well,almostexactlythesamename:asyouknow,wegivethemaletterwithanumberrelatingtowheretheyareonthepianokeyboard).Sincenotesanoctaveapartagreewitheachothercompletely,theresult

is soharmonious that itmightevenbeconsidereda little uninteresting.There are, however, other combinations which sound good without thenotes involved swallowing eachother’s personalities.We can illustratethisbyusingthenotesof“BaaBaaBlackSheep.”

Thenotes“BaaBaaBlackSheep”travelingtowardanear.

Hereyoucanseethatthefirsttwonotesarethesameaseachotherandthesecondtwonotesarealsoapair—buttheyaredifferentfromthefirstpair.Thepeaksoftheripplesofthesecondtwonotesareclosertogetherthan those of the firstpair and thesehigher frequency ripplesmake theeardrummovebackwardandforwardmorefrequently(whichiswhywehearahigherpitchnote).Whenwelistentoonepersonsingingthissongweobviouslyhearthe

notesoneaftertheother,butifwegettwosingersandaskoneofthemtosingthenotefor“Baa”andtheothertosingthenotefor“Black”atthesametime,theywillsoundverygoodtogether.Inthecaseofthesenotes,the“Black”hasaripplefrequencywhichisoneandahalftimesthatofthe“Baa.” Because of this simple relationship, these two notes soundalmost as pleasant together as two notes an octave apartdo. The nextillustrationdemonstrateshowthetwonotescombinetomakeanewwavepatternwhichissmoothlyrepeatingenoughtosoundgood,butdifferentenoughfromtheoriginalnotestosoundinteresting.

Thecombinationoftwonotesmovingtowardanear.Theripplepatternsofthetwoindividualnotesjointogethertobecomeacombinedpattern.Inthiscase,thenotefor“Black”isoneandahalftimesthefrequencyofthenote for “Baa.” This simplerelationshipmakes the combination of thenotessoundsmoothandpleasant.

So far we have looked at combinations of notes which have a simplerelationship,suchasdoubleorone-and-a-halftimesthelowerfrequency.Now let’s see what happens if we combine the ripple patterns of twonotes which have a complicated relationshipto each other. In theillustrationoppositeyoucansee thecombinedripplepatterncreatedbyjoiningtwonotestogetherwherethefundamentalfrequencyofthelowernote is seventeen-eighteenths the frequency of the upper one. Twoadjacentnotesonapianohavethisrelationshipand,ifyouplayanysuchpairtogether,itdoessoundjanglyandinharmonious.Adjacentnotesonapianoareonlyasemitoneapartinpitch,whichisthesmallestintervalweuse inWestern music. If you play twonotes this close together at thesame time, the resulting combination sounds as if the two notes aresimply out-of-tune versionsof each other—competing for our attentionratherthansupportingandaddinginteresttoeachother.Oneeffectofplayingtwonoteswhichareclosetogetherinpitchisthat

the loudness of the combined sound goes up and downseveral times asecond.Youcanseethisintheillustrationopposite,astheoverallsizeofthecombinedpressureripplecontinuouslyswellsandshrinks.Thiseffectis caused by the individual pressure ripple patterns from the two notesrepeatedlyfallinginandoutofstepwitheachother.Tounderstandhowthishappens,imagineyouarewalkingnexttoafriendwhotakesslightlylongerstrides,buthetakesslightlyfewerstridesperminute,soyouarewalkingat thesamespeed. Ifyoustartoff instepwitheachother, thenyouwillgraduallyfalloutofstep,butafteracertainamountoftimeyoursteps will synchronize again. This will happen in a repeating cycle—maybehetakestenstepsineachcycleandyoutakeeleven.Whenthis“in

step–out of step–in step–out of step” cycle happens with the pressureripple patterns fromtwomusicalnotes, as in the illustrationbelow, theoverallnoisehasanunpleasant,wobbly“WaWaWaWaWaWa”soundasthevolumegoesupanddown.Thiseffectisknownasbeatingorbeats.

Thecombinationoftheripplepatternsoftwonoteswhichdonothaveasimplerelationship.In thiscase,onenotehas17/18thsthe frequencyoftheother(whichisaboutthesameastheintervalbetweentwoadjacentnotes on a piano). This combinationsounds as complicated as it looks.The overall sound is one of two clashing notes and a “WaWaWaWa”effectastheoverallvolumefluctuatesupanddown.

The fact that a combination of notes with a complicated relationshipsoundsroughisthereasonwhyinstrumentswhichareoutoftunesoundawful. In fact, “out of tune” simply means that the nice, simplerelationships we prefer to have betweennotes have been replaced bycomplicatedones.Itdoesn’ttakemuchde-tuningfortherelationshipstoberuinedinthisway;theharmonioussoundoftwonotesanoctaveapartcanbe ruined if oneof the frequencies iswrongby just a fewpercent;110Hzplus220Hzsoundsgood,110Hzplus225Hzsoundsunpleasantbycomparison.Onefinalpointtomakehereisthatamusicalchordisacombination

of three, not just two, notes. But I have only usedtwo notes in mydiscussion in order to keep things simple. Three notes fit together in amorecomplicatedwaythantwo—buttheprinciplesofnotecombinationarethesame.

Howdoweusechordsandharmonies?Rhythmguitarists in rockorpopbandsplaychordsmostof the time toprovide the harmonieswhich accompany themelody ofthe song.Theirjob usually involves strumming several strings at once to produce achord,which they repeat a few times beforemovingon to another one.The notes which make up the chords are chosen to support the noteswithin themelodies, and thismeans that thechordsandmelodiesoftenusesomeofthesamenotes.Forexample,ifacertainbitofthetuneusesthenotesA–B–C–D–E,thenatypicalaccompanimentwouldbethechordmadeupofthenotesA,C,E.Wedon’tslavishlyfolloweverynote usedin the tune; we just pick suitable ones which fit. This chord wouldobviouslygivemostsupporttothenoteswithinit(A,C,E),sowewoulduseitifthosewerethenoteswewereemphasizinginthesong.IfwehadwantedtogiveprominencetothenotesBandDinthesamebitoftune,wecouldhaveusedthechordwhichusesthenotesB,D,F.Youmayhavenoticed that Iamnotusingconsecutive letters formy

chords.The simplest chordsdon’t involvenoteswhichare rightnext toeachotherinthescalebecause,asI’vediscussed,notesthataretooclosetogether produce harsh combinations.Consecutive notes of a scale areeither a semitone or a tone apart in pitch, and Imentioned earlier thatnotesasemitoneapartcompeteforourattentionratherthansupporteachother.Thesameis true, toalesserextent,fornotesatoneapart,soanyconsecutivenotesfromascalewillclash if theyareplayedat thesametime. For this reason, a chord made up of the notesA, B, and C, forexample,wouldsoundveryanguishedindeed,astheBwouldclashwithboth theA and theC. This sort of chordwould not be ofmuchuse inaccompanyingamelody,butitwouldberightathomeinsomethingverytenselike“TheDevil’sStaircase.”The notes in simple, harmonious chords need some breathing space

between them in order to support each other, and three alternatenotesfrom whatever scale is being used gives us the commonest type of

pleasantcombination.However,eveninpopsongsitiscustomarytoaddalittlebitofspicetooccasionalchordsbyfirstbuildinga“nice”teamofthreenotesandthenaddingasingleclashingnote.SowemightuseC,E,andG,withaBthrownintoaddabitoftensionbecauseitwillclashwiththe C. Our rhythm guitarist (who should really be called the harmonyguitarist)providesthesegroupsofnotesasabackgroundtothemelodiesproducedbytheleadguitaristorsinger.In other musical situations we don’t have one person providing the

melodyandanothergivingustheharmony.Solopianists,forexample,dobothjobsatonce,generallyplayingthemelodywiththeirrighthandandthe chords/harmony with their left.On the other hand, classical musicoften involves a large team of orchestral players. When an orchestraplays, only a fewof thememberswill be playingmelodies at any onetime, and the othermusicianswill play harmonies to accompany them.T h ecomposer will often pass melodies around from one group ofmusicians to another to keep the listener interested. InBoléro by theFrench composer Ravel, themusic gradually gets louder as the tune ispassedaroundtheorchestraandmoreinstrumentsjoinin.Theharmoniesarekeptpleasantandwarmuntil justnear theend,where thecomposerinjectsalotoftensionforadramaticfinalclimax.Chords and harmonies form the background to the melody and also

support thepunctuationof thephrasingof themusic. In fact,youcouldremovethewordsandtunefromanysongandstillbeabletotellwheretheendsoftheverseswerefromtheharmonyalone.Ifyouareaccompanyingamelodywithchords,thesimplestthingyou

can do is to repeatedly play all the notes of the chordtogether.Alternatively, you can add an extra layer of interest to the music byplaying the notes of the chords one at a timeas a sort of continuous,overlappingstreamofnotes.Achordplayedasastreamofitsindividualnotesiscalledanarpeggioandthisisthebasisofthepopularfolkguitartechniqueoffinger-picking.(Goodfinger-pickingguitarplayerscanplaythearpeggiosof thechordsandamelodyat the same time.)Arpeggios

addalayerofcomplexityandsubtletytomusicbecauseyoucanchooseexactlywhichnotesfromthechordwillcoincidewithparticularnotesinthetuneandalsoaddarhythmtothearpeggiopattern.Arpeggios are common throughout music and can be found in just

about any classical piece, particularly anything with “romance”in thetitle.ThefamousslowmovementofBeethoven’sMoonlightSonataisastreamofarpeggioswithatuneontop,butpossiblythebestexampleofapiece madeentirely of arpeggios is the “Prelude in CMajor” by J. S.Bach.There isno real tune, justaseriesofchordsplayedasarpeggios.Confronted with a piece like this, composed by Bach, most othercomposerswouldtreatit,quiterightly,asapreciousjeweltobeadmiredtothepointofjealousy.Notsothenineteenth-centuryFrenchcomposer,CharlesGounod.GounodtookonelookatBach’sPreludeandthought“Apiecemadeentirelyof arpeggios?What awaste…where’smybookofspare tunes?” The resultof this rush of blood to the head was “AveMaria”—accompanimentbyBach,tunebyGounod—andIhavetoadmithedidadamnfinejobofit.Rockandpopbandsalsolovearpeggios.Theopeningto“Stairwayto

Heaven”byLedZeppelinisaseriesofarpeggios,asis“HotelCalifornia”bytheEagles.StatusQuo,ontheotherhand,generallyeschewarpeggiosandconsiderthemtobeanambypambywasteofvaluablerecordingtime—they revel in rapid repeats of full chords for a high energy effect.BeethovenandStatusQuoareintotalagreementonthis“loud,repeatedfullchords=energy,”asyoucantellifyoulistentotheopeningsecondsof Beethoven’s “Hammerklavier” Piano Sonata or his Fifth Symphony(theonewhichgoesDaDaDaDaah!DaDaDaDaah!).The most complex type of harmony is calledcounterpoint.

“Counterpoint” describes the situation in which you accompany onemelody with another melody—in this way you can have two,three oreven more tunes playing at the same time. For most of us, the onlypersonal involvement we have in this are thosechildren’s songswheretwoorthreesingersstartthesamesongafteracertaindelay—likethis:

FrèreJacques,FrèreJacques,dormezvous?…FrèreJacques,Frère…

JIM:FrèreJacques,FrèreJacques,dormezvous?Dormezvous?Soggysemolina…KIM:TIM:OrLondon’sburning,London’sburning,fetchtheengines,fetchtheengines…

London’sburning,London’sburning,fetch…

London’s…

Thismethod of playing the same tune after a certain delay is called acanon.Thedelaymeansthatyouarebothsingingdifferentnotesatanyone time—which is a similar musical effect to both of yousingingdifferenttunes.Aslightlyclevererversionofthecanoninvolvesthisideaofsingingthesamesongafteraslightdelay—butstartingonahigherorlowernote.Counterpoint often employs these techniques, but can also involve

different tunes played at the same time. The tunesmustwork togetherand,usually,someofthetunesaccompanyingthemainmelodyarekeptfairly simple to prevent the whole thing turning to incomprehensiblemusicalmush.Youcan’tjust playanyoldtunesatthesametimebecausethecombinationsofnoteswouldoccasionallysounddreadful.Composershavetousealotofskilltowritecounterpoint—andapiece

whichreliesontheinterplayofcounterpointasitsmaincontentisoftencalled afugue.Amaster of this technique, such as Bach, can organizeeightormoretunesplayingsimultaneously.Butthisistoocleverforusmeremortals—ourearsprobablycan’tdistinguishmorethanthreetunesatonce. Ifyouwant tohear someexcellentexamplesofcounterpoint, Irecommend theConcerto forTwoViolins (inDminor)byBach,and ifyouwanttohearagreatfugue,it’sbesttolistentooneplayedonasoloinstrument so you can hear the separate tunes (calledvoices) clearly.Bach’s“LittleFugueinGminor”playedonapianoisagoodexample.Itstarts with a melody played without accompaniment,but before itfinishes the samemelody startsupagain,playedon lowernotes, and itstarts up again a bit later, playedon even lower notes. There are other

tunes mixed in but they are short and simple by comparison. Onedistinctive feature ofmost fugues is that they involve tuneswhichhavean easily recognized beginning, so that each time themain tune jumpsintothemixyoucanhearitclearly.One or more of the basic techniques of harmony (drones, chords,

arpeggiosandcounterpoint)willhavebeenusedinnearlyalltheWesternmusic you have ever heard—fromBach’s concertos to the Sex Pistols.Except for the case of unaccompanied melodies,harmony is almost asimportantasthetuneinWesternmusic.Asweshallsee,theWesternfascinationwithharmonymeantthatwe

hadtodevelopapeculiarlyscientificwayofdividingtheoctaveupintotwelveequal-sizedsteps,fromwhichweuseateamofsevennotesatanyone time. The theoreticalwork began over 2,500 years ago and it onlytook us 2,000 years to get itright. The final result was theequaltemperament system, which forms the subject of the next chapter. Butbeforewegetintoequaltemperament,it’sinterestingtotakeaquicklookat musical systems which haven’t followed this harmony-dominatedroute.

SomedifferencesbetweenWesternandnon-Westernmusic

ThebigdifferencebetweenWesternandnon-WesternmusicisthatonlyWesternmusicuseschordsandharmonyalotininstrumentalmusic.Forthis reason we have developed instruments which can produce severalnotes at the same time, such as pianos andguitars. As well as thesepolyphonic (manynotesata time)instruments,wehavea largenumbero fmonophonic (one note at a time) instruments such as flutes andclarinets,butWesternmusictendstousethemingroupssothatwecanaccompanythemelodywithharmonies.Thissystemofharmonyisbuiltonnoteswhichhave a strong family link.The relationshipbetween thefrequencies of the notes is kept as simple as possible in order for the

harmoniestowork—whichmeansthatthechoiceofnotesislimited.Non-Westerntraditionalmusicinvolvesmelodieswhichareallowedto

roam much more freely in pitch. This means that the accompanyingharmonymustbemuchsimpler,toavoiduglyclashes.Imaginethatyouarepartofafive-aircraftacrobaticsteam.Youcan eitherchoosetohavealimitednumberofcarefullyorganizedmovesandallworktogether,oryoucangiveonepilotfreedomtodowhathewantswhiletherestofyoustay low as a background attraction. In either case the crowd will beimpressed.Western music has developed in the first of these two ways—the

accompanying notes can do a lot of zigzagging around the melodybecausethenumberofnotesinvolvedislimited,andallthemusiciansareusingthesamegroupofnotes.Non-Westernmusichasoptedforfreedomof melody—and if three or four musicianstry zigzagging around eachotherwiththisleveloffreedom,oneofthemisboundtozigwhentheyshouldbezagging,andtheresultwouldbeamess.Forthisreason,traditionalnon-Westernmusicplacesfarlessemphasis

onchordsandharmony.Indianclassicalmusic,forexample,tendstouseone,orperhapstwo,melodicinstrumentstogetherwithpercussionand/orratherstatic,drone-likeaccompaniments.GoodexamplesofthistypeofmusiccanbefoundonmostrecordingsfromtheIndiansubcontinentwiththe word “raga” or “rag”in the title. “Raga” means color or mood inSanskrit—and is the name given to an improvised piece of music.ProbablythemostfamousmusicianofthisgenreisthesitarplayerRaviShankar,andagreatexample is“RagaAnandiKalyan,”whichheplayswithhisdaughterAnoushka,whoisalsoaworld-famoussitarplayer.Instrumentalistsofthiscalibregetinvolvedinworldtoursand,through

meetingWesternmusicians, have been involved in lots of “EastmeetsWest”musicalcollaborations.Someofthesearegreat(e.g.,NusratFatehAliKhansinging“MusttMustt”onthealbumofthesamename),someare interesting and some are… profoundly lamentable. Thesecollaborations usually involvesome sort of compromise between the

musicalstylesandscalesystemsinvolved—butthemusiciansdon’tcare,andtheresultscanbeexcellent.Themainadvantageofnon-equaltemperamentsystemsisthattheycan

allow more room for emotional expression in the melody.Theinstrumentalists train for years to swoopup anddownaround thebasicsevennotesofthescaletheyareusing.Westernbluesandrockmusiciansalso spend a lot of time “bending” notes on their guitars and mouthorgans, but the big difference is that the final destination pitch of the“bend” is clear to the listeners and other bandmembers. The notewilleventuallyturn out to be one which fits in with the harmony of theaccompanying chords. For an Indian instrumental musician there aremanymoreoptionsavailableasthefinalpitch—whichiswhyitwouldbeso difficultto prepare an appropriate harmony.However, over the pastfifty years or so, much of the popular musical output from IndiaandJapanhasfollowedtheEuropeanpatternandusestheequaltemperament(ET)system—withlotsofchordsandharmony.

8.WeighingUpScales

Duringyourschoolhistory lessonsyoumayhave learnedaboutarmiesofruggedmenusingscalingladderstogetintocastles.Similarly,inyourFrenchlessons,youprobablylearnedthattheFrenchwordfor“stairs”is“escalier.” Bothscaling ladders andescaliershave steps in themwhichhelp you rise from a lower position to a higher one—and both wordsderivefromtheancientLatinwordscala,meaningstepsorladder.Scalais also the basis of the wordscale in a musical context: a scale is asequence of notes arranged as a series of upward (or downward) stepswhich take us fromone note to another. Generally a scale covers anoctave. So we start at a note of one frequency and go up to a note ofdoublethatfrequency.Therearelotsofwaysofclimbingfromonenotetothenoteanoctave

above—and so there are lots of different types of scales.The mostcommononeweuse inWesternmusic is themajor scale and Iwill beexplainingwhatthatisinthenextchapter.OnethingIwanttomakeclearat themoment, though, is thelinkbetweentheterms“scale”and“key.”Let’s take C major as an example. The scale of C major involves aspecificgroupofsevendifferentnotes,buttheyareonlycalledascaleifyouplaythemoneafteranotherasarisingorfallingsequence.Ifyouusethesamegroupofnotestoproduceapieceofmusic,themelodywillbejumpingfromnotetonoteinallsortsofdifferentpatternsandsequencesand,aswearenolongermerelyplayingascale,wesaythatthemusicisinthekeyofCmajor.The system of intervals, ormusical steps,which produces amusical

scale is not set in stone and is different in differentpartsof theworld.Traditional Indian or Japanese music does not use exactly the sameintervalsasEuropeanmusic—which iswhy itsoundsexotic toWesternears.However,justaboutallscalesystemsfollowtwobasicrules:

1. Scales are based on a series of intervals, which are divisions of anaturallyoccurringintervalcalledtheoctave.

Wehavealreadyseenhowtwonotesanoctaveapartsoundgoodtogether.Thecloserelationshipbetweensuchnotesmeansthat,insomecases,youcan accidentally produce a note anoctave above theoneyouwant.Forexample,ifyoublowalittletoohardintoapennywhistleorarecorder,the note you normally get is replaced by another, higher notewhich isexactlyanoctaveabovetheusualone(youcanalsodothiswiththenoteyougetwhenyoublowacrosstheneckofabottle).Ifyoutwangaguitarstringandthentouchitgentlyhalfwayalongitslength(abovethetwelfthfret),thenotewillchangeintotheoneanoctaveabove.Jumpsinpitchofan octave occur naturally in birdsong and even in the sound of somesqueakingdoors,becausetheoctaveislinkedtothephysicsofhownotesareproduced,asweshallseelater.This sweet-sounding, easy-to-produce interval is the basis of all

musical scale systems. The octave is, however, a very bigmusicalinterval.*Therangeofanuntrainedsingingvoiceisusuallyonlyacoupleofoctavesorso.Itisthereforenosurprisethatallmusicalsystemshavefoundtheneedtodividetheoctaveupintosmallerintervalsinorderthatwecanhaveavarietyofnotestosing.

2.Musiciansdon’tgenerallyusemorethanaboutsevendifferentnotesatatime—eveniftheoctavehasbeendividedupintomorestepsthanthis.

We shall see that, although European (or Western) music divides theoctaveupintotwelveequalintervals,itgenerallyonlyuseschosenteamsofaboutsevendifferentnotesatatime.Thesegroupsofsevennotesarethemajorandminorkeys,theonesusedinnearlyeverypieceofWesternmusic you have ever heard. Each team of seven has its own name: forexample, thenotesC,D,E,F,G,AandBmakeupthekeyofCmajor;andthenotesF,G,A,Bflat,C,DandEmakeupthekeyofFmajor.

Thefactthatweonlychoosetousesevendifferentnotesatatimefitsin well with research carried out in the 1950s bythe Americanpsychologist GeorgeA.Miller, who studied the capacity of our short-term memories. After testing people on theirability to remembersequencesofnumbers, lettersand tones,hecame to theconclusion thatthe limit of our short-termmemoryis about seven items.This limit ofapproximately seven is also common in other musical cultures. Indianmusicians, for example,divide theoctaveup into twenty-twosteps,buttheyalsochooseagroupofsevennotestobethebasisofanyparticularpiece. (Indianmusicians also have access to groups of secondary notesassociated with their basic group of seven—as we shallsee, Westernmusicdoesn’tusesecondarynotesbecausetheywouldinterferewiththeharmoniesweuse.)InWesternmusicthecomposerorsongwriterisnotforcedtostickto

hisoriginalchosengroupofsevennotesthroughoutapieceofmusic;itiscommontomovefromonekeytoanotherasthepieceprogresses,toaddinterest to themusic.As thereareonlytwelvedifferentnotes tochoosefromoverall,andeachkeycontainssevenmembers,itisobviousthat,ifwe movefrom one team to another, some of the noteswill be in bothkeys. In fact, the most common key changes (ormodulations) involvemovingtoakeywhichhasonlyonenotedifferentfromthekeyyouarein.Manyofyouwillknowthat theword“octave”comesfromtheLatin

wordfor“eight”andyouwillhaveheardthatthereareeightnotesinanoctave. So you might be wondering why I keep referring to sevendifferentnotes.Well, if youplayor singa fulloctavescaleyoudouseeightnotes,butthetopandbottomonesareanoctaveapartand,asIsaidin the last chapter,notesanoctaveapartaremusicallyverysimilarandevenhavethesamename.Soinanoctavewehaveeightnotes,butonlysevendifferentones.Forexample,anoctavescaleofCmajorisC,D,E,F,G,A,B,C.Thethreemainthingstorememberaboutscalesare:

•weneedscalestoenableustomemorizetunes;• scales divide an octave up into smaller intervals—and give us aselectionofnotes;

• too fewnotes inplayatanyone timewouldbeboring,and toomanywouldbeconfusing.

The way we name the notes and the method by which we choose themembers of each team of seven will be discussed in the nextchapter.First,Iwanttoexplainhowwemanagedtodivideuptheoctaveintothetwelvedifferentnotesfromwhichwepickthoseteams.As you can imagine, the ancient societies didn’t get out of bed one

morningandarbitrarilydecidetodividetheoctaveupintotwelvesteps.Musicwas developed bymusicianswho didn’t know about frequenciesandsuchthings;theyjustknewwhatsoundedgood.Intheearlydaysofmusic, more than 2,000 years ago, things were simpler than they aretoday.Theydidn’tusetwelvedifferentnotesinanoctave,orevenseven.Theyusedfive.

Themotherofallscales—thepentatonicscaleAlthoughmostmusical systems around theworld nowuse about sevennotesatatime,nearlyallofthemusicalscalesystemsthathumanshaveeverused—fromwellbeforetheancientGreekstothepresentday—havebeenbasedonascalewhichusesonlyfivedifferentnotesintheoctave:thepentatonic scale (“penta”means“five”and“tonic”means“note” inGreek).A lotof Japanese,ChineseandCelticmusicstilluses thispentatonic

system—and it is also loved by blues and rock guitarists.Typicalexamples of the five-note system are the songs “Amazing Grace” and“AuldLangSyne.”(If,likemostfolks,youneedareminderofthelyricsof“AuldLangSyne,”theyare“Shouldauldacquaintancebeforgot…lalahlalalalah…lah,happynewyear!…hic!…giveusakiss…lalahla

la lah.”)Youwillalsofindaveryclearexampleofasimplepentatonicrisingscaleintheguitarlineatthebeginningofthe1960shitsingle“MyGirl”bytheTemptations.The notes in a pentatonic scale have a very simple mathematical

relationship to each other and this makes them form an excellentself-sufficient group—whether they are played in a sequence to produce amelody,orincombinationstoprovideaharmony.Next time you are near a piano, try using one finger to pick out a

melodyusingonlytheblackkeys—thisisthesoundofapentatonicscaleorkey.Allthemelodiesyouplayusingthesefivenotestotheoctavewillsound pleasant. Now try playingany two black notes at once—most ofthecombinationssoundharmonious.Onlywhenyouplaytwoblacknoteswhich are next toeach other does the harmony sound clashing andunsettled.InthemostcommonlyusedkeysinWesternmusic—thetwelvemajor

keys—wehavesevendifferentnotesinanoctave.Someofthenotesareonly a semitone apart and, as we know, this is themost inharmoniouscombination for notes played together.Also, as we shall see later, thearrangement of the seven notes in a major key is responsible for thestrong sense of punctuationwe feel at the end ofmusical phrases. Thereasonwhy the standard pentatonic scale is so incessantly pleasant forharmoniesisthatitcontainsnosemitones:the“crowdedtogetherness”ofsomeofthenotesisavoidedbyreducingthenumberofdifferentnotesinthe octavefrom seven to five.Also, if you have only five notes in anoctave thepunctuationofmusicalphrases isa littlevague.So,with thecorrect five notes to an octave you have a very supportive, mutuallycollaborative team with relaxed punctuation—andit’s very difficult tomakeajarringorunpleasantnoise.To get a pentatonic scale on our piano we have chosen a particular

groupoffivenotesfromanoctavewhichhasbeendividedupintotwelveequal steps. But ancient civilizations didn’t know about our modernsystemofdividingtheoctaveupintotwelvesemitonesandthenchoosing

which group of notes to use, so how did they manage to choose fivecorrectlyspaced-outnotesfortheirharpsandflutes?Togetadecentsoundingscalewewanttohaveateamofnoteswhich

have frequencieswhich are related to each other.Thesimplest stringedinstrument is a harp, and harps have been used by a large number ofancient civilizations. Let’s considera harp with a range of just oneoctave.The top string needs to have a fundamental frequencywhich istwice that of the loweststring—because it’s an octave higher—andeverythingisbasedaroundthisnaturallyoccurring,pleasantinterval.Foroptimumteamwork, the strings between these two should also havefrequencieswhich are related to the frequency of the lowest string:forexample,oneandahalf timestheloweststringfrequency,oroneandaquarter—anythingwhichinvolvessimplefractions.It’s important to realize that ancient civilizations all over the world

independently developed a system of tuning their instruments to thepentatonic scale. This tuning system had to be based on a naturallyoccurringphenomenon;otherwise itwouldnothavebeendiscoveredbylotsofcivilizations.Thephysicalphenomenoninquestioninvolvesthevibrationofstrings.

Obviously,youonlyhaveto twangastring tomakeitgiveoff itsusualnote—butitisalsoquiteeasytopersuadeastringtoproduceacoupleofothernoteswhicharecloselyrelatedtothefirstone.Thisallowsustosetupachainofeventswhichsoundsliketheplotofadetectivestory.Weget thefirstnotetotelluswhotheirbestfriendis,andthenwegetthatnotetotelluswhotheirbestfriendis—andsoonuntileventuallyweendup with a group of notes which all get on well with each other: thepentatonicscale.Onceyouhavemanagedto tuneaharp toapentatonicscale,youcancopythatpatternofintervalsforinstrumentswhichdon’thavestrings,suchasflutes.This ability to tune a harp to the pentatonic scale is the musical

equivalentoftheinventionofthewheel.Itisthecornerstoneofmusicaldevelopment,solet’sseehowit’sdone…

Let’simagineIamatraineeharpistinancientEgypt,tryingtotuneasix-stringharptoapentatonicscale.Someonehasdescribedtomehowtodoit,but thisismyfirstattempt.AtthispointIhaveonlytwoskills:Ican change the note producedby any string by putting more or lesstensiononit,andIcantellwhentwonotessoundthesame.“Hangonaminute,”Icanhearyousay,“whyareweusingsixstrings

for a five-note scale?” Good point. The answer’s quitesimple, as Imentioned earlier: anoctave scalebegins and endswith the samenote.So,forafulloctavescalewithfivedifferentnotesweneedsixstrings.Sohereweare in ancientEgypt,withnoaccess to tuning forks; this

means that the tuning system I use must be self-contained.The onlyequipment I can use to tune the harp is the harp itself. It sounds a bitdaunting,butactuallyit’squitestraightforward.Thestringsofmyharpareofdifferentlengths—thelongeronesarefor

thelowernotes,andIwillnumberthemfrom1to6withnumber1asthelongest string. I startwithall the strings slack, andbeginby tighteningstring1 (the longest one)until it is just tightenough toproduceanice,clearnote.Idon’tneedtoworryaboutthefrequencyofthisnotebecausethatmeeting in Londonwon’t decide on a standard pitch for notes foraboutanother4,000years.Anyniceclearnotewilldo.NowIneedtousethisstringtohelpmetunetheotherstringscorrectly

—buthowdoIgetthisstringtoproducedifferentnotesfromtheoneitusuallymakes?Iuseonehandtopluckthelongerstringwhilegentlytouchingitwitha

singlefingertipfrommyotherhand—andIgraduallymovemyfingertipdown the length of the string asI continue plucking. Generally, myfingertip stops the string frommaking its clear note and all I get is a“thunk”noise—butwhenmyfingertipisincertainpositionsIgetaclearnote.The loudest, clearest note is produced when my fingertip is exactly

halfwaydown the string—and thenoteproduced isanoctaveabove thenormal note given off by this string. So all I have to do ismatch this

“octave above”notewith thenormal notegivenoffbystringnumber6andlater,whenItwangthetwostringsnormally,theywillbeanoctaveapart.Fine,wehave the top andbottomnotes of our octave organized, but

how dowe get nice, related notes for the four stringsin between thesetwoextremes?Theanswer lies in thefact that, if Igobacktomyplucking/touching

routine,IwillfindthatthereareotherplacesonthestringwhereIgetaclearnoteratherthana“thunk.”AsIsaid,Igettheclearestnotewhenmyfingertip is restingon the string at the halfway position, but I also getclear,ringingnotesifmyfingerisexactlyonethirdoronequarterofthelengthofthestringfromtheend.It’sashamefulindictmentoftheshabbywaywelivenowadays,butwe

havetofacethefactthatmostofyouwon’thaveanancientEgyptiansix-stringharplyingaround.Ontheotherhand,youmighthaveaccesstoaguitar or any other stringedinstrument—and you can try to find theseclearnotes foryourself.Guitarsare easiest for this experimentbecausethe positions which are one quarter, one third and one half the lengthfromoneendofthestringareexactlyabovecertainfrets(infact,that’swhythefretsareinthosepositions).Ifyoutwangthestringwithafingerresting gently on it above the twelfth fret, then you have divided thestring inhalf—andyouget the“octaveabove”note.Ifyoudothesamething above the fifth fret, youhavedivided the string intoquarters andyouwillget thenotetwooctavesabovetheoriginalstring.Ifyoupluckthestringwhile touching itabove theseventh fret,as Iamdoingin theillustration below, you have divided it into thirds—and you get acompletelynewnote.Thisistheonlynewnotewehaveproducedbecauseat the “half” and “one quarter” positionsweweremerely getting noteswhich are one or twooctaves above our first note—which can beconsideredtobejusthigherversionsofouroriginalnote.

If I pluck a stringwithmy right thumbwhile touching it gentlywith afingerofmyotherhand,Iwillgenerallygeta“thunk”ratherthanaclearnote.Butwhenmyfingeris insomepositionsonthestring(asabove)Iwillgetaclearnote.

The phrase “Twanging the string with one hand while touching itgently with one finger of the other hand” can only be describedascumbersomeand,asthenoteproducedsoundslikea“ping”ratherthana“twang,” wewill call this method of producing a note “pinging” fromnowon.*So—“pinging”canveryeasilyproducethreenotesfromastring:

1.oneanoctaveabovetheusualstringnote2.onetwooctavesabove3.anewnote

Youcangetothernotesbypingingwithabitmoreskillandeffort,butwedon’tneedtoworryaboutthem—wewillonlybeusingthesethree.Thisabilitytoproduceoctavesandonenewnoteforeverystringisall

weneedtotuneoursix-stringharp.Sofarwehavetunedstring6tomatchthe“octaveabove”pingednote

ofstring1.

Thenweusethepinged“new”notefromstring1togiveusthenoteforstring4.Oncestring4hasbeentuned,wecanuseitsownpinged“new”noteto

tunestringnumber2.String2’spinged“new”notegivesusthenoteforstringnumber5.And,finally,string5’spinged“new”notegivesusthecorrectnotefor

string3.TokeeptheabovedescriptionshortandsweetIhaveignoredthefact

thatthepinged“new”noteswillbeeitheroneortwooctaveshigherthanthenotewewantforthenextstring.Butthisaddsonlyaminordifficultyto the tuningprocess. Ifyouwould like toknowexactlyhowtodo it, Ihave written out the full instructions in part C of the Fiddly Detailssectionattheendofthebook.Excellent:wehavemanagedtotuneourharpusingonlytheharpitself

—which is theonlyway it couldhaveworked in theolddays.Butwhystopatonlyfivedifferentnotes;whynotpressonandaddanother?Well, there isa reason. Ifyourepeat thepingingprocessanduse the

newnoteprovidedbystring3,yougetanotewhichisonlya semitonebelow string 6—and this produces a teammember which clashes withstrings 6 and 1.Nowadayswe enjoy anoccasional bit of harshness andclashinginourmusic,buttheancientsocietiesweren’tkeenonit,sotheystopped at fivedifferentnotes to thescale. (By theway, thispentatonicscale, with no semitones in it, goes by the catchy little nameof the“anhemitonic pentatonic scale”—and your task for this evening iscasuallytoincludethisphraseinaconversation.)Sowhatissogoodabouttheoriginalpentatonicscale?Whatdoesall

thispinging,twangingandoctavinggiveus?Well,whenyou’vedoneallthemathitworksoutlikethis:

•stringnumberonehaswhateverfrequencyyoufirstchose•stringnumbertwohasthefrequencyofstringonemultipliedby1•stringnumberthreehasthefrequencyofstringonemultipliedby1¼

•stringnumberfourhasthefrequencyofstringonemultipliedby1½•stringnumberfivehasthefrequencyofstringonemultipliedby1•stringnumbersixhasthefrequencyofstringonemultipliedby2.

(Stringsthreeandfivearenotexactly1¼and1buttheyareveryclose—onlyabout1percentoffineachcase.)Simplerelationshipsmakenotessoundgoodtogetherand,asyoucan

see from this list,we have a very strong group of simple relationshipsbetween these notes, which is why everyoneagrees that they soundpleasant.Thispentatonicgrouphasbeendiscoveredandadoptedatsomepointbyjustabouteveryhumansociety.AlthoughthetuningmethodwasprobablydevelopedalongthelinesI

have suggested above, it would not have been necessaryfor everymusician to go through all this palaver each time they tuned theirinstrument. Musicians develop pretty accuratejudgment of the size ofintervalsandwouldbeabletorememberthisscale.Atafairlyearlystageof training a harpistwould be able simply to tighten the lowest stringuntil it gave a nice clear note and then tighten the others until theysoundedright—possiblybyrememberingasongortwowiththecorrectintervalsinthem.Somesocietiesstayedwiththepurityofthisoriginalpentatonicscale,

someuseditalongwithalternatives,andinEuropeweeventuallyendedup with a system in which there are twelve different notes to choosefrom,butweonlyuseaboutsevenatatime.Inthenextchapterwewillconcentrateonchoosingourvariousteamsofseven.For therestof thischapterwewillbe lookingatwhy it tookusseveralcenturies todecidehow to divide the octave into twelve equal steps. The systemweeventuallydevelopedtodothisiscalledequaltemperament.

TheEuropean/Westernscalesystem:equaltemperament

Whydoweuseequaltemperament?

TheWesternscalesystemistheoneweusefornearlyalljazz,pop,rockand classical music. Its present-day version iscalled “equaltemperament,”orET,andwasdeveloped inEurope in the latterhalfofthe eighteenth century. By about 1850all the European professionalmusicianswere using theET system andwe are still using it today. Infact,it’ssuchausefulsystemthatwewillprobablykeeponusingituntilwe are wiped out by invading Martians (and even the Martians willprobably carry onusing it for their “light jazz and popular classics”coffeemornings).Yet, for all its popularity, the ET system is a compromise.And we

needacompromisefortheusualreason—becausewecan’thaveexactlywhatwewant.Whatwewantisamethodofdividingupanoctaveintotwelvesteps

whichalsoallowsthefrequenciesofallthenotestoberelatedtoalltheothernotesbysimplefractionssuchas1¼and1½.Thiswouldbegreat—because all those simple relationshipswould give us lots of goodharmonies.Thisistheideabehindthe“just”scalesystem—butthe“just”systemdoesn’tworkformanyinstruments,asweshallsee.

The“just”scalesystem

The “just” scale system dates backmore than 2,000 years and is builtupontheideathatsimplefrequencyrelationshipssuchas1½and1givethebestharmoniesandthattheoctaveshouldbedividedupinthisway.Unfortunately thearithmeticsaysthat thiscannotworkifyouaregoingto keep the frequencies of your notes fixed at set values, such as the110Hzwehavebeendiscussing.Tousethe“just”systemthemusiciansmustbeable to shift thenote frequenciesupanddownabitduringthepieceiftheywanttokeepallthechordrelationshipssimple.Let’s take an example of four people singing in harmony. Fred is

singingthebassline,andinthissongallhehastodoissingthenotesA,

B,C,A,B,Coverandover,whilehisfriendssinglotsofothernotes.Ifyou listen to the piece,youwould think that Fred is repeating himselfexactly—butifhedidthissomeof theharmonieswouldsoundhorriblyoutoftune.Usingthe“just”system,Fredwillhavetochangethepitchesofsomeofhisnotesoccasionallytomaketheharmoniesworkperfectly.His usual “B”couldwork finemost of the time, but hemight need toraiseitspitchatinybitforcertaincombinationsofnotes(let’scall thisslightlyhighernote“B*”)—sohewillbesinging

A,B,C,A,B,C,A,B*,C,A,B,C.

The reason for this is that even within the apparently “perfect”relationshipsofthe“just”pentatonicscaletherearecock-upsifyoulookintotherelationshipsbetweenallthestrings.Forexample,stringnumber4vibratesat1½timesthefrequencyofstringnumber1,soifthesystemis fair, strings 5 and 2 should share the same jolly relationship.Unfortunatelytheydon’t.Ifyoudothecalculation,youfindthatstring5vibratesslightlylessthan1½timesthefrequencyofstring2.Thismeansthatstrings1and4soundgreattogether,butstrings2and5soundoutoftune—soyouwouldhavetochangethefrequencyofoneofthenotestogetyourperfect“1½times”relationshipinthiscase.Thingsgetevenworseifyouextendthesimplefractionideatotwelve

notesinanoctave.Ifyoudothis,youfindthatthefrequenciesofsomeofthenotesneedtobechangedslightlyifyoumovefromonesetofsevennotestoanother,aswedowhenwechangekey.The “just” system can only be used to good effect by instruments

whichdon’thavefixednotes—likeviolins,violas,cellos,trombonesand,mostimportant,thehumanvoice.Ontheseinstrumentsitispossibleforgoodplayerstoadjusttheirnotesduringthecourseofapiecesothatthecombinations of notes always have lovely, simple relationships.However,youcanonlyusethissystemifalltheinstrumentsinvolvedarecapableofnoteadjustment.Theminuteyouintroduceaninstrumentwith

fixednotefrequencies,suchasapiano,guitar,flute,oralmostanyotherinstrument,the“just”systemhastobeabandoned.Thisisbecause,ifhalfthemusiciansadjustand theotherscan’t, the twogroupswillbeoutoftunewitheachother.The final outcome of all this is that choirs and string quartets (two

violins, viola and cello) tend to use the “just” systemto get the bestharmonies whenever they are not accompanied by “fixed note”instruments.The“fixednote”instrumentsneedadifferentscalesystem,onewhich compromises on the purity of the harmonies but allows thenotestostayfixed.Thatcompromiseistheequaltemperamentsystem—andittookuscenturiestodevelop.

Thedevelopmentoftheequaltemperamentsystem

INTUNEOROUTOFTUNE?

Weknowthatpeoplewereplayingharpsaslongagoas2500B.C.becausewehavepicturesofthemdoingsoondecoratedvasesfromthatperiod.Itis more than likely that the practice ofmusic goes back thousands ofyearsbeforethis.When people moved on from singing to the production of musical

instruments like the flute (made ofwood or bamboo), theywouldhavecomeacrosstheproblemofwheretoputthefingerholes.Thepositionoftheholesdeterminesthepitchofthenotestheinstrumentproduces,anditisveryeasytoproduceaflutewhichhasseveralnoteswhicharenot intunewitheachother.I’mnottalkingabout“outoftunetomodernears”here,I’mtalkingabout“someonethrowarockatthatidiotandchuckhisfluteon thefire”outof tune—thesortof“outof tune”everyonewouldagreeon.This sort of “out of tune” describes the situationwhere some of the

notes on a single instrument don’t agreewith each other. If you took apennywhistle and drilled another finger hole at some random positionyouwouldsoonhearthatyournewnotewasnotintunewiththeothers.

OnholidayinSpainrecently,Icameacrossoneofthosestreetmarketswhich sells earrings to young women, painted platesto middle-agedcouplesandchickensmadeofbentcoat-hangerwire toall thosepeoplewho think that life isahollowshamunlessyouownachickenmadeofwire. Narrowly escaping a vendor of basketwork teaspoons, I foundmyselfinfrontofastallsellingbamboopennywhistles.WhenInoticedthat someone had simply drilled a row of equally spaced holes alongthem, I knew thateverywhistlewould be out of tunewith itself—youcannotproduceamusicalinstrumentthatway.Raisingoneofthemtomylips,Iplayedthemostunrelated,mournfulcollectionofnotesithaseverbeen my displeasure to hear. Even the local dogseyedme with thinlydisguisedcontempt.So,ofcourse,Ihadtobuyit—andIpresentithereforyourdelectation.

A pennywhistlewhich is out of tunewith itself. Someonewith no ideaabouthowascaleworkshassimplydrilledarowofequalsized,equallyspacedholesalongthebodyofthisinstrumentinthehopethatthiswouldcreate a musical scale. Itproduces a sequence of notes which have norelationship to eachother—so if you try to playa tuneon it the jumpsbetweenthenotesarethewrongsizeandtheeffectissomewherebetweenfunnyandpainful.(Ifanytaxinspectorsarereadingthis, Iwouldliketomake it clear that I intend to claim the three euros I paid for thisinstrumentasatax-deductibleexpense,tooffsetagainstmyroyalties.)

Anyonecantellwhenaninstrumentisoutoftunewithitself:eachoftheindividualnotesmightsoundpleasantbut,playedinsequence,theydon’tformacoherent family. Ifyourharporguitar isoutof tunewith itselfthen you just have to stretchor relax someof the stringsuntil theyareback in tune. Strings are always going out of tune because the air

temperatureor humidity has changed,which iswhy guitars and violinshavetuningpegs(calledmachineheadsonguitars)attheendoftheneck.The situation is different if you are making a wooden flute. You canchange the notes a little bymaking the holes larger, but if you put theholes inthewrongplacetostartwithyouwillprobablynevermanagetogetitintunewithitself,letaloneotherinstruments.Thediscoverythatcertaincollectionsofnotessoundedgoodandothers

didn’t inspired the great thinkers of the ancientworld to look for somesort of rule fromwhich you could, for example, always put your fluteholesinthecorrectposition.Thusbeganthesearchfortheperfectscalesystem.

PYTHAGORASGETSITWRONG

Althoughtheremusthavebeenlotsofbrainytypeswhotriedbeforehim,our earliest records of an attempt at a scale systemwhich divides theoctaveupintotwelvestepsgobacktoPythagoras,wholivedinGreeceinthe sixth centuryB.C. Pythagoras, as you no doubt know, was amathematicianwithanunhealthyinterestintriangles,whospentalotofhis lifetrying todevelop theperfect shape forToblerone.Althoughhistriangleresearchwaswildlysuccessful,hisattemptatatwelvenotescalesystemwas,unfortunately…er…totalrubbish.TheideathatPythagorasdevelopedworkswellforpentatonictuning,butitcan’tbeextendedtoatwelvenotesystem.BeforewegooverwhatPythagorasdid,let’smakealistofwhathe(andanyotherscaledesigner)wastryingtoachieve:

1.Wewanttodividetheoctaveupintosmallerintervals(nottoomany,nottoofew).2.Wewantasystemwhichgivesusnoteswhichsoundgoodwhentheyareplayedtogetheraschords(and,ofcourse,whentheyareplayed inasequencetomakeamelody).3.Wewantasystemwhichallowsustostartourtuneonanynote.Ifwechangeourstartnote, themelodywillnotchange—thewhole thingwill

justbehigherorlowerinpitch.

Doesn’t sound too much to ask, does it? Surely our besandaled heroshould be able to come up with a system during his lunch-timestrolldowntothebeach?ThemusiciansofPythagoras’dayknewhowtotunetheirinstruments

—theyusedthickerorlongerstringsforthelowernotesandadjustedthetensionuntil theyhadthecorrectscale,but theydidn’tknowwhythosenotes worked well together. Theydidn’t have a theory for their tuningmethod,becauseyoudon’tneedatheorytomakegoodmusic.WeneedtobearinmindthatPythagoraswasnotamusician;hewasa

scientist—and he wanted to analyze what the musicianswere actuallydoingwith their pentatonic tuning and investigatewaysofgetting evenmorenotesintoanoctave.After carefully looking at how themusicians around him tuned their

harps to a pentatonic scale, Pythagoras worked out that,if they usedstringsmadeofthesamematerialunderthesameamountoftension,thenan“octavehigher”string(stringnumber6)wouldhavetobehalfaslongasthelowestnotestring(string1).Hethenworkedoutthatthefrequencyof the note producedwas directly related to the length of the stringinvolved—if you halved the length of the string you doubled thefrequencyofthenote.Following this line of thought, he gave the “pinging” method some

closeattentionanddiscoveredthat,withidenticalstrings,stringnumber4wouldbetwothirdsaslongasstringnumber1.“Excellent,”hethought,“I’llhavethisscalethingfinishedbeforetheycalllastordersdownatthetaverna.” Going back to his theory about the relationship betweenfrequency and stringlength, he worked out that a “two thirds” stringwouldgiveyouanoteofoneandahalf times thefrequencyof thefullstringnote.Oncehe realized that“pinging”givesyoua stringwhich istwothirdsaslongasthestringyoustartedwith,hemanagedtotunehissix-stringharpusingatheoryratherthanjusthisears—bingo!

Ifonlythenextbithadgonewellhewouldnowbethepatronsaintofmusicians or something, rather than “that bloke with the triangles.”Pythagorashadagreatdealoffaithinsimplenumberratiosandhelikedtheideathatjustbyusingtheratios(fornewnotes)and½(foroctaves)hecouldcontinuetoproducenewnotestofillupanoctavewithsmallersteps. In the end, he estimated that he could divide up an octave intotwelvestepsinthisway.Hedidsomeroughcalculationsanditalllookedprettygood,butwhenhetookacloserlookatthenumbershefoundthatthis plan doesn’t quite work. If you use this system to divide up youroctave, you end up with quitea lot of notes which do not sound goodtogether.Also,youcannotstartyoursongfromanynoteinthescaleandget the sameresult.Bothof theseproblemsare causedbecause—asweclimbfromthelownotesuptothehighnotes—someofthe“stepsintheladder” are different sizes. Pythagoras was so peeved that his cunningplandidn’tworkoutthathetookrevengeontheworldbyinventingmathexams.

THE“MEANTONE”SYSTEM

Peoplewerestillhungryforascalesystemwhichgavethemmorenotesthan the old pentatonic one, and by now they knew thatdividing theoctaveup into twelve stepswasagood idea.Over thenext2,000yearsmusiciansandtheoristsfiddledaboutwiththeunsuccessfulPythagoreansystemuntil,bythelate1500s,theyfoundanadjustmenttoitwhichjustabout workedfor most of the combinations of notes on a harp orkeyboard. This adjusted systemwas called the “meantone system” andinvolvedusing “two thirds and a bit” as its basis rather than the “twothirds”whichPythagorashadsethishearton.By1600themeantonesystemwasingeneraluseforthekeyboardsof

the day (harpsichords, organs, etc.—pianos were not inventeduntil theearly1700s).Thesystemworkedwellformostcombinationsofnotesbutnot all—one or two combinations soundeddreadful and were simplyavoidedbyallmusicians.For example, in themusical textbooks of the

timeitwasforbiddentoplaythenotesAflatandEflattogetherbecauseof thehorrible racket theymade.So thehunt for a theorywhichwouldgiveusatuningsystemwhichworkedforallnotescontinued.

SUCCESSATLAST

BoththePythagoreanandthe“just”systemswereattemptstousesimpleratios togetanacceptablenumberofnotes inascaleand tohave thosenotessoundgoodtogether(becausesimpleratiosmakegoodharmonies).Whatbothofthesesystemshadincommonwasthefactthat,ifyoukeptthemathassimpleaspossible,youwouldendupwithtwelvestepstoanoctave, butunfortunatelyfor thesesystems thestepswerenotallof thesame size. The two systems also agreed that, once you had assembledyour family of twelve notes, some of them were much more closelyrelated (and thereforemore important) than others.We continue to usethesetwoprinciplestoday:wehavetwelvenotestotheEToctavebutweonlyusesevenorsoofthemostimportantfamilymembersatatime.Throughout the late 1500s and early 1600s mathematicians tried to

solvetheproblemofproducingascalewhichworkedproperlyforallthecombinations of twelve notes. In the end they cracked it and were, ofcourse, ignored for about ahundredyears.Even thoughGalileo’s father(VincenzoGalilei)gotthecorrectanswerin1581,theequaltemperamentsystem didn’t come intocommonuseuntil the late1700s.TheChinesescholarChuTsai-YubeatGalileitoitbyoneyear,butwhenhepresentedhisresult to theChinesemusical fraternityhegot thesameresponseashisItaliancounterpart—“getbacktothetrianglesandleavemusictothemusicians.” The British can be particularly proud of the piano firmBroadwood,whorefusedtochangetothenew,bettersystemuntil1846—hurrah!GalileiandChuTsai-Yufoundthatcalculatingtheequal temperament

system is pretty easy once you have presented the problem in a clear,logicalway.Allyouneedarethreefocusedrules:

1.Anoteanoctaveaboveanothermusthavetwicethefrequencyofthelower one. (This is the same as saying that if you usetwo identicalstrings,onemustbehalfthelengthoftheother.)2.Theoctavemustbedividedupintotwelvesteps.3.Allthetwelvestepsmustbeequal.(Ifyoutakeanytwonotesonestepapart,thenthefrequencyratiobetweenthemmustalwaysbethesame.)

Butyoucan’tjustshortenthestringsbyacertainlengtheachtimetogetthe required result.You couldn’t, for example, take a long string of 24inchesand take1 inchoff the lengthof eachof thenext twelve stringsuntilyoureachthe“octaveabove”stringlengthof12inches.Youcan’tdo this because itwould be unfair to take the same amount off a shortstringasalongstring.Thatwouldbelikeasystemwhereeveryonepays$20,000taxnomatterwhattheyareearning.Asthedifferencebetweenthelengthsofthestringsmustnotbeaset

amount (like 1 inch), what you have to do is make thelength of eachstringacertainpercentageof the lengthof its longerneighbor. ImaginethatIamacarpenter.Ihaveanassistantwhoispaidlessthanmeandasupervisorwhoispaidmore—aperfectlynormalsituation.Let’ssaythatmysupervisorgets$100aday,Iget10percentlessthanthat($90aday)andmyassistantgets10percentlessthanme($81aday).Noticethatthedifference betweenmypay andmy supervisor’s is $10 per day but thedifferencebetweenmyassistantandmyselfis$9aday—eventhoughweused“10percent”forbothcalculations.Thereasonforthedifferenceisthatwetookaway10percentofthesupervisor’spaythefirsttimeandwetookaway10percentofmypaythesecondtime(mypayissmallerthanmysupervisor’s—sothe“10percent”issmallertoo).Thisishowweusethepercentagesystemtodecideonthelengthsof

thestrings;wesubtractacertainpercentageofthelengthofanystringtoget the lengthof its shorter neighbor.Ourmathematical friendsGalileiand Chu Tsai-Yu managed to calculate the exact percentage by whicheachofthestringsshouldbeshortenedtogetagradualreductioninstring

lengthwhichmadethe thirteenthstringhalf the lengthof thefirst.ThiscalculationisdescribedinpartDoftheFiddlyDetailssection,whereyouwill find that the actual percentage involved is that charming, easy-to-remember figure, 5.61256 percent.Thankfully, youwill notbe requiredto remember this number. If you wish to show off your extensivemusicologicalknowledgeataparty,justrememberthe5.6bitandmakeupalltheothernumbers—thetrickistostarethemintheeyeandsoundconfident.Themathematiciansproducedascale(theETscale)withexactlyfair,

equal steps, which allows us to start our music on anynote, and alsohappens toallowusa lotofgoodsoundingcombinationswhenweplaynotestogether.Theintervalbetweenanytwoadjacentnotesonthisscaleiscalledasemitoneandtherearetwelvesemitonestepstotheoctave.ThereisonedisadvantagetotheETsystembut,thankfully,itdoesn’t

interferewithourenjoymentofmusic.UsingtheETsystemwenolongerhave the exact simple fraction relationships between the notes whichwouldgiveus thebestharmoniesofall.Theonlyintervalwhichhasanexact,simplerelationshipintheETsystemistheoctave.Ifyoustartonaparticularnote and go up twelve semitones, the note you getwill havedouble the frequency of the note you started with. The next strongestrelationshipshouldbethatbetweenouroriginalnoteandthenotewhichshouldhave1½timesitsfrequency.IntheETsystemthishashadtobeadjustedbya tinyamount.All theothersimple relationshipshavebeenslightly increased or decreased.But as I said, it doesn’t matter muchbecausemostofusdon’tnoticethesedifferences,primarilybecausewehavebeenbroughtupontheETsystem.However, twelve semitones to the octave gives us rather too many

notes forourmemories tocopewith ifweuseallof themall the time.Forthisreasonweinventedthemajorandminorscales,whichonlyuseabout sevenof theavailable twelvenotesatone time.This reduction inthenumberofnotes involvedmakesmusiceasier toremember,andhassomeotheradvantageswhichIwilldescribeinthenextchapter.

9.TheSelf-ConfidentMajorandtheEmotionalMinor

MoodandmusicThere are a number of ways in which composers of symphonies, popsongsandcarrental jinglescanestablishorchangethemoodofapieceofmusic. Some of thesemood effects rely on the animal responses ofhumanbeingsandsomedependonasharedmusicalculturebetweenthecomposerandthelistener.For example, when listening to music, we often find an increase in

volumeexciting.Thisexcitementcanprompttheusualphysicalreactionsof increased heart rate and adrenaline production. This is because oursubconscious links an increase in sound volume(people shouting, lionsroaring)withpossibledanger.On the other hand, we associate slow violins accompanying a piano

withromance.Wedo thissimplybecausewehavebeen taught todosofromfilmmusicandTVperfumecommercials. In turn,wehave taughtourcomposers that theyneed to include someviolinsandpianostuff iftheywantustostartgettingoutthehandkerchiefs.Inthiscasethereisnoreal reasonfor thelinkotherthantheassortmentofculturalclichésthatwe are all familiar with—banjosmean hillbillies and accordionsmeanParis.When all is said and done, music is a form of entertainment, so it

doesn’t matter if our emotional response is “real” (adrenaline)or“learned” (clichés). We enjoy getting the Kleenex out when PrettyWomankissesRichardGere,andwelikeleaningintothecurvewhentheMillennium Falcon turns to attack the Death Star.Music helps tocompletetheexperience.Even in the era of silent films there was a mood music industry.

Pianists or small orchestras were hired to accompany theaction with

appropriate music. Sometimes the film came with specially writtenmusic,oralistofsuggestionsofsuitableclassicalpieces.Inmanycases,however, it was left up to the pianist to improvise while watching thefilm. You could also buy books full of pieces specifically written tomatch the moods of any film. These had great names like “DramaticTensionNo. 44” or “Hurry No. 2 (duels, fights),” and my favorites:“CraftySpy,”“AlluringTambourine”and“PatheticLoveThemeNo.6.”I’ve been involved in a few pathetic love scenes myself—and I couldhavedonewithsomebackgroundmusic.Whetheritaccompaniesfilmornot,thefollowinglinksbetweenmood

andmusicarefairlyreliable:

•We find increases in speed ( tempo), volume and pitch exciting—anddecreasesinthesethreehaveacalmingeffect.

• Anticipation is a good mood enhancer, so if the music is quietlyrepetitive we expect something (frightening or marvelous)to happensoonandtheanticipationhelpsthedramaticeffect.

• Music composed in major keys sounds more self-confident andgenerallyhappierthanmusiccomposedinminorkeys.

This last point is very important to this chapter, and needs someclarificationbeforewegoontodiscussthemethodbywhichwebuildupthecollectionsofnoteswhicharethemajorandminorscales.Themajorscaleismadeupofouroldfavorite,thepentatonicscale—

with a couple of extra strongly related notes added to fill the gapsandtake the total number up to seven. This may not seem a big jump innumbersbut itmakesasurprisingly largedifference. Whenweperformmusicweplaynotesoneaftertheotherand/oringroupsatthesametime—andwhenweadda coupleof extranotes into themixwegeta largeincreaseinthenumberofcombinationsavailable.Thinkofitthisway:iffiveofyouarehavinglunchtogetherandtwoofyouhavetogotothebartogetmoredrinks,therearetenpossiblecombinationsoftwopeoplewho

could go. If there were seven of you, there would be twenty-onecombinations of two people.You’ve only added two people but you’vemore than doubled the possibilities. It’s the same with notes—thecombinationsavailableriserapidlyasyouaddmorenotestothegroup.Thegroupofsevennotesthatmakeupamajorscale(orkey)arethe

mostcloselyrelatedgroupfromtheoriginalchoiceoftwelve.Thismakesthemsoundgoodandstrongtogether,whether theyareplayedoneaftertheotherasamelody,orsimultaneously, togiveuschordsandharmony.As a result of all this solidarity,music played in amajor key tends tosoundcompleteandconfident.Oneparticularaspectofmajorkeysisthattheyareverywellsuited todefinite“periods”and“commas”at theendofphrases.Minorkeys involvesubstitutingacoupleof themajorscalenotes for

less supportive members of the original gang of twelve—and theresulting music is generally more mysterious and vague, with lessdefinitepunctuation.Partlybecausethemusicsoundslessself-satisfied,andpartlybecausewehavebeentrainedtodoso,weassociateminorkeymusicwith sadnessandcomplexemotions.Oneof themainreasonswelinkminorkeyswithsadnessisthefactthatthelyricstosongsinminorkeys portray the wholegamut of human unhappiness, from “My babydoneleftme”togenuinetragedy,“Myprinterdonerunoutofinkagain.”It’ssurprisinghowearlywebegintoestablishourminorkey/sadness

link. The other day,Herbie, the three-year-old sonof a friend ofmine,turnedtohismotherandsaid,“Thisissadmusic…it’saboutacatwhogot left behind.” I have sinceinspected the sleeve notes of the CD inquestion and, although Rachmaninoff makes no overt references todisconsolatecats,myyoungfrienddoeshaveapoint.Itwillcomeasnosurprise that the music (the first part of Rachmaninoff’s SecondSymphony)isinaminorkey.This “major key happy/minor key sad” thing is not, of course, an

absolute rule. Leonard Cohen, for example, is quite at homebeing sadand complex in either minor or major keys. And someone obviously

forgot to tell Purcell that minor keys are sadbefore he wrote histriumphant,cheery“RoundO”inDminor.ItisalsoworthnotingthatinIndian traditional music, a scalevery similar to our minor scale isassociatedwithhappinessanddancing.Generally,however, theexistingtraditionwillensurethatmostWesternsongwriterswillcontinuetowritesadsongs inminorkeys—and the linkbetweensadnessandminorkeyswillcontinue.Oneofthebestwaysofrecognizingthedifferencebetweenmajorand

minor keys is to listen to a piecewhich changes fromone to theother.The first half of that famous short piece forpianobyBeethovencalled“Für Elise” is a good example. Likemost classical pieces this can beplayed at a range of speeds because the composers generally give youonly a rough indicationof speed such as “slowly” (largo) or “walkingpace” (andante). In this case we are instructed to play “with a littlemotion”(pocomoto),which I think is almost entirely uninformative—butwhoamI toarguewithadeadgenius? Ifyou listen toaversionofthispiecewhichlastsaboutfourminutes,youwilldiscoverthatitopenswitharathersadtunewhichbeginswithapairofalternatingnotes(dee-dah,dee-dah,dee…).Thispart is in aminorkey.This “dee-dah” tunerepeatsseveraltimesand,afteraboutaminuteandahalf,therearefourquickchordsand themusicchanges intoamuch jolliermoodforaboutfifteenseconds—thisisthemajorkeysection.Themusicthenreturnstothe “dee-dah” minor key theme, after which it goes off ina differentdirection,beforefinallyroundingoffwiththedee-dahtheme.Anothergoodexampleofachangefromaminorkeytoamajoroneis

the classical guitar piece “Adelita” by Francisco Tárrega.This piece isless than twominutes long and beginswith a sad tune in aminor key,whichis thenrepeated.After this thereisahappierinterludeinamajorkeybeforewefinishoffwitharepeatofthesad,minorkeytune.Movingfromonekeytoanotherduringthecourseofapieceiscalled

modulation, and this technique is commonlyused to add interest to themusic and alter itsmood.Modulation from amajor to aminorkey (or

vice versa) is a good method of mood manipulation, but music alsocommonlymodulatesbetweendifferentmajorkeys,orbetweendifferentminorkeys.Iwilldiscussmodulationinabitmoredepthoncewehaveestablishedexactlywhatmajorandminorkeysare.In the following discussion I’m going to be using drawings of the

patented John Powell UglyHarp to explainmy points. ThisinstrumentgetsitsnamefromthefactthatIinventedit…andit’sugly.“Whyinventan ugly harp?” you might say…. Well, it’s not so much a musicalinstrument—it’smoreavisualaid. I’veassumed thatall thestringsaremadeofthesamematerialandthattheyareallunderthesameamountoftension.Thismeansthatthelengthofanystringisdirectlyrelatedtothepitchofthenoteitproduces.Forexample,ifonestringishalfaslongasanotheritproducesanotewithtwicethefrequency.Theharpalsohasaflat bottom—with the ends of the strings in a straight line so we cancomparestringlengthseasily.Attheendofthepreviouschapterwehadascaleoftwelveequalsteps

from any note to the note an octave above it (theequally tempered, or“ET,”scale).ThismeansthatweneedthirteenstringsonourJohnPowellUglyHarptogetacompleteoctave.(Wehavetwelvedifferentnotesplusthe top note, which is an octave higher version of the lowest note.)Becauseof theequalsizeof thestepsbetweenthestringsweknowthatyoucan startyour tuneonany string and the same sequenceof up anddownjumpswillgiveyouexactlythesametune—theentiretunewilljustbehigherorlowerdependingonwhatstringyoustartedon.But,asIsaidearlier,thirteennotesinanoctavearetoomanyforourmemorytocopewith,whichiswhywecametodevelopthemajorandminorscales.

A thirteen-string John Powell Ugly Harp which covers one octave inequal,semitonesteps.ThestepsbetweenthenotesarechosenbytheETsystem.

MajorscalesChoosing a family or team of notes for a major scale is similar tochoosing a football team from a group of friends (in thiscase we aregoingtochoosethebestseventeammembersfromourgroupoftwelvedifferentnotes).Asimpledefinitionofamajorscalewouldbethatyoutakeonenote*

andchoosethesixnoteswhicharemoststronglyrelatedtoit,tomakeaself-supporting team of seven. We know that thesecret of goodharmonies is to use notes with simple relationships between theirfrequenciessothatthepressureripplesjointogethertomakearegularlyrepeating,evenpattern.Wecanachievethesesimplerelationshipsifthestringsonourharphavelengthswithsimplefractionalrelationshipssuchasor¾.Wehavealreadyseenthatyoucan’tmakeagoodscalesystemfromthesefractionsbuttheydogiveusthebestharmonies.ButourJohnPowellUglyHarpisnottunedtosimplefractionalstring

lengths;it’stunedusingtheETsystembytakingacertainpercentageoffthelengthofeachstring.“OhWoe!”youmightsay,“Allislost!”Butdo

notdespair—goandgetyourselfacalmingcupofmilkyteaandI’lltellyouaboutahandycoincidence.To create our thirteen-string harp to cover one octave using the ET

system,weprogressively reduced the lengthofeachstringbyabout5.6percent. Luckily this happens to give us a situation where a lot of thethirteen strings are almost exactly simplefractions of the length of thelongeststring.Forexample,ifwecallthelongeststringnumber1,thenstringnumber6willbe74.9percentaslongasstringnumber1,whichisverycloseto75percent—whichisthreequarters.Theotherstringsalsohave lengthswhicharecloseapproximationsof simple fractions.Theseapproximate fractions are so close to the real thingthat the harmoniesstill sound good. For the rest of this chapter I will refer to the stringlengths of our harp as fractionsof the longest string length. Pleaseremember that I do not mean theexact fraction—I am referring to itscloseapproximation,whichwearrivedatusingtheETsystem.Fortunately,theETchoiceofstringlengthsonourthirteen-stringharp

includes six strings which are a very good matchfor those used toproduce a pentatonic scale—and the pentatonic scale is an obviousstarting point if we are trying to createa seven-note scale of stronglyrelatednotes.Sonowwecandrawourharpwithjustthesenotesandseewhatitlookslike.IntheillustrationbelowIhavelabeledeachstringwithitslengthandfrequencyascomparedtothelongeststringsoyoucanseethateverythingisaswewantit—onlysimplefractionsareinvolved.

The initial choice of notes for our major scale are the notes of thepentatonicscale.Theirlengthsandfrequenciesareshownasafractionofthelongeststring.

Thepentatonicharp in this illustration looks fairlyuseful, butbothourears and eyes tell us that there are twobiggaps:onebetween strings3and 4 and another between strings 5 and 6. The obvious thing to do toincrease thenumberofnotes inourscale is toputonestring ineachofthesegaps—butwehavetochoosebetweentwopossiblestringsineachcase.Let’s look first at the gap between strings 3 and 4. The strongest

candidatewiththebestlinkwiththerestofthegroupisthelongerofthetwo—because it produces a notewhich is 1 times the frequency of thelongeststring.Tofillthegapontheright-handsidewechoosetheshorterofthetwo

possible strings. It gives a notewhich is 1 the frequencyof the longeststring—agoodteammember—anditalsogivesusan“almostthere”feel

tothefinalpartoftherisingscale,likethis:

String 1 2 3 4 5 6 7 8

(Home) (Closestrelative)

(Almostthere)

(Homeagain)

Onceweaddthesetwostringstoourscale,ourharplookslikethis:

The complete major scale of notes chosen from the original thirteenstrings. We have added two more team members to the originalpentatonicset.

When the “almost there”note appears in themelodyor theharmony itmakesa fairlycleardemand toget“there,”so the listenerhasa feelingthatthenextnoteshouldbethekeynote.Infact,thiseffectissostrongthat the technical term for the“almost there” note is theleading note,becauseitleadsusontothekeynote.Wheneverweheartheleadingnote

we build up an expectation of returning home tothe key note. Thisanticipation–resolution effect is used a lot in phrase endings, althoughsometimesthecomposermightdeliberatelyfrustrateourexpectationstomakelifemoreinteresting.Thereasonwhythepunctuationofphrasesisvaguer in the case of pentatonic music is because there is no “almostthere”noteinapentatonicscale.I’m using the words “phrase” and “punctuation” here in exactly the

same way we use the terms when we are discussing writtenlanguage.Musichascommas,periods,andparagraphs,anduses theminthesameway as a storyteller does. The technical termfor any phrase ending inmusicisacadence.Youwillnotice that therearenowonlytwosizesofgap(or interval)

between adjacent notes on our eight-string harp: eitherthe strings arenexttoeachotherandthereforeasemitoneapart;ortheyareseparatedbythe gap and are therefore twosemitones (one tone)apart.Starting fromthe lowestnote in theoctaveandcallingout thenamesof the intervalsbetweenthe notes, we would say: Tone, Tone, Semitone, Tone, Tone,Tone,Semitone.Ratherthancontinuewritingoutthisstreamofwords, Iwill,fromnowon,usejusttheinitialletters:TTSTTTS.Tocreateourmajorscalewehavetakenthestrongestgroupofall,the

pentatonicscale,andaddedtwomoremembers,oneofwhich(theleadingnote)helps to strengthen thepunctuationof themusic.Thisadditionoftwomemberstoourteamhasalsogivenusatremendousincreaseinthecombinationsofnotesavailableforharmonies,withoutoversteppingthebarrierof having too many notes for our memories to cope with—abargainallaround,Ithinkyouwillagree.The only drawback to the use of major keys is that there is a

continuous tendency toward definite, complete statements. Majorkeymusicsoundsratherself-confident,andsometimeswewantthemusictobelesscocky.Inthosesituationsweuseminorkeysaswell.

Minorscalesandkeys

Although Western music generally restricts itself to major and minorkeys nowadays, these two types were selected over timefrom a largergroupofscalesystemscalledmodes,whichusedvariouscombinationsoftonesandsemitonestogetfromoneendofanoctavetotheother.Thesemodes date backcenturies but can still be heard in folksongs such as“Scarborough Fair” and they are occasionally used to add a slightlyexoticflavortojazz,classicalandpopmusic.Iwilldiscussmodeslaterin this chapter, but for the moment let’s concentrateon modern-daymajorandminorscales.TheTTSTTTSmajor scale isactuallyoneof theoriginalmodes (it’s

calledtheIonianmode)anditwouldhavebeenwellknownasbeinggoodfor strong, well-organized harmonies because we are using the mostcloselyrelatedteam.Butstrong,well-organizedharmoniesmaybeabittooobviousifwearetryingtowritedreamymusic.InthiscasewemightchangesomeoftheteammembersanduseTSTTTSTorTSTTSTT,bothofwhicharevaguer.Ifyouwritemusicusingthesescalesthetunesdon’tcometosuchanobvious“period”attheendofevery“sentence.”By about 1700 most Western composers and musicians had chosen

theirtwofavoritetypesofmodeandhadjustaboutstoppedusingalltheothers which were available. As one of their favorites they naturallychosethestrongestteamofnotes—TTSTTTS—andcalleditthe“major”scale.Theotherfavoritescale,whichgavelessdefiniteperiods,andwasthereforesuitablefordreamyorsadmusic,wascalledthe“minor”scale.Butit’snotquiteassimpleasthat.Foranygivenmajorkeywealways

havethesamesetofsevennotes.Thereallyoddthingaboutminorscalesandkeysisthatwestartedoffwithonesetofnotes,thenwealtereditbyonenote.Thenwealtereditbyonenoteagain.“Sowhat?”youmightsay,“There’s nothing odd about that, John—it’s called progress. Thingsdevelopandmoveon—getagrip.”Ifwehadmovedfromtheinitialsetofnotestothenextversionandthentothenext,Iwouldagreewithyou.Butwedidn’tdothat.Somehowitturnedoutthat,forthepastcoupleofhundredyears,wehavebeenusing all three types at once.And I don’t

meanweusethisoneforthispieceandthatoneforthatpiece.Weuseallthree types ofminor scale within a single piece ofmusic.We use theoriginal one if the tuneis descending; one of the others if the tune isascending;andthethirdonetomakeuptheaccompanyingchords.If music was controlled by scientists this sort of untidy non-sense

would be forbidden. But music is organized by musicians,with theirunkempt hair and faraway expressions. Musicians eventually settle onwhat sounds best—and they decided that minorkeys are moreemotionally effective if they change a couple of notes depending onwhetherthetuneisrisingorfalling.This“deciding”processdidn’ttakeplace suddenly one night in the pub—it took centuries, as the otheroptionswerediscardedonebyone.Solet’shavealookatthesedifferentminorscales.

Thenaturalminorscale

Likethemajorscale,thenaturalminorscaleisoneoftheancientmodes.It’scalledtheAeolianmodeandyoucanreada littlemoreaboutitlaterinthischapter.IthasthepatternTSTTSTT,whichmeansthat,comparedtothemajorscale,threeofthestringsonourharphavebeenmoveddownone position, to the next lowest note. As you can imagine, thissubstitutionof three of the strongest teammembers weakens the teamquiteabit.Youcanseethenewarrangementintheillustrationbelow andcompareittothemajorscale.Twooftheoriginal“pentatonicteam”havebeenreplacedandthe“almostthere”noteisalsonolongerwithus.Thenewcomersstillmakeaveryprettynoise,buttheteamlackstheoomphithad,particularlyattheendsofphrases.Still,thewholepointofhavingthesealternativesetsofnotesistohave

adifferent flavor.Wedon’tactuallywantmuch oomphfromourminorkeys. When you’re singing songs about harvests failing, or yourdisappointing loft insulation, you don’twant every verse to endwith acheeryfullstop.Sometimesweneedsomegood,solidambiguity.

Tocreatetheminorscale, threeofthenotes(stringnumbers 3, 6and7countingfromtheleft)havebeenloweredbyonesemitone.Thisgivesusalesscohesivegroup.

The natural minor scale can be used alone to improvise or composepieces ofmusic, but it is usually employed as oneof theteamof threescalesusedinmostminorscalemusic.This natural minor scale was found to be just right for the parts of

melodies which were descending in pitch, so it is alsocalled thedescendingmelodicminorscale.Fortuneswhichwererisinginpitch,composersfoundthattheyreally

missed that “almost there” feeling of the next-to-lastnote of themajorscale—and also found that this notewas very useful for harmonies. Sotheydevelopedtheascending,orrising,melodicminorscale.

Theascendingmelodicminorscale

In the ascending melodic minor scale, two of our natural minor scalenotesare reinstatedback to theirmajor scalepositions.Thenext-to-last

note is returned to its original “almost there” pitch and its neighborfollowsitbackuptopreventtherebeingabiggapinthescale.Youcanseewhathashappenedintheillustrationbelow.

Theascendingmelodicminorscale.Thishasonlyonenotedifferentfromthemajorscale(stringnumber3hasbeenloweredbyonesemitone).

Sonowwehave thecompletesetofnotesformelodies inaminorkey.Weusethisscaleforascendingpartsofmelodiesand thenaturalminorscaleforthedescendingparts.But now, of course, we have a bit of a problem—because we need

chordswhichwillsuitboththerisingandfallingpartsofour tunes.Forthis reasonacompromisescalewasdeveloped fromwhichwecanpickour harmony notes. Not surprisingly, it’scalled the harmonic minorscale.

Theharmonicminorscale

Theharmonicminorscaleis,asIjustsuggested,acompromisebetween

thedescendingandascendingminormelodicscales.Inthiscasewetakethedescendingmelodic,ornatural,minorscaleandreturnonlythenext-to-lastnotebacktoitsmajorkey“almostthere”position(asyoucanseebelow).

Theharmonicminorscale:acompromisebetweenthetwomelodicminorscales,usedforchordsandharmoniesinminorkeymusic.

Sotherewehaveminorkeys.Aweakerrelationshipbetweenthevariousmembers of the team of notes results in a more complexmusicalexperience.Themusicsoundslessself-confidentthanmusicproducedinmajor keys and generally we have come to associate this comparativevaguenesswithsadnessorexpressionsofdeepemotion.

MajorandminorchordsThesimplestchordsconsistofthreenotestakenfromthemusicalscale.AsIsaidearlier,wegetharshcombinationsifwechoosenoteswhichare

nexttoeachother,somostchordsusealternatenotesfromthescale.Themostcommonchordsincludeabasicnote(whichgivesitsnameto

thechord)anditsmostcloselyrelatedteammember—theonewhichhasa frequencywhich is 1½ times that of the basic note. If we start withstring1ofamajorscalethenthe1½timesnoteisstring5.Thisisalsotrueofaminorscale,becausestring5doesnotmovewhenwechangetoaminorscale.(Thefactthatthe1½timesfrequencynoteisthefifthoneyoucometoineitherscaleisthereasonwhymusicianssayitis“afifth”above the key note. The usual technical name for this second mostimportant note in the scale is thedominant, because it dominates thetunesandharmony,alongwithitscloserelation,thekeynote,ortonic.)The third note we choose for a simple chord needs to go between

strings1and5butweshouldn’tchoosestrings2and4becausetheyarerightnexttooneoftheothersandtheywouldclashwithit.Sowechoosestring3.Ifwechoosestrings1,3and5fromamajorscale,wegetwhatiscalledamajorchordand,ifwechoosethesamestringsfromaminorscale,wegetaminorchord.So a major chord is a frequency we choose, plus 1¼ times that

frequencyplus 1½ times that frequency. In aminor chordweexchangethe1¼for11/5,whichislessstronglylinkedtotheothertwonotes.Asweknow,everynoteinvolvesaseriesofharmonicsandinclosely

related notes some of the harmonics of one note willbe the samefrequencyascertainharmonicsof theother.Forexample,ouroldmateA2 has harmonic frequencies which are multiples of 110Hz, and itsstrongest teammember,E3, has harmonic frequencies based on 165Hz.Twotimes165is330,whichisthesameasthreetimes110.Thismeansthat thethird harmonic of A is the same frequency as the secondharmonic ofE.There aremany othermatches of harmonic frequenciesbetweenthesenotes,andthat’swhytheysoundgoodtogether.Usingthistypeofmatchingwecanshowthatthe1¼frequencyinthemajorchordisamoresupportivematchfortheothertwonotesthan11/5, so theminor

chord notes form a less self-confident-sounding team. Once again, aswith all things to dowith aminor key,we have come to associate thislackofself-confidencewithsadness.A chord is a combination ofany threeormorenotes.Themajor and

minorthree-notechordswehavejustdiscussedarethesimplestandmostharmonious-soundingones. Minor chords sound less confident thanmajorchords,but theyarestrongerandmoreconfident-soundingthanalotoftheotherchordswecangetbyputtingthreeormorenotestogether.For example, by adding “clashing” notes to simple majorand minorchords,wecanproducechordswhichsoundmorecolorful,interestingortense. There are also lots of possible chordswhich don’t include thestrong1½,1¼or11/5teammembers.Morecomplexchordslikethishelptoaddmovementtothemusicbecausetheydonotsoundrelaxedorfinal.Ourearstellusthattheremustbemorestepsinthejourneybeforewegetto theendof thephrase.Whenweeventuallygettotheendofaphrasethemusicislikelytorelaxintoasimplemajororminorchord.

NamingnotesandkeysAttheendofchapter1,Imentionedthefactthatnoteshavenameswhichconsist of one of the first seven letters of thealphabet and sometimesthese letters are followed by the words “sharp” and “flat.” Back inchapter1Iaskedyousimplytoacceptthissystemandnotworryaboutit,but now it’s time to look into it properly becausewe can’t discuss ournext subject—movingfromkey tokey—without referring to thenamesofnotesandkeys.Themainreasonwehavenamesfornotesissothatwecanteachand

discussmusic.Althoughtherehasalwaysbeena traditionofpassingonmusicbysimplycopyingwhatsomeoneissinging,thisdoesn’tworktoowellforcomplicatedmusicifyouwantittobereplicatedexactly.TheWestern system of writing music and naming notes began with

monks who wanted to record their masses and hymns. They neededto

make everything easy to remember so they didn’t want to useall thelettersofthealphabetasnamesforthenotes—theychosetouseonlythelettersAtoG.Anytwonotesanoctaveapartweregiventhesameletterbecause they are so closely related as far as our ears are concerned—althoughnumbersandothertechniqueswereusedtoidentifywhichDorEyouweretalkingabout(D1,D2,D3,etc.).So—sevenletterstonameallthenotesinourmajorscaleandthelast

notewouldhave the samenameas the firstnotebutbewritten slightlydifferently,ornumbered,likethisforthescaleofC:

C1,D1,E1,F1,G1,A1,B1,C2,D2,E2,F2,G2,A2,B2,C3,etc.

Well,thisisallprettyclearsofar.Let’sdrawatwo-octaveJohnPowellUglyHarpwiththelongeststringasC,puttingallofthetwelvenoteswediscussedinchapter8intoeachoctave.

A two-octave harp showing the notes of theCmajor scale (the longeststringisaC).

Thisillustrationintroducesustosomethingwhichisratheroddandneedssomeexplanation—wehaveusedupallourlettersbutwehaven’tnamedall the strings (this is a pretty obvious result if you remember thatweonlyhavesevenlettersbutwehavetwelvedifferentnotestotheoctave).Forexample,thestringbetweenCandDhasnonameintheillustration.What do we call such “in between”notes? Well, unfortunately, thesenoteseachhavetwonames.Wecanrefertothemasbeinghigherthanthenote below thembyusing theword“sharp,”orwecan refer to themasbeing lower than the note above them by using theword “flat.”Whenmusicianswritethesenamestheyusuallyusethesymbol“#”toindicatesharpand“ ”toindicateflat.So“Fsharp”isF#and“Bflat”isB .IntheillustrationonthenextpageIhavelabeledallthenotes—giving

the“inbetween”notesboththeirflatandsharpnames.

A two-octave harp with all the notes named. Certain notes have both“sharp”and“flat”names.

Ifyouhaveaspareminuteyoucanpickanynoteandcountupthestrings(from long to short)with the TTSTTTS pattern toidentify the notes inanymajor scale….On the other hand, life is too short for this sort ofshenanigans—andyoudidn’tbuythisbookasanactivitieskit—soI’lldoanexampleforallofus.IfwestartthescalewithA,wegouponeTonetoB,upanotherTone

to C#, up aSemitone toD, etc., and the noteswe get are theAmajorscale:

A—B—C#—D—E—F#—G#—A

Andit’sassimpleasthatreally:pickanyofthetwelvedifferentnotesasyour key note or team leader—and the TTSTTTSsystem will identifywho your team members are to give you the strongest, most closelyrelatedgroup—yourmajorkey.*(IhavewrittenoutthenotesforallthemajorkeysinpartEoftheFiddlyDetailssectionattheendofthebook.)Youcan,ofcourse,dothesameforaminorkeyusingtheappropriate

“T, S” pattern: for example, themelodicminor risingscale isgivenbythepatternTSTTTTS,andifyoustartoffonEyouwillget:

E—F#—G—A—B—C#—D#—E.

Of course, the sharp/flat notes are no different from the simple letternotes—theyareallequallyimportant—it’sjustanamingsystemthathasbeenpasseddowntous.Oneofthehistoricpeculiaritiesaboutthesystemisthattheonlymajorscalewhichdoesn’tincludeasharporflatnoteisCmajor.ThismakesthekeyofCmajorlookimportantinsomeway—butitisn’t;it’sjustthewaythenamingsystemevolved.

Changingfromonekeytoanother:modulationItisclearfromthelastsectionthatwehavetwelvemajorkeysand,asI

willexplainlater,theyareallemotionallyidentical:onekeywillmerelyhavethesamepatternofnotesmovedupordownabitinpitch.Solet’sreturntothequestionofwhywehavesomanykeys.Composersandmusiciansareinacontinualbattleagainstboredom—

not their own boredom, but the boredom of their listeners.They knowverywellthatiftheyboreyoutheirincomewilldropandtheirchildrenwill starve—or, at least, they won’t beable to go out for a burger onWednesday.Musicisaformofentertainmentandsoithastostimulatethe emotions—from jollityto fear (and if you think fear is a bit of anextreme claim for music, you haven’t seen the shower scene fromHitchcock’sfilmPsycho).One of the ways a composer can keep up the interest level of his

listenersistochangekey—fromonesetofsevennotestoanother.Ifthishappens,oneormoreofthenotesischanged,andthelistenercantellthatthe team leader of the grouphas also changed. This team analogy isparticularlyhelpfulhere: imagineyouarethemanagerofa teamwhosestyleofplaybecomesabitstaleduringthefirsthalfofagame.Athalf-time you can put extra life into the team by exchanging a coupleofplayersforsubstitutesandaskingtheteamtovoteinanewcaptain.Sonowyouhave a slightlydifferent teamwith anew team leader—

whichisexactlywhathappensifyouchangekeyinthemiddleofapieceofmusic.Youmightthinkthatanon-musicianwouldnotbeabletospotthe change in team leader (orkeynote) but, in straightforwardWesternmusic such as pop, rock, folk, blues and most of the classical musicwrittenbetween1700and1900,thekeynoteisfairlyeasytospot,evenfor an untrained listener. In more complicated music, such as modernclassicalorjazz,theteamleader,andthereforethekeyofthemusic,mayshiftabouteveryfewsecondsormaybedeliberatelyhidden.Inthiscase,thesenseofakeybecomesconfusedorlost.Whenwearelisteningtoapieceofstraightforwardmusicweidentify

thekeynoteintwoways,althoughyouprobablywon’trealizeornoticethatyouaredoingit.First,asongoranyotherpieceofmusicisdivided

upintophrasesandthekeynotewilloftenbethefinaloneofaphrase.Ifyouplayjustaboutanypopsong—evenoneyouhaven’theardbefore—youwillbeabletohumthekeynotewithinaminuteorso.Justpretendthat the tune is ending and hum the note it should end on—thatwillalmostcertainlybethekeynote.Ouroldfavorite“BaaBaaBlackSheep”does this: it hits the key note on the word“full” and the final word,“lane.”Theothercluewhichhelpstoidentifytheteamleaderishowoftenthe

variousnotesof thescaleoccuras themelodyprogresses—andherewecometoanexampleofmusicologicalfortitudeaboveandbeyondthecallof duty. Brett Arden of Ohio State Universityspent many monthscheckingthousandsofmelodies(morethan65,000melodynotesforthemajorkeysandmorethan25,000fortheminorkeys)tofindoutexactlyhowofteneachofthenotesinascaleoccurs.Forexample,ifwenumberthenotes from1(thekeynote) to7(the“almost there”note),hefoundthat, in major keys, note 5 occurs most frequently and will be playedabout four times as often as note 7, the least commonmember of thegroup.Thereareotherrelationshipswhichhold trueformost tunes.Forexample,inamajorkey,notes1,3and5makeupalmost60percentoftheheadcountofnotesinatune.Yourbrainrecognizestheseproportionsandthishelpsustotellwhichnotethekeyisbasedupon.Obviously,youare notawareofyourbrainanalyzing theserelationships.You justpickup these clues subconsciously, as youdowhenyou assesswhichof theguilty-looking eight-year-old ruffians in your garden just kicked thefootballthroughthekitchenwindow…Themostcommontypeofmodulation is tochangefromthekeyyou

areintoakeywhichcontainsonlyonedifferentnote.Forexample,wecouldbeplayingawayinthekeyofCmajor,which

containsthefollowingnotes:

C,D,E,F,G,A,B.

AndwecouldeasilyshiftovertothekeyofGmajor:

G,A,B,C,D,E,F#,

whichhasthesamenotes,excepttheFhasbeenchangedforanFsharp.Ifwedothis, themusicreceivesanemotional liftbecauseoneof the

noteshasbeenraised.Wealsogetextra(subconscious) interestbecausethekeyhaschangedandwecansensethechangeofteamleader—fromCtoG.On theotherhand,wecouldchange fromCmajor toFmajor,which

contains all the same notes asC except for the fact thattheB is takendownasemitonetoBflat.Inthiscaseweoftenget theimpressionthattheemotionalintensityofthemusichasswitcheddownagear,althoughwestillgettheenhancedinterestfromthechangeinteamleader.This “up a gear” or “down a gear” effect has nothing to dowith the

actual properties of G major or F major—the differentkeys have nointrinsicemotionalshading.It’stheprocessofchangewhichgivesustheemotionalimpact,andtheeffectfadesoffquiterapidly(withinafewtensof seconds). Imagine yourself standing in a big hamster wheel—it hasbeen stationaryfor awhile and you’re bored, so you take a single stepforwardonto thenext rung.Everythinggetsa lotmore interestingforalittle while, but soon the step you moved to becomes the one at thebottom of the wheel and it’s all boring and stationaryagain. Steppingbackward onto the rung behind you has a slightly different effect—butit’s still transitory. The rungs are identical: it’s the changeoverswhichareinteresting.Ifyouwanttokeeplifestimulatingyouaregoingtohavetokeepchangingrungs.Composers occasionally inject a surge of interest by shifting several

rungsatonce—toakeywhichhasalotofdifferentnotesinit—fromCmajor to Emajor, for example. Ravel does this as a dramatic flourishneartheendofhisBoléro.Butmostoften,keyschangetoaneighboringkey(onewithonlyonedifferentnote).

Modulating a repeated phrase to a key that is a semitone or a toneabove the one you start in (shifting up from B major toC major, forexample)neverfailstobrightenthemusicbecauseitfeelslikeachangein gear, which is why it has becomeknown as the “truck driver’s gearchange”or“truckdriver’smodulation.”Thetechniquealsorevelsinthename“thecheesemodulation”(“cheese”beingthegeneralnamegiventopopmusicwhichhaspassedits“bestbefore”date).Thismodulation iscommonlyused togivea sudden lift inenergy to

popsongs,particularlyincaseswherethechorusisrepeatedalot.“IJustCalledtoSayILoveYou”byStevieWonderusesthistechniqueacoupleoftimes,butthemostnotableexampleoccurswhenthetitleofthesongisrepeated,threeandahalfminutesintothetrack.Anotherveryeffectiveexampleofthistypeofmodulationcanbefoundin“ManintheMirror”byMichaelJackson.Inthiscase,thekeychangeoccurs(asMichaelsingstheappropriateword)twominutesandfiftysecondsintothesong.If amodulation involvesmovement between twomajor keys or two

minorkeys,anychangeinmoodwillbeshort-lived,becausetheeffectislinked to the action of changing—you are just changing rungs on thehamsterwheel.If,however,youchangefromamajorkeytoaminorone(orviceversa)thechangeinmoodwillremaininplace.Thisisbecause,although the effect willbe strongest just after the change, you havegenuinelymovedfromonemusical landscape to another—like jumpingfromasteelhamsterwheeltoonemadeofwood.Changingfromamajorkeytoaminoronewillresultinamorecomplex,emotionalorsadmoodand a move in the other direction will make the music soundmoredeterminedandself-assured.If you change key very often (as some jazz and classical composers

do), then the listener may become rather confused and themusic willsound a little unstable. If, on the other hand, you don’t do this oftenenough (like some pop bands), the musiccan become very predictableandbland.

Thesameteamofnotescansoundminorormajorifyouchangetheteamleader

Ifweconsiderthesimplestversionofaminorkey,thenaturalminor,wecan construct either a minor or a major key outof one set of sevendifferentnotes.Forexample,thescaleofCmajoris:

C—D—E—F—G—A—B—C

andthescaleofAnaturalminoris:

A—B—C—D—E—F—G—A

This is thesamegroupofnotesexcept that, for theminorkey,wehaveAsatthetopandbottomofthescaleinsteadofCs.Wecanpullthesametrickwithpentatonickeys.Thepentatonicmajor

scalewhichstartsonCis

C—D—E—G—A—C

ThisusesexactlythesamegroupofnotesasthepentatonicminorscalewhichstartsonA:

A—C—D—E—G—A

Yes—I agree—this sounds bonkers. How can the same bunch ofcarefullychosennotesbeeitherCmajororAminor?Butit’strue—usingthesamesetofnotes,youcangiveaminor(sad,

reflective,weakfullstops)oramajor(happy,positive,strongfullstops)feeltothemusicsimplybychangingtheteamleader.“Aha!”yousay,“butifI’mhearingexactlythesamenotes,howdomy

earsknowthattheteamleaderhaschanged?”Well,as Isaidearlier,theteamleader,thekeynote,isfairlyeasytospotinstraightforwardmusic.It’s really all about emphasis—andweare all used to small changes inemphasis making a big difference to what we say. For example, thefollowingtwosentenceshaveverydifferentmeaningsbecause,althoughIhave used all the same words in the same order, I have changed theemphasisbymovingthecomma,whichmakesonesentenceinsultingandtheothercongratulatory.

“I’mnotafoollikeyou,Ispendmymoneywisely.”“I’mnotafool,likeyouIspendmymoneywisely.”

SoifwetakethenotesofthekeyofCmajor(C,D,E,F,G,A,B)anduseC,E,Gasourfavorites,particularlyCattheendofphrases,wewillhearthemusicashavingamajorkeyfeel.Ifweusethesamenotes,butmakeA,C andE our favorites,particularlyA at the endof phrases, then themusicwillhaveaminorfeel.The“team”analogycomesinusefulagainhere:ifyou tookanysoccer teamandchanged therolesofsomeof theplayers(bygivingthegoalkeeperthecenterforward’sjob,etc.),thentheteamwouldperformwithadifferentstyleeventhoughtheplayerswerethesame.If you have access to a piano you can check this for yourself. Try

making up simple tunes using one finger and playing onlythe whitenotes. If you end all your phrases on the noteC, themusicwill soundfairlycheeryandstrong.IfyoustayonthewhitenotesandendallyourphrasesonthenoteA,thenthemusicwillsoundvaguerandsadder.

ChoiceofkeyComposersneedseveralkeys,sotheycan,iftheywish,hopfromonetoanotherduringthecourseofapiece.Butwhatmakesthemdecidetostartapieceinaparticularmajorkeyifthereisnomooddifferencebetween

anyofthemajorkeys?And,similarly,whywouldtheychoosethisminorkeyinsteadofthatminorkey?Well,thereareanumberofreasonstochooseaparticularkeytostart

your piece—but none of them have anything to do withemotionalcontent. These reasons can be divided into five categories: instrumentdesign; range; composer delusion; perfectpitch; and “first come firstserved.”

Instrumentdesign

AlotofpopsongsandmostclassicalguitarpiecesarewritteninthekeysofC,G,D,AandEbecausethesearetheeasiestkeystoplayonaguitar—the chords and tunes in these keys allow you to get the maximumrewardfortheminimumeffort.Forexample,ifyouareatotalbeginner,Icould teach you to play the chords to a simple pop song written in Gmajorinaboutfifteenminutes,andyoucouldaccompanyasingerwithafairlyshabbyversionafterabout threehours’practice. Ifwemoved thekeyonesemitoneup—toAflat—oronesemitonedown—toFsharp—itwould takeyoutentimesas longtogetevenashabbyversiontogether.Thisisbecausethefingerpositionsforthechordsarealotmoredifficultasaresultofthewayguitarsaretuned.Lotsofotherinstrumentsarealsoeasier toplay in somekeys thanothers,and thechoiceofkey isdrivennotbymusicalconsiderations,butbyergonomics.Forexample,thesortof“bigband”whichaccompaniedsingerslikeFrankSinatrainthe1950sand1960sinvolvedtrumpets,clarinetsandtrombones,whichareeasiesttoplayinthekeyofBflat,soalotofthosesongsareinthatkey.

Range

Every instrument has a top note and a bottomnote.You have tomakesurethatthepieceyouarewritingfitsontheinstrument—andthiscouldaffect your choice of key. For example, the lowest note on a flute ismiddleC,sotherewon’tbemuchsolomusicwrittenfortheinstrument

in the key of B because it’s useful to have the key note close to thebottomoftheinstrument’srange.Also, the key of a song may have to be raised or lowered to suit a

particularsinger’svoice.

Composerdelusion

Many composers, like lots of other musicians, suffer from belief in amythIwilldiscusslaterinthischapter,whichsuggeststhatcertainkeyshavespecificmoods.SotheywritegloomymusicinA andjollymusicinAbecausetheythinkthatthosearethemostsuitablekeys.

Perfectpitch

Ifyouareacomposerwithperfectpitchyouwillhearspecificnotes inyourheadeverytimeyouthinkupatune.Whateverkeyitappearsinwillprobablybetheoneyou’llusewhenyouwriteitdown.

Firstcomefirstserved

If, like most composers, you have not got perfect pitch and you quiteoftencomeacrossusefultuneswhenyouarefoolingaroundonapianoorsomeotherinstrument,youwillprobablystickwiththenotesinthekeyyou first found them in, unlessthere is a good reason to change them.Somecomposers have favorite fooling-aroundkeys.A famous exampleof this is the songwriterIrving Berlin (who wrote Bing Crosby’s hit“WhiteChristmas”and“Let’sFacetheMusicandDance”).Byhisownadmission,Irving Berlin was a dreadful pianist, so he played andcomposed nearly everything in the key of F#major, a keywhich fallsunder the fingers very nicely (it uses all the black notes on a pianotogetherwithonlytwowhitenotes).Hecouldn’twritemusicsohepaidmusicianstowatchhisfingersandwriteitalldown,andlatertheywould,ifnecessary,changethekeytosuitanyinstrumentsorsingersinvolved.

ModesAlthoughourmajorandminorkeysareadevelopmentfromtheancientpentatonicscale,wehavenotyetdiscussedthestoryofhowwegotfromone system to the other. It all began with the ancient Greeks, whodeveloped a selection of different scales,all involving seven differentnotes in an octave,which they calledmodes.Thehistoryofmodes is asubject of Byzantine complexity, which makes me glad I’m not ahistorian.Basicallyitgoeslikethis:Sometime before 300B.C. the ancient Greeks used different scale

systemsoftonesandsemitonestodividetheoctaveup,andnamedthemafterthepeoplesandterritoriesofGreeceanditsneighbors.Forexample,the Lydianmodewas named after the area called Lydia, which is nowcalledWesternAnatolia.TheChristianchurchdevelopedamethodofsingingcalledGregorian

chantfromabout750onward,whichusedsevendifferentscalepatterns.The church gave these modes the names of the Greek modes withoutworryingaboutwhethertheywerethesameastheGreekones.SowenowhaveChristianmodeswithrandomGreeknames.The Holy Roman Emperor Charlemagne decided to improve the

popularityoftheseChristianmodesbythreateningtheclergywithdeathiftheydidn’tusethem.Themodesbecameverypopular.Themodeswereusedsuccessfullyforseveralhundredyearsbutsome

ofthembecamelessfashionablethanothers.Eventually,byabout1700,most music was using only two of the original seven—and these twobecameknownasthemajorkeysandtheminorkeys.Today,modes are used less frequently than themajor orminor keys

but youwill find them in folkmusic and some jazz, classicaland popmusic (when the composer wants themusic to have a slightly unusualflavor). Just like themajorkeys, eachmodeconsistsofa setpatternoftonesandsemitonesasyougoupanddownthescale.Sohowdowepickourteamofnotesformodes?Surprisinglyenough,

allthemodesusethesameteamasamajorscale—buttheydon’tuseitinthesameway.Thissoundsabitweird,butlet’sgobacktoouroldfriend,the Ugly Harp. The next illustrationis a two-octave harp showing thenotesoftheCmajorscale,andIwillnowdemonstratehowallthemodescanbeplayedusingthesamenotesastheCmajorscale.Wealreadyknowhowtoplay thescaleofCmajoron thisharp—we

juststartwiththelongeststringandplucktheCscalenotesoneaftertheother.Butnowwewanttoplayamodeusingthesamenotes.Thereareseven modes and they have the followingnames: Ionian, Dorian,Phrygian, Lydian, Mixolydian, Aeolian and Locrian. (Yes, they do allsoundlikeheroinesfromLordoftheRings—exceptforMixolydian,whoisobviouslyoneofthoseelvishbowmenwiththefancyhelmets…butIdigress…)Allthesemodescanbeplayedonaharptunedtoamajorscalelikethe

oneabove.Themajorscaleandallthemodesuseexactlythesameteam—theonlydifferencebetweenthemisthechoiceofteamcaptain.

A two-octave harp showing only the notes of the C major scale (thelongeststringisaC).

WehavesevendifferentnotesinourscaleofCmajor(C,D,E,F,G,A,B), and seven modes. Each mode uses a different startnote (teamcaptain), sooneof themmuststartonC—exactlyasourCmajorscale

does.ThemodewhichdoesthisistheIonian,whichiswhyweneverhearof this mode; it’s the one we chose to be our modern major scale, sothat’s what we call it. The other sixmodes use the following notes astheirteamcaptainiftheyareusingthenotesfromaCmajorscale:

DorianmodePhrygianLydianMixolydianAeolianLocrian

ToplaytheDorianmodescaleonourharp,wewouldstartandfinishontheDstringssoinsteadofthescaleofCmajor,CDEFGABC,wewouldplayDEFGABCD,andplaytunesandharmonieswhichkeptreturningtoD.ToWesternears thissoundsa little oddbecause,giventhatgroupofnotes,ourearskeepexpectingtunestoendonCorG.However,onceyougetusedtoit,theDorianmodemakesanicechange.ThebasicfeeloftheDorianmodeissimilartoaminorkey.Thisisnot

really surprising because the only difference betweentheDorianmodeplayedfromDtoDandourmodernkeyofDminor(natural)isthattheBis lowered to B in D minor—all the other notes are the same. TheDorianmodeisusedalot inCelticmusicandisalsothebasisforsuchsongsas“ScarboroughFair”andTheBeatles’“EleanorRigby.”As I said earlier, the major keys all have a TTSTTTS pattern of

intervalsaswerisethroughthescale.IfweplayaDorianscale,weplayfromDtoDandthisgivesusanintervalpatternofTSTTTST.Aslongasyouusethisintervalpatternyoucanstartonanynoteyoulike(usinganinstrument with all the twelve different notes on it) and you will beplayingaDorianmode.Youcould,forexample,startwithanAandplay

thenotesA,B,C,D,E,F#,G,AandthatwouldalsobeaDorianmode(justasyoucanstartfromanynotetoproduceamajorscaleifyoukeeptothecorrectTTSTTTSintervalpattern).If twomusicians get together to play a songwritten in amajor key

which they both know well, they won’t say “let’s play it in major”becausethatdoesn’ttellthemverymuch.They’llsay“let’splayitinGmajor”or“let’splayitinEmajor”andofftheygo.Inthesameway,iftheywantedtoplay“ScarboroughFair”theycan’tjustsay“let’splayitin Dorian”—theymust identify which note the Dorian mode they aregoingtousebeginswith.Theycouldsay“Let’splayitinDDorian”andusethenotesD,E,F,G,A,B,C,Dbuttheycouldjustaseasilysay“let’splay it inGDorian” (G,A,B ,C,D,E,F,G)or “BDorian.” Just likemajorkeys,therearetwelvedifferentDorianmodes.Ifyoupickthenotesfromanymajorscaleandmakethesecondnoteof

that scale the team leader, thenyouareplaying intheDorianmode.Toplay in a differentmode, you choose a different note from yourmajorscaleasyourteamleader:

For the Phrygian mode the third note of the major scale is the teamleader.

FortheLydianmodeit’sthefourthnote.FortheMixolydianmodeit’sthefifthnote.FortheAeolianmodeit’sthesixthnote.FortheLocrianmodeit’stheseventhnote.

The Lydian andMixolydianmodes are very similar tomajor keys—ineachcaseonenote from themajor scalehasbeenmovedonesemitone.Music played in these modes sounds only slightly less definite andunambiguousthanmajorkeymusic.TheDorian,PhrygianandAeolianmodesareallverysimilartominor

keys.Infact,theAeolianmodeisthenaturalminorscalewemetearlierinthischapter.Musicperformedinthesekeyssoundsrathervagueinits

punctuation—and,asIsaidearlier,thiscanbeapleasanteffectforsadorromanticmusic.TheLocrianmode isnotclosely related toeitherourmajororminor

keys—to our ears it sounds as if a mistake has beenmadesomewherealongtheline.Forthisreasonitisonlyrarelyused.

DodifferentETkeyshavedifferentmoods?Iwouldnowliketodestroyamythaboutmajorandminorkeyswhichisbelievedbyanumberofmusicians andmusic lovers.Thismythhas anexcellentpedigree—Beethovenbelievedinitandlotsofothercomposersandprofessionalmusicianshavebelievedit—butitsimplyisn’ttrue.Themythisthat,evenwithequaltemperament,differentkeysconvey

differentemotionalmoods.I’mnottalkingaboutthedifferencebetweenmajor and minor keys here—theyare different from each other in thewaysIdescribedabove.No,themythsaysthat,forexample,EmajorhasadifferentmoodfromFmajor,andDminorhasadifferentmoodfromBminor. I testedaclassofmusicstudentson this,and,beforewestartedthetests,threequartersofthembelievedthatdifferentkeyshaddifferentmoods.Ithenaskedthemtowritedownwhichmoodtheyassociatedwitheach key. Without discussing it between themselves, they tended tochoose very similar moods forany given key. For example, there wasgeneral agreement thatAmajor andEmajor are “bright and cheerful”and C major is“neutral and pure.” If you are one of the people whobelieves in themoodsofkeys I suspect thatyouwouldalsohavemadethe same basicmood choices for these keys.Youwould probably alsoagreewiththestudentsthatEflatmajoris“romanticandserious.”Well,Ihatetobeapartypooper—butthisisallwrong…Do you remember that committee we discussed back in chapter 1?

TheymetinLondonin1939todecideonthefrequenciesweweregoingto use for our notes from then on. They only had to decide on thefrequencyofonenote—becauseyoucanthenworkoutthefrequenciesof

all theothers from theoneyouhavedecidedon.Afterconsuming theirownweightinchocolatechipcookies,theseearnestfolksdecidedthatthefundamentalfrequencyofthe“A”justabovemiddleCshouldbe440Hz(440 vibrationsper second). They didn’t choose this frequency formusicaloremotionalreasons—theychoseitbecauseitwasaniceroundnumberwhichwassomewhereinthemiddleoftherangeoffrequenciesbeingusedforthenote“A”alloverEuropeatthattime.Let’sgobacktolookattwokeysandtheirsupposedmoods:

Emajorissupposedtobe“bright,joyfulandlively”;Eflatmajorissupposedtobe“romanticandserious.”

These two key notes (E and E ) are next to each other on a pianokeyboard—EisonlyasemitonehigherthanE —yetthesupposedmoodsoftheirkeysareverydifferent.TheideathatEmajorisjoyfulandE isseriouswasfirstproposedbyseveralauthors in listsofkey–moodlinkspublished in the late eighteenth century.Theideas put forward in theselists have survived to this day even though the pitches of the notesinvolvedwere not fixed until1939 and are known to have varied by atleastacoupleoftonesovertheyears.Onthedayofthecommitteemeetingtherewouldhavebeenpianosall

over Europewith Es lower than the new standard E and other pianoswithE shigher than thenew standardE. In spite of the large rangeoffrequenciesinvolved,manyofthepianoownerswouldhaveinsistedthatthekeyofEontheirpianowasmuchbrightersoundingthanthekeyofE—and theywould still insist that thiswas true after their piano tunertunedtheentirepianohigheror lower, tomatchthenewstandardpitch.So if there is a key–mood link it can’t have anything to do with thefrequenciesofthenotesinvolved.Also,itcan’thaveanythingtodowithslightlydifferenttuningsystemsforthetwokeys.Pianotunersnowadaysaretaughttousetheequaltemperamentsystem,whichtreatsallkeysinexactlythesameway.

When I was investigating this phenomenon of key–mood links, theonly thing leftwhich Icould thinkofwhichcouldgivealinkwouldbethe physical layout of the piano keyboard: the black notes are fartheraway from your wrists when you are playing,so there might be somesubtledifferenceinthewaytheblacknotesareplayed,anddifferentkeysusemoreorlessblacknotes.OntheotherhanditcouldbelinkedtosomeeffectIhadn’tthoughtof.Iwas very skeptical of any key–mood link but thought that the idea

deserved to be fairly tested. So, together with a professionalmusicologist,Dr.NikkiDibben, I gathered together the aforementionedclassofmusicstudentsandaskedthemtolistentoaspeciallymadetaperecording.Onthetapeweretwoshortpiecesofmusic—onewassimpleandjolly,andonewasdramatic—playedfourtimeseachinvariouskeys.Between each short piece there was a recording of some Indian sitarmusic—which was not inany Western key—to prevent the musicstudentsfromworkingouthowthekeyofthepianomusichadchanged.We asked the students (none of whom had perfect pitch and three

quartersofwhombelievedinkey–moodassociation)totrytoidentifythemoodofeachpieceandthekeyitwasplayedin.Theresultsshowedthatthesimple,jollypiecestayedsimpleandjollynomatterwhatkeyitwasplayedin,andthestudentsthereforeusuallyguessedthatthemusicwasbeingplayedinthe(supposedlysimple)keyofG,CorFwheninfactitwasbeingplayedinFsharpmajor(whichissupposedtobecomplexinnature). We got a similar result for the dramatic music—it stayeddramaticnomatterwhatkeyitwasplayedin—andthestudentsguessedthekeysincorrectly.Nowwehaveour answer—there is no linkbetweenkey andmood. I

think there are at least a couple of reasons why this mythhas becomegenerallyaccepted:

1. Composers in the past believed it and wrote their music in the“appropriate”keys.Thischoosingofcertainkeysforcertainmoodsleads

music students to believe the link is real—so they write their owncompositionsinthe“appropriate”keys.2. When we learn the piano, or any other instrument, we begin withpiecesinthekeyofCbecauseitistheeasiesttoreadasithasnosharpsorflatsinitskeysignature(thekeysignatureiswrittenontheleft-handside of each line of music andtells you which notes are to be playedsharpor flat throughout thepiece).Aftera fewweekswestart tocomeacrossmusicwhichbeginsinCbutthenchangeskeytoG(whichhasonesharpinitssignature)orF(whichhasoneflatinitssignature).ChangingfromCtoGmakesthemusicsoundbrighter,andchangingfromCtoFmakesitsoundlessbright.Becauseweseethattheadditionofasharptothekeysignature(aswechangetoG)addsbrightness,andaflat(aswechange to F) reduces brightness,we start associating flatswith calmorsadness and sharps with brightness. In fact, it isn’t true that G isintrinsicallybright—it’s just that the change up in key makes thingssoundbrighter.IfyouchangefromthekeyofCtothekeyofGthebrightnessofthe

musicincreases,butifyoumovefromDtoGthebrightnessdecreases:inonecaseGisthebrighterkeyandintheothersituationit’sthelessbrightkey.

Now a final note for hardliners—the peoplewho still aren’t convincedthatthereisnolinkbetweenkeyandmood…EarlierinthischapterImentionedthe“truckdriver’sgearchange”—

which involves modulating from the key you are in toone a tone orsemitoneabove.Theextra“lift”giventoanysongbythismethodisveryclear—andthisiswheretheargumentofmood–keysupporterscollapses.Ifyouplaytherelevantsectionofpopsongswhichdothisonapiano,the“lift”alwaysworks,nomatterwhichkeyyoustartoffin.ItworksfromB(whichhas3 flats in it) toB (5sharps)but italsoworks justaswellfromA(3sharps)toB (3flats)orfromE(4sharps)toF(1flat).Theselast two examples, by the argument of thosewho believe in key–mood

links,should not work because they involve moves from supposedlybrightkeystolessbrightones.Thereareotherexamplesofthistrick inpopmusicwhere themovementupward ismore thanawhole tone,butonceagain, itdoesn’tmatterwhichkeysyoumovefromor to—it’s themovementupwardwhichinfusesthesongwithnewlife.Sothereweare—it’sthemovementfromkeytokeywhichprovidesa

changeinmood.Thekeysthemselvesdon’thavemoodsoftheirown.

Themainthingstorememberaboutkeyscanbesummarizedinjustfourshortparagraphs.

1.Major keys are a team of seven notes which are strongly related totheir team leader. The punctuation of phrases in majorkey music isgenerallyclearanddecisive.2.Minorkeyshaveacoupleofdifferentnotesdependingonwhetherornot the tune is going up or down in pitch. The team ofnotes is not asstrongly relatedasamajorkey teamand themusical experiencenotasdecisive and clear-cut—particularlyat the end of phrases. We havelearnedtoassociatesadnesswiththismorecomplexinterrelationshipofnotes.3. Music changes from major key to major key to keep our levels ofinterest up, and the same is true fromminor key tominorkey. Certainchangesincreasethebrightnessofthemusicforashortwhile,andotherscan diminish the brightness. The effectdoes not last long because it iscausedbythechangeitself.4. Changes from amajor key to aminor key, or vice versa, involve astrongchangeinmood.Inthiscasethemajor(brighter)orminor(sadder)mood does not fade away—it is not merely linked to the action ofchanging.

Butone thingwehaven’tcoveredso far iswhygenerationsofunhappychildren have been forced at knife-point to practiceplaying scales on

theirinstrumentswhentheycouldbehavingmuchmorefunplayingrealpiecesofmusic.Therearetworeasonsforthis,butIthinktheyareratherfeeble when you take into account the degree of boredomwhich scalepractice induces,and the number of kids who have abandoned musicbecauseofit.Thefirstreasontopracticescalesisthatitmakesyougetusedtousingallthenotesonyourinstrument.Thesecondreasonisthatlots of tunes involve fragments of scales. In fact,if you look at themclosely, most melodies are made up of a combination of arpeggios,repeated notes and parts of scales.In “Baa Baa Black Sheep,” forexample,thewords“sheephaveyoua…”arefournotesofamajorscale.Becausescalefragmentsturnupsooftenintunesit’shelpfultohavethewholescalelockedintoyour“muscularmemory”* in thesamewaythatit’s useful to memorize multiplication tables—it saves a lot of effortlater.On thewhole, though,I thinkfar toomuchemphasis isplacedonscale practice in the early years ofmusical education. If the student isgoingto takeupmusicasmorethanahobby,shecanmoveontoscalepractice later ifshewantsorneeds to.WhileI’mfeelingallhot-headedand revolutionary, why don’t all you music students abandon scalepracticeinfavorofimprovisationpractice?Although playing scales is tedious, an understanding of how scales,

keys and harmonies work is an important part of musicaltraining.Anappreciationofwhat’sgoingon isveryusefulwhetheryouareplaying,improvising,composingorjustlistening.Nexttimeyouarelisteningtoapop song which suddenly getsa lift in energy, smile knowledgeably,pointatthespeakersandsay“ah…atruckdriver’sgearchange.”Chooseyour timecarefully, though—youareonly allowed tobe this

weirdaboutonceayear.

10.IGotRhythm

Igotrhythm,Igottempo,IgotmeterThere is a strong linkbetween rhythmandvegetarians. I’mnot talkingabouttherelativedancingabilitiesofvegetariansandomnivoreshere,asIhaveobservedexamplesofexcellentandexecrablehoofingfrombothcamps. I mean that there is astrong link between the waywe use thewords“vegetarian”and“rhythm.”Whenwesay“Kayisavegetarian”wedon’tnecessarilymeanthatshe

eatsonlyvegetables.Lotsofvegetariansalsoeatawiderangeofthingswhicharenotvegetables,suchaseggs,legumes,cheese,andmanyotherfoods packed with revolting vitamins.We are using “vegetarian” as aconvenientlabel.Anypieceofmusicconsistsofastreamofsoundsspreadoveracertain

amountoftime,andweusethewordrhythmtodescribehowweorganizethetimingandemphasisofthosesounds.Butweareusingthewordasaconvenient label. Infact, when we talk of rhythm in this way we arereallyreferringtothreethings:tempo,meterandrhythm.Thetempoofapieceofmusicisitspulserate—howoftenyouwould

tapyourfoottoit.Themeterishowoftenyouwouldemphasizeoneofthefoottaps.For

example,ifyouarelisteningtoawaltzyouwillemphasizethefirsttapofgroupsofthree—one, two, three,one, two, three.Ifyouare listeningtorockmusic(ormostotherWesternmusic),youwillstressthefirstbeatofgroupsoffour—one,two,three,four,one,two,three,four.The rhythm is the pattern of long and short notes being used at any

particular time. For example, the beginning of Beethoven’sFifthSymphony(DaDaDaDaah)hasarhythmofthreeshortnotesfollowedbyalongerone.Youcanplayitasquicklyorslowly asyoulike,butyouwon’tchangetherhythm—itwillalwaysbethreeshortfollowedbyone

long.Having explained all that, I will now return to the normal,

conversationaluseoftheword“rhythm”fortherestofmydiscussion.WhenIwasputtingthisbooktogetherIconsideredallsortsofmethods

for drawing pictures to explain how rhythms work,but eventually Irealizedthattheclearestandsimplestpicturesofrhythmsweretheonesweuseinstandardwrittenmusic.TheWesternsystemofwrittenmusicisa diagram which tells musicians which notes to play, when each noteshould start andstop, and which ones to emphasize. We can use thissystemforourdiscussionofrhythm—butdon’tpanic,Iamnotgoingtoexpectyoutobeabletoreadmusic.Actually, learning to readmusic is a pain in theneck—anddon’t let

anyonetellyouotherwise.It’sveryinterestingforapproximatelythefirsttenminutes,whenyou’relearningwhatit’sallabout.Afterthatthereisalongstrugglebeforeyoucangetyourfingerstoobeytheinstructionsonthe page and produce music. This long struggle is similar to the oneinvolvedinlearningalanguage,andtherewardsarejustasgreat,butinthischapterweareonlygoingtocoverthoseinterestingfirsttenminutes.

ThedevelopmentofwrittenmusicThe trouble with ancient history is that, as far as I can tell, the vastmajorityof it tookplaceahellofa long timeago.Thismeans that it’sverydifficult toknowwhenwrittenmusicwasfirstattempted.There issome evidence of ancient writtenmusic of various levels ofsophistication in China, Syria and ancient Greece. One of the earliestcomplete compositions we have discovered so farwas inscribed on atombabout2,000yearsago.Thissong,knownastheSeikilosEpitaph,iswritteninanancientGreekmusicalnotationwhichtellsyouwhichnotetosingforeachwordandhowlongeachnoteshouldbe.Thelyricsofthesong encourageus, in the truerockandroll tradition, toshinewhilewelivebecauselifeisshort.

ThewrittenmusicsystemweuseforWesternmusicdatesbacktothetime when monks and nuns were much more a feature of thenationalmusic scene than they are today (although therewere also professionalmusiciansaround).Intheearlydays,themusicwouldbethoughtupbyatalentedmusician,monkornun,andtaughtdirectlytohisorherfriendsby singing or playing.Eventually, however, the music became morecomplicated and composers realized that writing it down would be ahandy way ofteaching and recording it. Also, by aboutA.D. 750 theChristianchurchwasbeginningtoinsistthatmassesshouldbesungusingvariousstandardizedrules.Forthesereasonstherewasalotofinterestinwritingmusicdown.Someearlycomposersusedtodrawpicturesofhowthemusicwentupanddownbutthiswasn’tveryaccurate.ByaboutA.D.800therewasgeneralagreementonthefollowingrules.

1.Youneedtousedifferentsortsofdotsorshapesfordifferentlengthsofnote.

2.Thedotsshouldbedrawnoneafteranother,readingfromlefttoright.3.Thedotsshouldbedrawnona“ladder”toshowhowhighorlowthenotesare.

Writingdownmusicinvolvedgivingnamestothenotesandsotheydrewtheir“ladder”andnamedthenotesfromAtoG.Theearliestladderhadelevenlines,likethis:

One early idea was to write the notes on an eleven-line “ladder,” or“stave,”likethis,butasyoucansee,it’sverydifficult toidentifyquicklyexactlywhichlineorspacethenotesareon.

This ladder (orstaveasit iscalled)hadsomanylevelsthatitwasverydifficulttoread,socomposerssplititintotwosections,low(orbass)andhigh(ortreble)likethis:

The modern stave split into two sections (treble and bass) for easyreading. (Note that middle C is stuck in the middle betweenthe twostaves.)The twosymbolson the leftare just there to identify the trebleand the bass sections of the stave becausesome instrumentsdon’tneedthisenormousrangeofnotesandonlyusethetreble(e.g.,violin)orbass(e.g.,cello)partfortheirwrittenmusic.Thesymbolsarecalledthetrebleclefandthebassclef.

Splitting thestave into twoparts leavesonenote,aC,between the twosections.This is the famous“middleC”youhaveheard about—it’s themiddle note on a piano as well. Middle C has no special musicalsignificance—it’s just a convenient referencepoint. Musicians, forexample, will say things like “I can’t sing this twaddle—my singingrangeisonlyuptotheGabovemiddleC.WhodoyouthinkIam?FreddybloodyMercury?”Intheillustrationbelowyoucanseethefirstlinesoftwoofthesongs

wehavebeenusingforreferencethroughoutthisbook.Ihaveonlyusedthetreblepartofthestavebecause—forthesetunes—Idon’tneedthebigrangeinpitchwhichbothstaveswouldgiveme.

The first lines of “BaaBaaBlack Sheep” and“ForHe’s a JollyGoodFellow.”

Wewilllookathowrhythmsandnotesofdifferentlengtharenoteddowninaminute,but first let’s lookathowtheverticalpositionof thenotestellsushowthepitchofatunegoesupanddown.Ifyousingthesongswhilelookingatthewrittennotesyouwillnoticethatthenotesgoupanddown the ladder, just as your voice does as the songs progress. I havestartedbothsongsonthesamenotesothatyoucancomparethemeasily.Ifyouhumthesesongsyouwillnoticethatbothofthembeginwithnotesof the samepitch and then there is a big leapup to “black”or a smalljumpupto“he’s,”dependingonwhichsongyouarehumming.Ineverycase themusical jump you hear is accurately identified by the verticalpositionofthenotesonthewrittenstave.Remember,asIsaidinchapter2, youdon’t need to start on the correct note (“C” in this case) tosingwell—unless you are being accompanied on an instrument. The mostimportant thing is the size of the jumps in the tune.It takes a lot oftrainingtobeabletolookatanewtuneandsingthejumpscorrectlyjustbyreadingthemusic—buttheexactinformationisallthere.

KeysignaturesIn the last chapter we discussed the fact that different keys involvedifferentnotes.Forexample,thekeyofAmajorincludes thenotesA,B,

C#,D,E,F#andG#.Ifacomposeriswritinginthiskeyhedoesn’twanttobebotheredwithputtingasharpsigninfrontofeveryindividualF#,C# andG# so hewrites a general instruction at the beginning of everyline of the music—calledthe key signature. The key signature of Amajor,withtheinstructiontoplayalltheFs,CsandGsasF#,C#andG#,lookslikethis:

ThekeysignatureofthekeyofAmajor.ThethreesharpsignsarewrittenonthelineswhichrepresentthenotesF,Cand G(readinglefttoright).Thisisageneral instructionwhichmeans“EveryF,CandGshouldbeplayedasF#,C#andG#.”

Writingdownrhythms

Differentlengthsofnote

Our two songs involve notes of various lengths and we use differentsymbols to indicate how long each note is compared totheothers.Thenote symbols and their nameswere agreed upon centuries ago and arelisted below.As you can see, the notesget shorter in a very organizedway:westartwithaverylongnote(or“breve”)anddivideit inhalf toget a half note (or semibreve),then continuedividing the lengthof thenotes in half to get shorter and shorter notes. Nowadays we also talkabout“wholenotes”and“quarternotes”and,justtoconfuseeveryone,ithas come to be generally accepted that the semibreve, not thebreve,shouldbecountedasawholenote—asyoucanseeintheillustration.

Symbol Name

Breve

Semibreve(wholenote)

Minim(halfnote)

Crotchet(quarternote)

Quaver(eighthnote)

Semiquaver(sixteenthnote)

Demisemiquaver

Hemidemisemiquaver(no,Iamnotjoking)

Alistofthedifferentsymbolsfornotesofdifferentlengths.Eachnoteistwiceaslongastheonebelowit.

If this“halving”systemwasallwehad todescribe the lengthofnotes,thenourmusicwouldberatherdullrhythmically,sowehaveacoupleofadditionstogiveusmoreflexibility:

1.Adotwrittenimmediatelyafteranotemeans“thisnoteshouldsoundoneandahalftimesaslongasnormal”(youcanseesuchadotafterthe

note for “fe” in “fellow”). A double dot after the note is much lesscommonbutmeans“thisnoteshouldsoundforoneandthreequartersaslongasusual.”2.Youcanwriteasmall“3”aboveagroupofthreenotestoindicatethat“these threenotesshould takeupthesameamountoftimeastwonoteswouldnormally.”Thisisafairlycommondeviceandyouwillhavehearditinactionmanytimes.Ratherlesscommonisthewritingof“5”aboveagroupoffivenotes,oranyothersimilarcombination. Ineverycase themessageis, “thisgroupofnotes shouldbesqueezed into theamountoftimeallowedforagroupofthissizeminusone,”i.e.,5shouldonly takeas longas4usuallywould,13shouldtakeas longas12usuallywould,etc.

Sometimesnotesarewrittenasindividuals(thisiscommonforsinging)butmoreoftentheshorternotesarejoinedtootherstomakelittlegroups,asyoucanseeinthesongs.Thisjoiningtogetherdoesn’taffectthelengthofthenote—itjusthelpsthemusiciantoreadthemusic.

Theshorternotesareusuallyjoinedtogetherbytheir“tails”ratherthanwrittenindividually.Thetwoquaversdrawnabove(ontheleft)eachhaveasingletailandwouldbejoinedbyasinglestraightline(asontherightoftheillustration).Semiquavershavetwotails,sotheyarejoinedbytwolines,andsoon.

Lookingbacktothenotesfor“BaaBaaBlackSheep,”andreferringtothelistabove,youcanseethatthenotesfor“have”and“you”arehalfaslongasthosefor“black”and“sheep,”whichare,inturn,halfaslongasthe note for “wool.”You might have thought that the notes you were

singingwerejustrandomlylongerorshorter—butyouareinfactsingingnoteswhoselengthsarecloselyrelatedtoeachother.

Stressoremphasis:theuseofbarlines

“BaaBaaBlackSheep” is a simple song but itwould be simple to thepoint of dullness if all the noteswere the same lengthand they all hadequalemphasis.Youwillnoticethatthereareverticallinesdrawnonthestave at a regular distance apart,which do not have any note or soundassociatedwith them. These are called bar lines. The distance betweentwobarlines(wherewewritethenotes)istechnicallycalledameasure—buteveryoneI’veevermetcallsitabarsothat’sthewordI’lluse.Oneoftheconventionsofwrittenmusicisthatthefirstnoteafterabar

line is given extra emphasis, or stress.When yousing “BaaBaaBlackSheep”youstressthefirst“Baa,”theword“have”andthefirst“yes.”Inthewrittenversionofthemusic,thesewordsappearjustafterabarline.If you haven’t noticed that you emphasize in this way, try singing thesongwith deliberate stress on “sheep” and “any.” It all sounds a bitMontyPython,doesn’tit?Nowsingitagainwiththeemphasiswhere itshouldbe—on“Baa”and“have.”Youmaynowbeover-emphasizingbutthestressisintherightplace—justafterthebarline—soitsoundsOK.Now,without lookingat thewrittenmusic, sing the first lineof“For

He’saJollyGoodFellow”acoupleof times. It’sonlysixwords,but itinvolveseightnotes:For,he’s,a,jo,lly,good,fe,llow.Imaginethatyouaresingingthesonginafunny/dramaticwaytoafriend.Forextraeffectyou have brought a cymbalwith you. The noise from a cymbal lasts alongtimesoyouwillonlyhititonceineverylineofthesong.Singthesongaloudacoupleoftimesandimaginewhichoftheeightsoundsyouwould choose to hit the cymbal on.Will it be “For,” “he’s,” “a,” “jo,”“lly,” “good,” “fe” or “llow?” Using my mysterious powers, I canconfidentlytellyouthatyouwillhavechosentomakeyourbigcrashingnoiseoneither“he’s”or“fe.”Nowhavealookatthemusic—yes,“he’s”and“fe”arebothimmediatelyafterabarline.

Inmanycaseswewouldautomaticallychoosethefirstnoteofthesongas one of the notes to be emphasized. In “Baa Baa BlackSheep,” forexample,youwouldhaveclashedyourcymbalonthefirstword,“Baa,”ortheword“have.”Inthecaseof“Forhe’s…,”however,wewouldnotchoosethefirstnote“For”becauseitdoesnotcomeimmediatelyafterabarline—thesongdoesnotstartatthebeginningofabar.Justinfrontoftheword“For”thereiswhatmusicianscalla“rest,”amark(inthiscasetwomarks) indicating that the first part of the bar is silent. This maysounda littleweird—startinga tunewithasilence—butwedo it togetall thestresses in thesongor tune tofall in thecorrectplace, justafterthe bar lines. Hereare a few examples of songs with the accentedsyllablesprintedinboldtype.Tuneswhichstartatthebeginningofabar:

Twinkle,TwinkleLittleStar(TwinkleTwinkleLittleStar…)FrèreJacques(FrèreJacquesFrèreJacquesdormezvous…)LondonBridgeisFallingDown(LondonBridgeis…)

Tuneswhichdon’tstartatthebeginningofabar:

WhentheSaintsComeMarchingIn(Oh,whentheSaints…)OnTopofOldSmoky(OntopofOldSmoky…)AuldLangSyne(Shouldoldacquaintancebeforgot…)Greensleeves(Alasmylove…)

Ifyouever see these tuneswrittendownyouwill see that thebar linescomeimmediatelybeforethesyllablesIhavehighlighted.

Dividingupthebar—timesignaturesYouwillnotice thatour two tunesbeginwithnumberswhich look likefractions. These numbers (called thetime signature) tell the musicianhowmany “beats” there are to each bar and, roughly, how long those

beatsare.

Howmanybeatstothebar?Theuppernumberinthetimesignature

Theuppernumberinatimesignatureisthemostimportantone—itgivesyouthemeterofthemusic,thatis,howmanybeatstherearetothebar.Let’stakethetwomostcommonvaluesforthisnumber:3or4(4isbyfarthemostcommon).Ifthetimesignaturehasanuppernumberof3thentheoverallpulseof

the music will be:one two three,one two three—like a waltz. Theredoesn’thavetobeanoteplayedforeveryoneofthethreebeats,andthetune may sometimesinvolvemore than one note per beat; in any caseyourmindwillretainthissenseofapatternofthreebeats.Similarly, if themusichasa4as the topnumberof the timesignature,the music retains an overall “one two three four,one two three four”rhythmicpulsenomatterhowmanynotesareplayedduringeachpulse.Mostpeoplewhohavenothadanymusicaltrainingfindthisdifficulttounderstand.Whenaskedtoclapouttherhythmicbeatofafamiliartunetheytendtoclaponcepernotelikethis:

Baa baa black sheep haveyouan-ywool?

clap clap clap clap clapclapclapclapclap

Inthiscaseyougetfourevenlyspacedclapsfollowedbyfivefasterones.Amusician,askedtoclapoutthebasicrhythm,woulddoitthisway:

Baa baa black sheep haveyouan-y wool?

clap clap clap clap clapclap clap clap

Nowwegeteightequallyspacedclaps:themusicianclapsregularlyevenwhen there ismore thanonenoteperbeat (“haveyou”and“any”), and

keeps clapping at the same rate through long notes or silences (in thiscasethereisaone-beatsilencebetweentheendof“wool”andthe“yes”whichfollowsit).Ifweaskthemusiciantoemphasizethenoteatthebeginningofeachbarwewouldget:

Baa baa black sheep haveyouan-y wool?

clap clap clap clap clapclap clap clap

Thistellsusthatthismusichasfourbeatstothebar.Askingthemusiciantodothesamejobfor“America,”wewouldhear:

My coun try, ’tis ofthee sweet land

clap clap clap clap clap clap clap clap

Herewe can see that the beats come in groups of three—so the uppernumberinthetimesignaturewillbeathree.Themostcommontimesignature(whichcoversthevastmajorityofpopmusic and most classics) divides the bar up into fourbeats—here is aslightlymorecomplicatedexamplethan“BaaBaaBlackSheep”:

OhwhentheSaints OhwhentheSaints

clapclap clap clap clapclap clap

Whateverthetimesignature,words(notes)sometimesoccurbetweenthebeats (“Oh” and “the” from “When the Saints,” and “of”from“America”); sometimes notes last longer than one beat (“tis” and“Saints”); and sometimes a beat happenswhen there isno note (before“Oh”).

Ifthepieceofmusichasthreebeatstothebar,thenthefirstbeatisthestrongoneandtheothertwoareweaker(onetwothree,onetwothree).Inthecaseoffourbeatstothebar,thefirstbeatisthestrongestbutthethirdbeat (thehalfwaypoint inthebar)isthenextstrongest.Thesecondandfourthbeatsarebothweakbycomparison—sothestress inafour-beat-to-the-barpieceis:onetwothreefour,onetwothreefour.Anothercaseofsplittingthebarinhalfoccursiftherearesixbeatsto

the bar—which is common in Irish jigs.As you cansee in thewrittenexample,“ForHe’saJollyGoodFellow”hassixbeatstothebar.Togettheemphasiscorrect, this timesignatureisusuallycountedaloudin thefollowingway:onetwothreetwotwothree,onetwothreetwotwothree.The second two (in italics in themiddleof thebar) is stressed,butnotquiteasmuchastheone—forhe’sajollygoodfellow.Four beats to the bar is, as I mentioned, the most popular case in

Westernmusic of any sort and three beats (mostly waltzes), two beats(mostly marches) and six beats (mostly jigs) are used in most of theremaining cases—all other numbers are fairlyrare. Modern jazz andmodern classical music sometimes make a point of using five, seven,eleven, or more beats to the bar(sometimes just to be clever andunusual),butthereareonlyafewreallypopularsuccesses:

five beats to the bar—“Take 5” by theDaveBrubeckQuartet and“Mars”fromThePlanetsbyGustavHolst;seven beats to the bar—“Money” fromDark Side of theMoon byPinkFloydandvariousbitsofTheRiteofSpringbyIgorStravinsky(whichalsocontainsmanyotherunusualrhythms);ninebeatstothebar—usedinaparticulartypeofIrishjig,calledaslipjig,whichdividesthebarupintothreesetsofthreebeats(onetwothree,twotwothree,twotwothree).

Syncopation

Syncopationisamethodofaddinganextralayerofinteresttomusicby

deliberately emphasizing beats which would normallybe unimportant.Therearesometypesofmusicwhichdeliberatelyavoidstressingthefirstbeatofthebarinordertogivethemusicaparticularfeel.Somerockandpop songs keep the “one twothree four” emphasis for the tune butdeliberatelyemphasizebeatstwoandfourwiththebassguitaranddrums,a technique knownas “back beat” which was very popular with theBeatles(e.g.,“Can’tBuyMeLove”).Reggaemusictakesthisideaevenfurtherbyhavingthefirstbeatofthebarleftalmostsilentbytherhythmsectionof theband.Ingeneral, thedrummerandbassguitarplayer inareggaebandbothemphasizebeatnumber3andtherhythmguitaristplaysbeats2and4.Back beat, rock and reggae use specific types of syncopation which

form part of their identity, but syncopation is used tosome extent innearly all forms of music. You can even syncopate “Baa Baa BlackSheep”toaddinteresttoyourperformance:“BaaBaaBlackSheepHaveYouAnyWool…”Syncopationdoesn’tevenneedtoinvolveafullbeatofthemusic.You

can emphasize just a part of a beat—“Have you any wool?”Whereveryoucomeacrossit,syncopationmakesthemusicsoundlesspredictableandmoresophisticated.

Whatlengtharethebeats?Thelowernumberofthetimesignature

Thelowernumberofthetimesignatureisalwaysa2,4,8,16or32.Ofthese,4isbyfarthemostcommonand,really,couldbeusedinallcases.Thereasonforthisisthat,althoughthechoiceoflowernumberchangeshowthemusic lookson theprintedpage,itdoesn’thaveanyrealeffectonhowthemusicsounds.Thisoddfactneedssomeexplanation—soI’dbettergetonwithit.Iamgoingtousetheterm“wholenote”ratherthan“semibreve”inthe

followingdiscussiontokeepthingsasclearaspossible.Whenacomposerwritesa“3”overan“8”asthetimesignature,sheis

sayingthateachbarwillhavethreebeats,eachofwhichisoneeighthof

awholenote long—so“3”over“8”simplymeans“threeeighthsof thelength of awhole note per bar,please.” Similarly, 5 over 4means thateachbarwillcontainfivebeatswhichareallonequarterofawholenotelong(“fivequartersofthelengthofawholenoteperbar,please”).Theproblemisthatnoonehaseversaidhowlongawholenoteis.In

themostcommontimesignature (4over4),eachbarisonewholenotelong(fourquarters)—butifyoupicktwentydifferentpiecesofmusicandmeasure how long the bars arewith a stopwatch youwill have twentydifferent results.Althoughnooneknowshow long awholenote is,weknow the approximaterange involved—awhole note (equal to a bar of4/4 time)willgenerallybeshorter thansixsecondsbut longer thanonesecond.Thisis,ofcourse,anenormousrange—somusiciansneedmoreinformationthanjust the timesignature if theyare toplaythemusicasthecomposerintended.Musiciansgetabitofhelpfromawordprintedabovethebeginningof

the music which tells you (usually in Italian or German)how fast themusicshouldbeplayed—“presto”meansfastand“adagio”meansslow.But these are, of course, rather vague terms—two different performersmightdifferinspeedby50percentormore.Inanattempttominimizevagueness,composersoftenputmetronome

marksnexttothespeed-indicatingword.Theywill,forexample,drawanoteof a certain length (e.g., ) followedbyan“=”signfollowedbyanumber(e.g.,120).Thenumbertellsthemusicianhowmanyofthattypeofnotewouldlastforoneminute,so“ =120”meansthatyoucouldfit120oftheseeighthnotesintooneminute—orthateach note lasts forhalf a second. (Ametronome is just a devicewhich you set to tick asslowlyorasquicklyasyouwantitto—inthiscaseyouwould,ofcourse,set it to tick120 timesperminuteand thenplayalong in timewith theticks.)The use of metronome marks sounds logical until you find out that

most professionalmusiciansdon’t takemuchnotice of them—theyjustplayas fastor slowlyas theywant to.For example, Ihavea coupleof

recordingsof thefamousguitarconcertobyRodrigoinfrontofme(theConcierto deAranjuez) and the CD boxes tell me that JohnWilliamsplaystheromanticsecondmovementinjustundertenminutesbutPepeRomerocompletesthesamepieceinjustovertwelveminutes(that’sa20percentdifference,andithasnothingtodowithhowwelltheybothplaytheir instruments; Pepe just likes the extra romance of playing itmoreslowly). The piece has ametronomemarking at the beginning but alsoincludesvagueinstructionstospeedupandslowdownatvariouspoints—so there is no “correct” completion time. It is also well known thatmanycomposerscannotdecideonthecorrectnumberforthemetronomemark and, if they have been recorded, often go considerably faster orslowerthantheirowninstructionsindicate.Sotherewehaveit—thebottomnumberofthetimesignaturegivesus

little or no information about how the music sounds.You could, forexample,writeapiecein3over8andmarkit“slow”orwriteitin3over4andmarkit“fast”—themusicwouldsoundthesame.Infact,themusicin 3 over 4might be played fasterthan themusic in 3 over 8 because“fast”and“slow”aresuchvagueterms.Nomatterhowwelltrainedyouareyoucannottellwhetherthemodernjazzpieceyouarelisteningtoisin3/4or3/8(ortell thedifferencebetween5/4and5/16).Ifyouhad tomakeabet,youronlyguidewouldbethat,traditionally,biggernumberson the bottom of the time signature are usuallyassociated with fastermusic.Forexample,aromanticViennesewaltzwillalmostcertainlybewritten with a time signatureof 3/4 rather than 3/8, 3/16 or 3/2.Similarly,anIrishjigwillgenerallybewrittenin6/8ratherthan6/4or6/16.Thisquickguidetohowwrittenmusicworkscanbereduceddownto

fivepoints.

•Theverticalpositionofthenotestellsyouthesizeofthejumpsinthetune.•Notesofdifferentlengthshavedifferentsymbols.

• Notes which appear immediately after the bar line are (usually)emphasizedorstressed.•Thetopnumberof thetimesignaturetellsyouhowmanybeats tothebar.•Thelengthofthebeatsisgivenapproximatelybythelowernumberofthetimesignaturetogetherwithawordindicatingthespeedofthepiece.Sometimesthisspeedinformationisgivenmoreaccuratelyintheformofametronomemark.

DancingandrhythmIfwe go back tomy point that rhythm can be divided up into rhythm,tempo and meter, it may come as a surprise that rhythmis the leastimportant of these three components where dancing is concerned. Thelengths of the different notes in the music are far less important to adancerthantempoandmeter.Thetempoofthemusictellsyouhowfasttodanceandthemetertellsyouwhattypeofdancingyouareinvolvedin.ThevastmajorityofWesternmoderndancemusicis inameteroffourbeatstothebarwithasimple1,2,3,4countandsotheonlyimportantvariableisthetempo.Thereisawidelyheldmisconceptionthatyourheartratetriestomatch

thepulserateofthemusicyouarelisteningto.Thisbeliefprobablyarosebecausetherangeofpulseratesformusicandhumanbeingsissimilar.The tempo of music is usuallybetween 40 and 160 beats per minute(bpm),andhumanpulse rates rangefromabout60fora relaxedpersonwith a slower thanaverage heart, up to above 150 bpm for a healthyyoungadultdancinghissocksoff.Ifyouareahealthyyoungadultdancinginaclub,themusicwillhave

atempobetween90and140bpm,andyourheartwillbebattingalongatasimilar rate.But theexcitingnoiseof themusic isnotwhat’sdrivingyourheartrateup—it’sthedancing.Themusicwillhaveanaveragebeatrateofapproximately120bpmbecause this isasustainable, funrateat

whichtobewagglingyourvariousbitsabout.Youcanmoveyourbodyand limbs twiceasecond(120bpm)foranhourorsowithoutanythingsnappingoff.Yourheartwillberacingalong,fasterthannormalbecauseyouareconsumingalotofenergy.Next timeyouareinaclub,trytakingthe pulse of a friend who is dancing and comparing it to one who isslumpedatthebar.Thedancerwillhaveaheartrateclosetothepulseofthemusic,buttheslumper’sheartwillbemuchslower.Butdon’t forget—weslumpersneedlovetoo.Of course, dancing is nothing new, and people have always enjoyed

shakingtheirbits inthegeneraldirectionofpeopletheyfancy.Dancingusually involves raising your heart rate and thewaltz does this in twoways. The first reason for an increasedpulse is the physical effortinvolved.Awaltzhasatempoofapproximately100bpm.Thisisalowertempo than the 120 ofthe music found in the clubs today, probablybecauseyouhavemoreworktodo.Twopeoplehavetocoordinatetheirmovementsandthensteerthemselvesaroundthedancefloorratherthanmerely hopping up and down in one spot. It’s also fairly certain thatsweatinglikeapigusedtobelessfashionablethanitpresentlyis.Thesecondheartrateacceleratorofthewaltzisthereasonwhyitwas

almostbannedwhenitwasfirst introducedintopolitesociety—itwasamethodofactuallygettingyourhandsonthebodyofyourbeloved,orbe-fancied.Even the torridwaltz,however, isnotquiteas“handson”asamuch earlier dance with a three-beat meter, the volta, which was afavorite of QueenElizabeth I. The volta involves a lot of lifting andlowering of the woman, with plenty of opportunity for mutuallyenjoyable,accidental hand slippage. If enough of you readers vote infavor,wecouldtrytogetitreinstatedasthebiggestdancecrazearound,asitwasinLondoninthelate1500s.

RhythmandpolyrhythmIfyouaresittingandlisteningtomusic,ratherthandancing,youhavea

muchdeeperappreciationofthesubtletiesofrhythm.Meter,rhythmandtempoallplay theirpart inourenjoyment.Althoughourpulse ratesdonot linkthemselvestothetempo,wecertainlyfindslowertemposmorerelaxingandfasteronesmoreexciting.Thistensionisprobablylinkedtoourdislikeofuncertainty,particularlyourfearofnotbeingabletocopewithasituation.Ifthesoundswearehearingaremovingatwalkingpaceorslower,thenthereisnoneedforanxiety.Ifthingsarerushingalongwemightneedtobepreparedtorunawayorprotectourselves.Onegoodwayofgetting a lot of emotionout of apieceofmusic is

through a technique calledrubato. The word means “robbed.” Themusicianstealsabitof timeoffacoupleofnotes inorder tomake thenotebeforeorafterthemlastalittlelonger.Insteadofhearingthenoteswithasteadyrhythm,“Daa,Daa,Daa,Daa,Daa,Daa,”wegettheeffectofarushuptoalongernote,“Daa,Daa,Daa,Da-Da-Daaaa,”whichaddsdramaandromancetothemusic.Changesofmeterareagoodwayofkeepingour interest levelshigh,

andunusualmeterssuchassevenbeatstothebaralsokeepusinterestedbecausetheysoundunsettledorincomplete.ButalotofWesternmusicisnot very rhythmically adventurousor sophisticated.Themusic tends toconcentrate on four or three beats to the bar with simple, regular sub-divisionsofthesebeats.AfricanandAsianmusicaltraditionsandseveralothers often employ greater rhythmic complexity, including the useofpolyrhythms.Polyrhythminvolvesplayingtwoormorenon-collaborativerhythmsat

once.Toexplainwhat thismeans, let’s taketheexampleofyouandmetappingoutrhythmsonyourdining-roomtable.Ifwebothtaptogetheringroupsoffour,wearejusttappingthesamerhythm.IfItapeighttimesto every four of yours, then our rhythms will collaborate—we will behittingthetableatthesametimeatregular,frequentintervals,andeveryextratapofminewillfitexactlyintothegapsbetweenyours.If,on theotherhand,Itapthetablefivetimesforeverytwelveofyours,thenourtapswillnotcoincideveryoften,andmostofthetimemytapswillnotbe

synchronized with yours in any obvious way. The two rhythms are nolongercollaborating.Wearetappingpolyrhythmically.The idea of polyrhythms is not completely new to Western music.

Mozart used a pulsing accompaniment based on threes againsta tunebasedontwosinthesecondmovementofhisPianoConcertoNo.21(thispiece isnowadaysknownas “ElviraMadigan”because itwasused inafilmof thatname).Morerecently, some jazzand rockbandshaveusedpolyrhythms and I think that they will gradually become morecommonplace. This will beuseful for people like me, because whenpeopletellmeI’mdancingreallybadly,Icanjustclaimtobedancingtotheotherhalfofthepolyrhythm.

11.MakingMusic

ThemythofmusicalityFor some reason, a lot of people think that if you haven’t studied amusicalinstrumentbythetimeyouaretwentythenitisalreadytoolate.Also,peoplewhodidn’t studymusicaschildren,orwhohadahorribletime learning an instrument whenthey were kids, often declarethemselvestobe“unmusical”buttheywould“lovetobeabletoplayaninstrument.”Ifyouasksuchpeopleaboutanyotherskilltheywouldliketoacquire,suchasmakingpotsorknitting,theydon’tdeclarethemselvesto be “unpotterly” or “unknitty,” they quite sensibly say that theyprobablycoulddoitiftheyboughttheequipmentandtooksomelessons.They realize that they would probably never be able to compete withprofessionalsbutcouldeventuallyproduceworthwhilestuffandhavefunintheprocess.Thereisgeneralagreementthatanyonecanacquirealmostanyskillto

some level of competence. But music is considered aspecial case—apparentlyyou’reeithermusicallytalentedoryou’renot.Thankfullythisviewisentirelywrong:playingamusicalinstrumentisjustaskilltobelearned like any other. Some people (especially children) pick up theskillsinvolvedfasterthanothers(whichistrueofanyskill),buteveryonegetsbetterwithtimeandeffort.Anothermythaboutmusicisthatittakesyearstolearnaninstrument.

Thisisonlytrueifyouhaveveryhighexpectations.IfyouwanttoplayBeethovensonatasinpublic,thenyes,itwilltakemorethantenyearsandyouwill have to practice formore than an hour a day. If, on the otherhand, you want to play aBobDylan song at a campfire singalong youcouldprobablybereadyinamonthifyoupracticedforafewminutesonmost days.By the end of the year you could have more than a dozensongswhichyoucouldplay. It is alsovery important to rememberthat

learninganinstrumentisalotoffunfromthebeginning.Theonlypainintheneckisthatitinvolvesalotofrepetition—buteventhatisOKwhenyoucanhearyourselfgettingbetterandbetter.Oneofthemostdauntingthingsaboutmusiciansisthewaytheyseem

tobeabletorememberaninhumanamountofnotesandregurgitatethemat will. This is particularly true of musicians playing classical musicfrommemory:sometimesthemusicianhastoproducethousandsofnotesin exactly the correct order and if they get even one wrong it will benoticedbytheaudience.Ifanon-musicianseesthissortoffeatitputsheroff the idea of learning an instrument because she is sure that hermemory(andfingers)couldn’tworkthatwell.Withoutinanywaydiminishingtheachievementofsuchperformers,it

is useful to know that they are being assisted by somethingknown as“muscularmemory.”Obviouslymusclescan’tactuallyrememberthings,butcomplexsequencesofmuscularmovementcanbestoredbythebrainasasinglememory.Ifthissoundsalittleunlikely,justthinkabouthowlittlemental effort andmemoryyouneed inorder to tieyourshoelaceseverymorning.Nexttimeyoutieyourlacesjustwatchyourfingers—it’sa namazingly complicated set of muscular movements, but your brainjust sends out a single instruction, “tie shoelaces now.”A trainedmusician can render a whole piece of music down into a sequence oflinked“shoelace-tying”setsofinstructions.Thebrainisnotsendingoutinstructions for each fingermovement; it’s saying “next comes the bitwith the jiggle in themiddle; now there’s the bit with the three loudchords.”Gettingyourbraintodothisforapieceofmusicrequiresalotof repetition or practice—but there is nothing magical about it. Themagicisinthesoundswecreateandhowpeoplerespondtothem.So those of you who have been saying “I’d love to play a musical

instrumentbut I’mjustnotmusical”cangodownto themusicshoponSaturday and buy an instrument. Everyone is “musical”—becoming amusician is simply amatter of learning a skill.Youwillbeworse thansomeandbetterthanothersbutyouwillbeamusician.

Ifyouhavedecidedtotaketheplunge,thefollowingnotesmighthelpyou choose themost appropriate instrument—all instrumentsinvolve alearningprocessbutsomearekindertothebeginner(andtheirneighbors)thanothers.

ChoosinganinstrumentThereare far toomany instruments in theworld forme to list themallhere,butIcangiveyousomepointersaboutsomeofthemorecommonones.Musical instruments can be categorized in a number of differentways. For example, there are instrumentswhich can only produce onenote at a time (such as flutes), ones onwhich it is difficult to producemore than one note ata time (suchasviolins) and thoseonwhich it iseasytoproducelotsofnotesatonce(suchaspianos).Anothercategorizationwhichmaybeusefultoabeginneristhatsome

instruments have definite places where you put yourfingers to get acertain note (e.g., pianos, flutes, guitars), and some instruments don’t(e.g., violins and trombones). Forthose of you who have never held aviolinortrombone,thismayneedsomeexplanation.To take the simplest case of an instrument with set places for your

fingersforeachnote,lookatthepiano.IntheillustrationbelowyoucanseethatifIwanttoplaythenotewecall“middleC”Ijusthavetopressthe correct key. Pressing thatkey will always produce that note and Ican’t get that note by pressing any other key.Because the key itself isquite largecomparedtomyfingertip,Idon’thavetobeveryaccurateinhittingit,solongasImissthekeysoneithersideofit.(Bytheway,I’massumingthatthepianohasbeentuned.)

To hear the note “middle C” on a piano, all I have to do is press thecorrectkeywithonefinger.

Now let’s have a look at how you get notes from a guitar. In theillustration opposite, you can see that I have shortenedthe string I amabout to pluckbypressingone ofmy fingers on the neckof the guitarbehind one of the frets. When I pluckthe string, I will get the noterelevanttothelengthofthestringbetweenthefretandthebridgeoftheguitar.Onceagain,Idon’thavetobeextremelyaccurate—myfingercanbe right up against the fret (as in the left-hand photo below) or a fewmillimetersawayfromit (as in themiddlephoto).Thenotewillbe thesame in both cases because the position of the fretdetermines thenoteproduced,nottheexactpositionofmyfinger.

TogetachosennoteonaguitarIneedtwofingers.Onefingerplucksthestring and a finger from the other hand presses the string against theneckoftheguitartotrapitoveroneofthefrets.Asisthecasewiththepiano,myfingersonlyneedtobeaccuratewithinafewmillimeters.Thefinger positions shown in the two illustrations produce the same notebecause—eventhoughmy finger hasmoved—the fret stays in the sameplace. The final photo shows the bridge of the guitar, which holds theotherendofthestrings.

Ifwenowlookataviolin,youcanseethattherearenofrets—thepitchofthenoteproducedisdeterminedbytheexactpositionofyourfingerasittrapsthestringagainsttheneckandmakesitshorter.Whereveryouputyour finger, you geta note—but only a very small percentage of thosenoteswillbe theonesyouwant. In thiscase thepositionofyourfingerhastobeaccuratewithinamillimeterorso.

Thelackoffretsonaviolinneckmeansthatitismuchmoredifficultforabeginnertoidentifywheretoputtheirfingerdowntoshortenthestring.Also,thepositionofthefingermustbeaccuratetowithinamillimeterorso.

Ifyouwanttoplaythefirstthreenotesof“ThreeBlindMice”onapiano,youusejustonefingertodingout“E,D,C”—ittakesabouthalfaminuteto learnandyoucansoundproficient in twominutes.Toplay thesamenotesonaguitarinvolvesbothhands(oneforplucking,oneforthefrets).Ittakesalittlelongertolearnandtobecomeproficient,becausefretsarenot as easy to use as pianokeys.Nevertheless you should bemaking aconvincing “Three Blind Mice” noise after abouttwenty minutes: youlearnwhich fretsyouhave togetyour fingersbehind foreachnoteandyouonlyhavetobeaccurateinyourfingerplacementtothenearestfewmillimeters.Thesituationisentirelydifferentifyounowtrytoplaythetuneona

violin, even if we ignore the fact that using theviolin bow is prettydifficult in the first place. Let’s imagine that you have had weeks oftraining on the use of the bow,but this is the first time you have triedshortening the strings by pressing them against the neck of theinstrument. Thereare no frets and there is nothing to use as a visualguide, so it’s very difficult to knowwhere to put downyour fingers. If

youpressyourfingerdowneventwomillimetersawayfromthecorrectplaceyouwillproduceanotewhich isnoticeablywrong.Also,becauseyouhavetoholdtheinstrumentupunderyourchin,you’relookingalongtheneckandit’sdifficulttojudgethesedistancesproperly.Takingallthisintoaccount,Ithinkit’sperfectlyreasonabletodeclare

that the guitar and piano are kinder to total beginnersthan the violin.However, don’t bemisled into thinking that a trained violinist ismoreskilled thana trainedpianistorguitarist—nearlyall instrumentsrequiresimilar amountsof skillonceyouhaveprogressedbeyond thebeginnerstage.“Why,”youmightwellask,“iftheviolinismoredifficulttostartwith, doesn’t it remainmore difficult?” The answer to thisquestion isthatmusicaltrainingisdesignedtogetthebestoutofeveryinstrument.Withinafewweeksatraineepianistwillbeaskedtoplaymorethanonenoteatoncemostofthetime.Bythetimehehasbeenlearningacoupleof years he may be playing four, five or even more notesat the sametime.Violinistswillonlyrarelybeaskedtoplaymorethanonenoteatatimeandwillnotattempteventwotogetheruntiltheyhavebeentrainingforseveralyears,becauseitismuchmoredifficulttodoontheviolin.Ineach casethemusicianistrainedwithinthelimitsoftheinstrumentsheistryingtomaster.Which instrument should you take up?Well, of course, that’s up to

you.Iwishyouluckwhicheveroneyouchoose.Myonlyadviceisthat,ifyouareovertwentyandyou’veneverplayedaninstrumentbefore,don’tputyourselfoffbystartingwithoneoftheinstrumentswhicharereallytough on total beginners—the slide trombone, French horn, bassoon,violin,violaandcellofallintothiscategory.Slide trombones, for example, make a marvelous noise but they

involvemoreskillthanmostinstrumentsforthebeginner.Tostartwith,you have to learn how to use the sliding bent tube which makes theinstrument longer or shorter—a longer tubegives a lower fundamentalfrequency.Therearesevendifferentcorrectpositionsforthisslidebutnoindication of wherethey are—you just have to practice getting it right.

Onceyouhavepushedtheslideintothecorrectposition,youcangetoneof about ten possible notes depending on the type of farting noise youmakewithyourlips—whichisdeterminedbyhowtightlyyoupressyourlips together and how hard you blow. These different notes are theharmonicsofthetubelengthyouchoosebymovingtheslide.Intheearlystagesoflearningitisveryeasytogetcompletelythewrongnote,eitherbyputtingtheslideinthewrongplace,orbyblowingtoohardorpursingyour lips in thewrongway. I have a lot of admiration forpeoplewholearnoneoftheinstrumentswhichareextratrickyforbeginners,butmyadmiration is tempered by NIMBYism—Iwouldn’t want a traineetrombonistlivingnextdoor.Ifyouwanttotakeupaninstrumentyoublowinto,Isuggeststarting

withtheflute,saxophoneortrumpet,instrumentswithclearpositionsforyourfingers.Youcanthenchangeinstrumentsafterafewmonthsifyouwant to. You might also want to consider portability and storage (it’seasier to store andcarry a clarinet thanaharp), andhowsatisfying theinstrumentis toplaysolo—becauseyouwillbepracticingonyourownmostof thetime.Forexample, thereisafarmoreinterestingrepertoireofprintedmusicforthesolopianothanthereisforanyotherinstrument.Bytheway,ifyoudodecidetogoforthepiano,Irecommendoneofthehigh-quality electronic keyboards rather than a real piano, because youcan practicewithheadphonesonwithoutdisturbingyourneighbors,andyoucanfoolaroundwithalltheothersoundstheymakeifyougetboredpracticing.Finally, I would suggest that you join an evening class or find a

teacher.You can make decent progress if you have a half-hour lessononceaweekorsoandthenpracticeforanhourorsoeveryweek.

Howdocomposerslearntocompose?Tomostnon-musicianstheprocessofcompositionistotallymysterious.Otherjobsorhobbiesseemprettystraightforwardbycomparison.Ifyou

spend a long time training, you can become a dentist, portrait painter,cranedriverorgardener—andthesortsofthingsyouwouldhavetostudyhaveverylittlemysterytothem.Training to composemusic of any sort always involves a lot of trial

anderror. If youare starting a rockbandwithyourfriendsyouusuallystartoffplayingotherpeople’smusic,buteventuallyyoumightstart towriteyourown.Thiscaneitherbeacollaborativethingormightinvolvejustonewriter.Initiallythemusicwillbeveryimitativeofyourfavoritemusicians, but eventually your own musical personality will comethrough.Thistypeofinformal“on-the-job”trainingforwritingmusicisverycommonforrockandpopmusicians.It is alsopossible to studycompositionat acollegeoruniversity.At

onepointIstudiedcomposition,andmyfriendsusedtoaskmewhatIdidwithmytutor—apartfromdrinktea.IsupposemostofthemthoughtthatIwouldthinkupatuneandthenmytutorandIwouldmessaboutwithituntil it became a piece of music. Nobody really understood how youcould train todo something as “artistic” as composition.Eventually, toexplainwhatwasactuallygoingon,Idevelopedthefollowinganalogy.Imagineyou are training to be aTVcomedy scriptwriter—you are a

fairlyamusingpersonandyouhavedevelopedsomewritingskills.Youhavethoughtupafunnysituationbutitjustdoesn’tworkverywellonceyouhavewrittenitdown.Ifyoutakethesketchtoyourtutor,shewilluseher experience to try to find ways of getting themaximum amount ofaudience pleasureout of your original idea. She will probably suggestchanges,suchas:

•maybeit’stoolongortooshort…•maybealltheinterestingstuffhappenstooearlyortoolate…•maybetherearetoomanyortoofewpeopleinvolved…•maybeyouneedtoremovealinewhichgivesthepunchlineawaytooearly—oraddonetomakethejokeclearer…

Thetutor(ifsheisanygood)willnotworkdirectlyonthepiecewithyou—butshewillsuggestspecificareasyoumightwanttolookat.Thisisbasicallyhowcompositionistaught—yougoinwithamusical

idea and the tutor assists youwith suggestions likethe ones above andalsohelpswith the technical issues. Inmusic thereare lotsof technicalissues. If you are writing forinstruments you don’t play yourself youneed to learna lotabout them if themusic is tobeplayable.Thereareobvious simple mistakes—“flutescan’t go that low”—and less obviousones—“this trumpeter’s lipswent completely numb about twominutesago.”Sothesortoftrainingyougetisprettystraightforward,andalotofit

issimilartothesortoftrainingyouwouldgetasascriptwriter—it’sallaboutcontentandtiming.As far as the original musical idea is concerned, that’s no great

mystery either.You don’t necessarily start with a tune—it might be arhythmor a “bass line” (a repetitive bass accompaniment). Itmight besomethingyoufoundyourselfhummingorsomethingyoumisplayedonthepiano.Forexample, theEnglishcomposerVaughanWilliamsbasedthe second movement of hisThird Symphony on a single mistake heheardanarmybuglermakewhilehewasworkingasanambulancedriverduringtheFirstWorldWar.Anyone can make up a tune. Just hum to yourself for a couple of

minutesandeventuallysomethingworthwhilewillpopout.Oryoucouldsitatthepianoplayingwithonefingerquiteslowly—occasionallytuneswillappear.Thedifficultyisnotinproducingtunes.It’sinrememberingthemandthendevelopingharmoniesand,finally,writing italldownorrecording it.Thisiswheremusicaltrainingisuseful;itwillhelpyoutorememberyourtuneandwriteitdown.Unlessyoucanrecordyour ideaorwriteitdown,itwillbedifficulttoworkonandimproveitand,inanycase,nobodyelsewilleverbeabletohear itbecauseyouwillprobablyforgetwhatyouwrote.Sowhetheryouarewritinganoperaorthenextrockclassic,thebasics

ofmusicalcompositiongolikethis:

1.Comeupwithoneortwo(generallyveryshort)musicalideas.2.Writethemdownorrecordthem(therearecomputerpackagestohelpyou).3 .Use them todevelopaccompanyingmusic (i.e., if you startedwith atune, try different accompaniments; if you started witha bass line,developatuneand/orchords).4.Writeitalldownorrecordit.5.Noworganizetheoveralltiming.Justlikeawell-toldjoke,doesitneedto be made longer by repeating bits? Does it needthirty seconds ofdroning,mysteriousintroductorymusic?6.Writeitalldownorrecordit.

And there you are—your own composition. At first you might onlyproduce themusical equivalent of “knock knock” jokes, buteventuallyyour stuffwill becomemore sophisticated and (hopefully) enjoyable toothers.(Ifyoumakeafortunefromfollowingthisadvice,pleasesendacheckfor5percentofyourannualincomemadeoutto“JohnPowell”—creditcardsarealsoacceptable.)Whileweareonthesubjectofcomposition,Iwouldliketoofferyoua

few notes on a subject which baffles a lot of peoplewhen they firstencounterclassicalmusic.

Whydoclassicalpieceshavesuchlong,complicatednames?

If you listen to any classical music station for an hour or so you arebound to hear the announcer say something like, “Thatwas the allegrofirstmovementfromMozart’sConcertoforPianoandOrchestraNo.17in G major, K453” or, “Next, we are going to hear Prokofiev’s PianoConcerto No. 3 in Cmajor, Opus 26.” This is one of the reasons that

many people find classicalmusic unapproachable—even if they hearsomethingtheylike,it’sdifficulttoknowhowtoaskforitinashop.Thepiecesneedtohavenamesifwearegoingtobuyarecordingordiscussthem—butwhydothenamesneedtobesocomplicated?Oneway to disentangle the origins of the names is to explain a few

examples.Let’sstartwiththeMozartoneabove.

Decoding“TheallegrofirstmovementfromMozart’sConcertoforPianoandOrchestraNo.17inGmajor,K453”

CONCERTOFORPIANOANDORCHESTRA

The two most common types of classical music which involve anorchestraarethesymphonyandtheconcerto.A full orchestra playing a symphony involves about a hundred

musicians but generally they don’t all play at the same time.Thecomposerchooseswhichinstrumentsdowhatatanygivenmoment.Ifthemusic is to soundwistful, the composermightwritea tune fora singleoboe, accompanied by violins and a harp. The same tune might bereintroduced later in a more dramaticsection played by brassinstruments,accompaniedbydrums.Thesechangesininstrumentaltonehelptosustainthelistener’sinterest.Theperformanceofasymphonycanthereforebedescribedasanorchestraallworking togetherasa team—passingthemusicalworkaroundandoccasionallyallplayingtogether.The only difference between a symphony and a concerto is that a

concertoalsoinvolvesasoloistwhositsorstandsatthefrontofthestageand shows off throughout the piece. The soloist might be playing anyinstrument (in this case it’s apianobut therearealsoconcertoswrittenforcello,guitar,trumpet,etc.),butthepointofthesoloinstrumentisthatit addsextra drama to themusic.The soloist doesmorework than anyothermusician,asherarelytakesabreak(healsogetspaidmore).Foraconcertothecomposermightwritemusicforstringsandsoloisttogether;followedbybrassandsoloist;soloistalone;fullorchestraalone;thenfull

orchestra with soloist, and so on. Musical “conversations” or even“arguments”canbesetupwherethesoloistisplayingonethingwhiletheorchestra is responding with something else. Basically the on/offrelationshipbetweenthesoloistandtheorchestramakesthemusicevenmorevaried than a symphony—andalsomore interesting towatch at aconcertbecauseyouhavea“staroftheshow.”Thisdescriptiononlyfitsconcertos written since around 1800. Before that time the word“concerto” justmeant“apieceofmusic,”whichmightinvolveasoloist(asinBach’sConcertoinAforViolinandOrchestra),ormightnot(as inBach’sBrandenburgConcertos).When we discuss a particular concerto, we usually refer to the solo

instrumentaswell as theorchestra, sowegetnames like“ConcertoforPianoandOrchestra.”

FIRSTMOVEMENT

Classicalmusicenthusiastsmightfindthefollowingprosaicdescriptionoftheorganizationalmotivesofcomposersverydifficult toaccept,butitis important to remember thatcomposershavealwaysneeded tohaveaprofessionalattitudetowardstheirmusic.Swanningaround,insistingthatyouarean“artist,”won’tpaytherent.Traditionally, classical music was written for live concerts, a

straightforward entertainment which resulted in the composerand themusiciansgettingpaidandeveryoneelsehavingagoodtimeforanhouror two.From thepointofviewofaworkingcomposer likeMozart, thefollowingtwoguidelinesareimportant:

1.Theorchestrashouldchangepieceseveryfewminutestokeepinterestlevels up—so the audience doesn’t start chatting, noddingoff, orplayingtic-tac-toe.

2.Thepiecesshouldbepresentedingroupsofthreeorfourtocutdownontheamountofdisruptionandeffortinvolvedinapplauding.

Fromthesetwofairlysimplerules,mostcomposersfromabout1750onhave presented three or four individual pieces of music(each betweenfiveandtwentyminutes long)asparts(ormovements)ofabiggerpiecewhichtheycallasymphony,concerto,orinthecaseofsoloinstruments,a sonata.There isa short silencebetweeneachmovementduringwhichyou are not supposed to clap—yet another source of confusion to thenewcomer.Youareonlysupposedtoapplaudattheveryend.Insomecasestheremightbeamusical linkbetweenthemovements,

but they can also be specifically designed to clash (inorder to keepinterest levels up). In the piece we are discussing there are threemovements: thefirst isabout thirteenminuteslong;thesecondisabouttenminutes;andthethirdisabouteightminutes.

ALLEGRO

Apartfromhavingdifferent tunes, themovementsareoftenpieceswithdifferent speeds: it is common (but not a rule) tostart with a fastmovement, then have a slow romanticmovement, and then finishwithanotherfastmovement.Themovementscanbereferredtoeitherbytheirnumber(first,second,etc.)orbytheirspeed,whichisusuallyindicatedinItalian,FrenchorGerman.Inthiscasetheword“allegro”issimplytheItalianfor“fast.”Havinggivenusthenumberofthemovement,ourradioannouncersdo

notneedtotellusthespeedaswell—buttheyoftendo.

MOZART

Obviouslyweneedtoknowthenameofthecomposerifwearetotrackthepiecedown.

NO.17

Mozart wrote over twenty piano concertos, so we need to knowwhichnumberitis.Theconcertosarenumberedintheorderinwhichhewrotethem.

INGMAJOR

ThisisatotallypointlesspieceofinformationunlessMozartonlyusedGmajor for one of his piano concertos—in which casethis informationcouldbeusedinsteadofthenumbertoidentifyit.Apartfromthisminorpoint I don’t know why everyoneinvolved in classical musicbroadcastingkeepstellinguswhatkeythingswerewrittenin—itmakesnodifferencetoanyofus.

K453

AmusichistoriancalledKöchel(pronounced“Kerkul”)spentalargepartof his life catalogingMozart’smusic and numberedevery piece in theorder it was composed. So now we refer to each piece by its “K” or“Köchel”number(aswellastheseparateconcertonumber).

COULDWESHORTENTHENAMEOFTHISPIECE?Yes, we could: the radio announcer could have given us all theinformationweneedbycallingitanyofthefollowing:

•“TheallegrofromMozart’sConcertoforPianoandOrchestraNo.17”•“ThefirstmovementfromMozart’sConcertoforPianoandOrchestraNo.17”

•“TheallegrofromMozart’sConcertoforPianoandOrchestra,K453”•“ThefirstmovementfromMozart’sConcertoforPianoandOrchestra,K453”

Let’shavealookatafewmoreexamples.

Prokofiev’sPianoConcertoNo.3inCmajor,Opus26

ThisisverysimilartothetitleoftheMozartpiece,exceptfortheword“Opus,” which means “piece of work.” In music theopus numbergenerallyreferstoapieceofpublishedwork—suchworksarenumberedchronologically—sothispianoconcertowasthetwenty-sixthworkwhich

Prokofievmanaged to get published (only very high-quality pieces getpublished).

Tchaikovsky’sSymphonyNo.6,Opus74,the“Pathétique”

As I said earlier, a symphony involves anorchestrawithout a soloist—although the composer might choose to use individualsfor short solosduringthepiece.Mostsymphonieshavefourmovements,eachofwhichis usually between five and twenty minuteslong. Symphonies arenumbered and sometimes also have names—as in this case, the“Pathétique,”or“sad.”

ThePrelude,FugueandSarabandefromBach’sLuteSuiteNo.2inCminor,BWV997

Bach,andothercomposersofhistime,oftengroupedtogetheraboutsixshortpiecesintoasuite.Thesesuitesusuallybeganwithaprelude(“pre”meaning“before,”and“lude”meaning“play”)andthenwerefollowedbyseveraldances.Thefact that theywerecalleddancesmerelymeant thattheyhadthedistinctiverhythmofcertaindances(inthesamewaythatacomposermight call amovementof their symphony awaltz because ithasan“um-pa-pa”rhythm),butyouwerenotsupposedtodancetothem.The dances inBach’s suites had names such assarabande, gigue andminuet.Therhythmofasarabandeislikeaslowwaltz.Thefugueinthistitleisawordwhichmeans“flight”inEnglish.Asfar

as music is concerned, a fugue is generally a difficult piece whichinvolves lotsofcounterpoint—theplayingofmore thanone tuneat thesametime.Thisparticularsuitewaswrittenforasinglemusicianplayingthelute,

whichissimilartoaguitar.TheBWVnumberis,liketheKnumberforMozart’swork,acatalognumbertoidentifythepieceaccurately.

Beethoven’sPianoSonataNo.14inCsharpminor,Opus27,

“Moonlight”

Sonatas are almost always pieces for one or two instruments and aregenerally in three or four movements (for the usual reasons—seemyearliercommentson“FirstMovement”).Apianosonataisalwayswrittenforasolopianobutaviolinorcellosonatawillusuallyincludeapianoaccompaniment. (There is a rather stingy tradition among composers,concertpromoters,radioannouncersandCDsleevedesignerstorelegatethepianisttotherankof“accompanist”ratherthantreatinghimlikeonehalf of a duet—whichwould be closer to the truth.) By the way,Beethovendidn’tcallthispiece“Moonlight”—hecalledit“SonataQuasiuna Fantasia.”One of the criticswho reviewed the piece, aman calledLudwig Rellstab, wrote that the first movement reminded him of themoonlightonLakeLucerne—andtheideastuck.

Nowthatyouknowallabouttheopusnumbering,keynaming,andsoon,wecandealwithafewmorebitsofclassicalmusicjargon.

STRINGQUARTET

Astringquartetiswrittenfor,andperformedby,twoviolins,aviolaandacello.Thereareusuallyfourmovements.

STRINGTRIO

Astringquartetwithoutthesecondviolin.

STRINGQUINTET

Astringquartetwithanextraviolaorcello.

PIANOQUINTET

Astringquartetwithapiano.

CLARINETQUINTET

Astringquartetwithaclarinet.

CANTATA

A piece for choir and (usually) orchestra with occasional solo singers.Theseareoftenquitelong(anhourorso)andmadeupoflotsoffive-orten-minutemovements.

CHAMBERMUSIC

Theoriginalideaforchambermusicwasthatitshouldbeperformedbyasmall number of musicians in a room (chambre) rather than a concerthall.Nowadaysthetermjustmeansanymusicwrittenforuptoabouttenmusicians(suchasstringquartetsorquintets).

LIEDER

“Lieder” is the German word for “song.” The term “lieder” generallydescribesasolosinger(withclaspedhandsandafancydress,orclaspedhandsandabowtie)singingtoapianoaccompaniment.Nowwehavedecodedthetitlesofclassicalpieces,Iwouldliketostay

on the subject of classical music for a little while,in order to answeranotherpuzzlingconundrum.

Howdoconductorsjustifytheirenormouspaychecks?

If you go to a classical symphony concert youwill find that there areaboutahundredpeopleonthestagedoingalltheworkwhileoneperson,withtheirbacktoyou,waftsastickaround.Surprisingly,itisthestick-wagglerwho is the star of theshow—and the best paidmember of theband.Tomany this arrangement seemsunfair.Apart from the fact thatwaggling a stickis demonstrably easier than playing an instrument, noone in the orchestra seems to be paying a blind bit of notice to thewagglesofthestickinquestion.In fact, by the time everyone gets on stage, the conductor has done

most of her work. This preliminary work takes place duringrehearsalsandinvolvesmakingalotofchoicesaboutspeed,balanceandloudness.“Why do these choices need to be made?”youmight ask. “Didn’t thecomposermakeallthesechoicesinthefirstplace?”Well,thesurprisinganswertothatquestionis“No.”Theamountofinformationthecomposerwritesdownontheprintedpagevariesaccordingtothecomposerandthehistoricaldate of the composition: for example, music written before1800oftenhasnoindicationofthespeedatwhichitshouldbeplayed,oranyotherextrainformation—allyougetonthepageisastreamofnotes.Musiccomposedinthepast200yearsusuallyhasinformationwritten

alongsidethenotestellingthemusicianswhentospeeduporgetlouder,but these instructions tend to be rather vague. A piece of music willcommonlystatewhatspeed tostartat(bymeansofametronomemark,whichtellsyouhowmanynotesperminuteyoushouldplay),andmightthen tell you to slowdown for awhile—butwill not generally indicatehowmuchtoslowdown.Similarly, therewillbevarious indicationsonthewrittenmusicastowhentoplaylouder—butonlyaroughindicationabouthowloudtoget.Youmightwonderwhycomposersaren’tmoreexactinthesematters,

but the point is that a single page of orchestralmusicalready containshundredsofpiecesofmusicalinformation,asyoucanseeintheexamplebelow, and more detail might cloudthe musical message rather thanclarify it. In any case, a bit of variability adds interest to each newperformance. One ofmy favorite stories about this flexibility concernsthe Finnish composer Sibelius. He was listening to a rehearsal of hisviolinconcertowhentheviolinsoloistaskedhimaquestionabouthowtointerpretacertainpassage.“Doyoupreferthispassageplayedlikethis…[hethenplayeditwithaverysweettone],orlikethis…[playingitwithadryer tone]?” Sibeliusthought for a few seconds and then pronouncedjudgment:“Ipreferbothversions.”Apart from all this vagueness about loudness and speed, there is the

choiceoftheoverallbalanceofthesoundoftheorchestra,whichwill,of

course,changeduring thepiece.Quiteoften thewrittenmusicgivesnoindication that, for example, the violinsneed to get gradually louderduringaparticularsectionbecausetheywillbetakingoverthetunefromthe woodwind instrumentsin the next bit.The conductor can color andshade the overall sound of the piece by deciding which instrumentsshouldplayloudestatanypoint.Thisisnotasstraightforwardasitmightseembecauseyoudon’talwayswant todo theobvious thingofplayingthetuneloudlyoveraquieterbackgroundharmony.There are, in fact, hundreds of important decisions to make during

rehearsals-and it’s theconductor’s job tomake themall.Allconductorsmake different, equally valid decisions and some of them change theirmindsabouthowapieceshouldbeplayedastheygetolder.Thismeansthat each concert or recording of a piece of classical music is unique,whichiswhypeopleoftenhaveseveralrecordingsofthesamepiece.

Atypicalpagefromanorchestralpiece,showingthateachpagecontainshundreds of pieces of information. In this case,all the informationrepresentsabouttwelvesecondsofmusicfortwenty-sevendifferenttypesofinstrument,allplayingatthesametime(e.g.,thetoplineisforafluteandthebottomlineisforthedoublebasses).

Things are better organized nowadays, but toward the end of thenineteenthcenturyitwasdifficultfortheconductortopassonhis ideasaboutthemusictotheorchestra,becausemanymembersoftheorchestraweren’t actually there for rehearsals.Hangovers, illicit love affairs andbetter paid gigs meant that a lot of the orchestral members had betterthings to do in the afternoonsthan go to rehearsals, so they paid“deputies”totaketheirplaces.Thedeputywouldplaytheinstrumentofthemissingmusiciantomakesure therewereenoughviolins,clarinets,orwhatever,attherehearsal.Thiswasfineifonlyafewpeopledidit,butit eventuallybecame fairly common for overhalf theorchestra to senddeputies. Sometimes the deputy would also playthe concert, butgenerallyalargenumberoftheplayersattheconcerthadnotbeenattherehearsal.Another problem conductors had to deal with in those days was

naughtypercussionists.Inalotoforchestralscoresyouneedtwoorthreepercussioniststodoalotofimpressivebangingandcrashingatparticularclimaxesofthemusic,butsometimestheyhavenothingtodofortwentyminutes or more. Obviously, these long breaks bring out the naturaltendencyofthemusiciantoslinkofftothepubforaquickpint.Backin1896SirHenryWood(theconductorwhoinventedtheProms)foundthattheonly way to stop the slinking percussionists was to lock the exitdoors. In his autobiography he describes the result: “Iwould see thesefellows creeping up, one by one, bending double in the hope of beinghiddenby themusic stands.Theywouldgentlypush thebarof theexitdoor,followingupwithagoodshove.Theywouldthenreturn,creepingalong,bentdoubleandwithapuzzledexpressionontheirfaces—perhapstowatchsomeoneelsegoingthroughthesameantics.”Of course, in these modern, professional times, percussionists are

paragons of virtuewhowould never dreamof nipping roundthe cornerforaquickoneinthemiddleofasymphony.Once everyone is on stage and playing, the conductorwill spend his

time nodding, winking and glaring at the musicians aswell aswafting

that stick around.Someof these signals are simply to remind someonethat,afternotplayingforseventeenminutes,shehastogetreadytoplaythatbigfanfare.Othersignalsvaryinmeaningfrom“Don’tforgettoplaythisbitveryquietly”to“You’refired,youbutter-fingeredoaf…”Asfarasthestickwaftingisconcerned,theup-down,side-to-sideactionofthestick isused to indicate thebeats in eachbar and thus the speedof themusic.*Thereasonwhymostoftheorchestraaren’twatchingmostofthetime is that they are busy reading the music and can onlyglance upoccasionallytogetinformationfromtheconductor.

ImprovisationImprovisation is making music up as you go along. Various sorts ofmusic involve different levels of improvising: if you listento asymphonywrittenbetween1800and1900thetotallevelofimprovisationinvolved is—zero.At theotherendof thescale,youget jazzmusicianslikeKeith Jarrett,whocan turnup at a venue and improvise thewholeconcert.As far as improvisation is concerned, the first step isusually toplay

your own versions of well-known tunes. This oftenmeans playing thetuneas itwasoriginallywritten to startwith, and thenmakingupyourownvariations.Thevariationsofteninvolvestrategieswhichamusicianhaslearned,whichcanbeappliedtoanytune.Forexample,imaginethatyou areone of those irritating, glazed-eyed hotel lobby pianistsimprovisingon“MyWay”tomakeitlastuntilyournextcoffeebreak. Ifyouwanttomakeitsoundromantic,playitslowly,withlotsofpauses,andaccompanythetunewithchordssplitintoarpeggios(whereyouplaythenotesof thechordoneafteranother rather thanall together). Ifyouwantittosoundhymn-likeandspiritual,simplifythechordsandplayonechordforeverystrongbeatoftherhythm.Hymnssoundlikethisbecausetheyarespecificallydesignedtobeperformedbynon-expertmusicians.Ifyouwanttomakeitsoundheroicordramatic,thendon’tletthemusic

restonthelongnotes;replacethemwithrepeatednotes.Ofcourse,ifyoucarry ondoing this for too long you are likely to find a certain authorcreepingupbehindyouwith agarrote inonehandandbodybag in theother.Thistypeofvariation/improvisationcan,ofcourse,bedonebygroups

of musicians as well as solo players. Good musicianswill not onlyarrange the notes in different ways, they will introduce new notes andchange the tune. When they are improvising,the best jazz musiciansmerelyhintattheoriginalmelodyeverynowandthen—it’slikegettingaglimpseofafamiliarlandmarkwhenyouthoughtyouwerelost.Itmightsound a little chaotic at times, but improvisingmusicians learn lots oftechniquesforreestablishingorderwhenevertheywantto—andcansteerthe audience through an emotional cycle of familiarization,disorientation,expectationandgratification.Or, inmygirlfriend’sviewofjazz,disorientation,irritation,horrorthatitmightneverend,andreliefwhenitdoes(herwords,dictatedtomeasIwritethis).Anothertypeofimprovisationinvolvesasoloistormembersofaband

makingupnewmelodiesoverawell-knownsequenceofchordsorabassline.Thisisepitomizedintheleadguitarsolo.Leadguitaristsloveleadguitar solos—everyone else repeatssomething prettymundane, andwegettopranceandpose.We’vegotbetweentwoandtwenty-twominutesto get back to the tuneand it doesn’t reallymatter what we do in themeantime as long as it’s loud and has lots of notes in it. There areexamplesof musically meaningful guitar solos, but the guitaristsinvolved are just being unnecessarily clever and letting the sidedown.Oneofthecommonestplatformsforaleadguitarsolois thetwelve-barblues.Thetwelve-barbluesisnotanallusiontothepreviouselevenpubsyou’vebeentothatevening,tryingtoforgetthefactthatyourgirlfriendjust left you because you insisted on listeningto toomuch jazz—it’s averysimplemusicalstructurewhichisthebasisofmostbluesandalotofotherpopmusic.The twelvebarsare just twelve short timeperiods.Aswesaw in the

previouschapter,musicisdividedupintobarsoftimeandeachofthesetime periods has several notes in it. In the context of an average bluessong,abarlastsaboutthreesecondsandcontainsfourbeats,withaslightemphasisonthefirstone:

dumdumdumdum,dumdumdumdum.

During a twelve-bar blues, the rhythm guitarist churns out a standardsequenceofchords. In thesimplestversions thereareonly threechordsinvolved—let’scallthemchordsX,YandZ.Althoughtherearequiteafewvarieties,inastandardtwelve-barbluesyoumightexpecttherhythmguitarplayertostrumchordXforfourbars,thenchordYfortwo,backtochordXfortwo,ZfortwoandbacktoXforthefinaltwoofthetwelve.This routine then repeats itself, andall thewhile thebassguitar is alsosupplyingnotesinanX–Y–X–Z–Xcycle.Thissimplestructureexplainswhy blues bands can play after any amountof alcohol intake, andwhytheir natural habitat is the pub. Over this straightforward musicalbackground the leadguitaristscanlarkaroundhowever theywant to,aslongastheyavoidcertainnoteswhichclashwiththesechords—andthuswastheendlessbluesguitarsoloborn.Ihavenointentionofbelittlingbluesbands,becausesomeofthemare

tough-lookingbuggerswhoIwouldn’twanttomeetinadarkalley.SoIwouldliketopointoutthat,likemanysimplemusicalsystems,therearelots of added complicationsandnuanceswhich thebestplayershave tomasterbeforeanyonewillpaythemtoperform.Improvising in Western music is not a new thing; it just became

unfashionable in nineteenth-century classical music. Back in theeighteenthcenturyitwasverypopular:forexample,oneofBach’smostwell-known pieces, the Brandenburg Concerto No. 3, consists of threemovements but only two of them are writtenout in full. The writtenmusic for themiddlemovement is just two chords long—whichwouldonlylastabouttenseconds.Itispossible,ofcourse,thatBachwascalled

away in the middle of his writing to take part in the birth or, indeed,conception,of one of his twenty children, and forgot to finish it. Themore traditional historical view is that the second movement wouldconsistofa three-minuteviolasolobyBachwhowouldthennodat therest of the band—and they would finish off with thesetwo chords.Nowadays,inmostrecordingsofthispiece,themusicianschickenoutonthe improvisation and just play the twochords—and who can blamethem? I certainly wouldn’t want any of my own improvised drivelsandwichedbetweentwopiecesbyBach.Improvisationiscommontoallmusicalsocieties.Forexample,Indian

traditionalmusicconcentratesheavilyuponit.ThetrainingofaWesternclassicalmusician involves lots of repetition in an attempt to play thenotes written by a composercorrectly. Traditional Indian musicaltrainingisallabouthowtocomposeyourownmusiconyourinstrumentasyougoalong.Theideaisthatyouhaveagroupofnotesasyourbasicbuilding blocks, and you use them to improvise a piece lasting severalminutes.Eachgroupofnotes,or“raga,”isassociatedwithamoodandatimeofday.The ability to improvisewell is a highly respected talent and it can

leadtosomeinterestinginterplaybetweenthemusiciansinvolved.Itcaneven become competitive, as the musicians drive each other to newheights. Speaking of competition, thereare international improvisationcompetitions between classically trained organists.You can’t cheat byplayingsomethingyoucomposedearlier,becausetheyhandyouabrand-new tune tobaseyour improvisationononlyanhourbeforeyoubegin.Afteryouaregiventhetune,youhavetomakeupapieceofmusiconabig church organ, in front of a crowd of other competitors andtheirfriends.So,nopressuretherethen…Whateverlevelyoureach,improvisationisfunfortheplayer.Evenif

you are a complete beginner, you can make up your owntunes reallyeasilyifyouhaveaccesstoapianoorsimilarkeyboard.Useonefingerfromeachhandandplayonly theblacknotes.This automaticallygives

youapentatonicscale—andit’sreallyquitedifficulttomakeahorriblenoiseusingthistypeofscale.Ifyouputyourfootontheright-handpedalthenoteswillmergeintoeachother,whichgivesagreat“full”effect,butyouneedtoraiseyourfootandputitdownagainquicklyeveryfiveorsixnotes.Thispedalletsthenotesringoutforalongertime,andthenotesofyourmelodywilloverlapandharmonizewitheachother.Everytimeyouraiseyourfootyoukillthatgroupofnotes.Youneedtodothisbecausetoomanyoverlappingnotessoundmessy.Thepedalontheleftgivesthenotes avery short lifetimeand is for realpianists—not for the likesofyouandme.

12.ListeningtoMusic

ConcerthallacousticsLet’s imaginethatyouandaviolinplayerhavegoneforapicnicinthecountryside. Ifyouboth stop in themiddleofalarge, flat fieldand thevioliniststartsplaying,youwillfindthat theviolinsoundsalotquieterthanitdoeswhensheplaysitinherlivingroomathome.Inaroom,theviolinis louderbecauseyouarereceivingthepressure

ripples from each note several times over. You get the ripples whichtraveldirectlytoyourears,plustheoneswhichweretravelingawayfromyou but have been turned backin your direction after bouncing off thewalls,floorandceiling.Apartfromtheincreaseinvolume,thisbouncingaroundalsomeansthatthesoundiscomingatyoufromalldirections,soyoufeelbathedinmusic.Out in the field, the violin sounds quieter because you are only

receivingadoubledoseof thenoise,oncedirectly fromthe instrument,and one reflection off the ground.All the other sound travels in otherdirections,awayfromyourears.So,thebenefitofreflectedsoundisthatwehearthemusiclouder,and

wealsogettheimpressionthatwearesurroundedbythemusic.Thesizeoftheroomandthematerialsthatthewalls,floorandceiling

arecoveredwithdeterminetheacoustic“liveliness”oftheroomyouarein.Youcancheckthe“liveliness”ofaroombyclapping yourhandsandlisteningtohowquicklyorslowlythesounddiesaway.Inasmallroomfull of furniture and heavy curtains,the sound dies away almostimmediatelyand the roomis said tobeacoustically“dead.” In a largerroomwith hard walls, the sound bounces back and forth off the wallsseveral times before the sound dies away,and the room isdescribed as“lively.”Inaconcerthall,itmighttakeaslongasacoupleofsecondsforthisreverberationofyourhandclaptodieaway.Musicianssoundbetter

in a “live” room than a “dead” one,which iswhy your singing soundsbetterwhenyouareintheshower,surroundedbyhard,tiledsurfaces.Althoughweenjoytheeffectofsoundslastinglongerbecausetheyare

bouncingaroundtheroom,wewantallthebouncedsoundfromeachnotetooverlapsothatitreachesourearsasasingle,longnote.Ifthewallsoftheroomarealongwayaway,thetimebetweenbounceswillbetoolongandwewon’thearasingle,extendednote.Wewillhearthenote,thenagap,thenthenoteagain—thedreadedecho.Concerthalldesignersliveinthe hope that their designs will give the audience lots ofpleasantreverberation, but no echoes. This is a tricky balance, because botheffects are caused by sound waves bouncing off the walls, ceiling andfloor.Thedifferencebetweenaconcerthallandalivingroomisthat,unless

you are theQueen, the concert hallwill be a lotbigger, andoneof themoreinescapablesymptomsofalargerspaceisthatthewallsarefartherawayfromeachother.Inalargeroomlikethisthereflectedsoundhastotravelalongway,fromtheviolinallthewayovertothewallandbacktoyour eardrum. The soundwhich comes directly from the instrument toyoureardoesn’t take thisdetour, and thereforearrives first.So the twosoundsareheardasseparateevents—oneisanechooftheother.In a small room, the reflected sound ripples and the direct sound all

arrive at our ears at about the same time, because theround-trip to thewall and back is not much farther than the direct route.Although thedirectsoundarrivesfirst,thereflectedsoundishotonitsheels.Ifthegapbetween their arrival is lessthan forty thousandths of a second, ourhearingsystemjustassumesit’sallpartofthesamesound.Weonlygetatime differenceabove forty thousandths of a second if the round-triptakenby the reflectedsound ismore than40 feet longer than thedirectroutefromtheviolintoyoureardrum.Thiscouldonlyhappeninaverylargespacelikeaconcerthall.The acoustic engineers who design concert halls can reduce echo

problems by putting absorbent material (which does not reflectsound

verywell)inplaceswheretheround-tripofthereflectedsoundwouldbea long one. They can also angle the wallsso that the sound bouncesaround the room in the optimum way to give a “full of sound” feelwithoutechoes.Some concert halls have moveable or adjustable absorbing panels

whichcanbearrangedtosuitdifferentsituations.Forinstance,youwantless reflection for a public lecture or a comedian than you do for aconcert. Panels like this can also be used toimprove the acoustics ofbuildingswithechoproblems.OnefamousexampleofthisistheceilingoftheAlbertHallinLondon.Inthiscase,thecurved,highceilingusedtoreflect sound back down as an echo, until big, sound-absorbing“mushrooms”wereinstalled.

Hi-fi,lo-fiorsci-fi?Homesoundsystemsandrecordedmusic

Microphonesandspeakers

Microphonesandspeakersareverysimilardevices—infact,itwouldn’ttakemuchefforttoturnanymicrophoneintoaspeakerorviceversa.Theillustrationoppositeshowsus thatamicrophoneconsistsofonly

twoimportantbits:

1 .A small paper or plastic cone which is light enough to tremblebackwardandforwardwhensoundwaveshitit.2. A device for turning this backward-and-forward trembling into anelectrical signal. The electrical signal goes up and downin exactly thesameway as the paper conemoves backward and forward—asyou cansee in the illustration. It is clear thereforethat if the cone is tremblingbecause of thewave patterns of themusic, then the electrical signal isalso“trembling”inthesameway—wehavemadeanelectrical“copy”ofthemusicsoundwaves.

Amicrophoneturnsthebackward-and-forwardmovementofapaperconeinto an electrical signal. We can increase the power of this electricalsignal by putting it through an amplifier—and use it to make the bigpaper cone in a loudspeaker move backwardand forward—in order toreproducetheoriginalmusicatahighervolume.

Aspeakerisjustamicrophonewhichisbacktofront—ithasadeviceforturning an electrical signal into backward-and-forwardtremblingwhichisattachedtoapaperorplasticcone(whichisusuallybiggerthantheoneinthemicrophone).Ifwewanttomakeasinger’svoicelouder,weaskthemtosingintoa

microphone. The electrical copy of the sound is thenmade and passedthroughanamplifierwhichmakesitmuchmorepowerful(oramplified).Wethenusethispowerfulelectricalcopytomakethe(generallylarger)paperconeintheloudspeakertremblebackwardandforwardinthesamewayastheconeinthemicrophonedid,andthemusicisreproducedataloudervolume—easy-peasy.

Therecordingandplaybackofmusic

Instead of using a microphone and amplifier to produce louder musicimmediately (asat a liveconcert),wecan take theelectricalsignalandstore it somewhere.Theelectricalwigglescan, for example,beused todriveamachinetocutawigglygrooveinaplasticormetaldisk.Lateronwecanuseamachinesimilar to theone thatcut thegroove to turn themechanical wigglingback into an electrical signal—which we can put

throughanamplifiertopushaspeakerconebackwardandforwardsowecanhearthemusicagain(thisisexactlyhowvinylrecordswork).There are, of course, many other ways of storing the musical

informationproducedbythemicrophone,includingmagnetictape,whichstoreswigglesofmagnetization,andsiliconchipdatastorageorcompactdiscs(CDs),wherethewigglesareconvertedintoastreamofdigitaldata.Everytechniqueusesthesameprinciple:youtakethesoundandconvertit into stored informationandthen, later,youdecodethe informationtogetthesoundback.

ArevinylrecordsbetterthanCDs?

EversinceCDsbecamefreelyavailableinthe1980safiercedebatehasragedaboutwhetherornot theyprovideabettercopyofthemusicthanthevinylrecordstheyreplaced.Muchofthisdebatehascenteredonthedifference between analog and digitaltechnology—so I would like todescribewhatthatdifferenceisbeforeIgoanyfurther.

THEANALOG/DIGITALDIFFERENCE

To keep this part of the discussion simple, I won’t talk directly aboutmusic. Instead, I will discuss the copying and reproductionof a visualimage—soIcandrawanexampleforyou.Let’s say we want to copy a wavy line by analog methods and by

digitaltechniques.

AnalogreproductionAnanalogrecordingsystemsimplytakesawigglylineandtriestomakeadirectcopyofitbyfollowingitscurves.Theprincipleissimilartohowacyclistfollowsthelinedownthecenterofawindingcountrylane.Theaccuracyof thecyclistwillbedeterminedbyhowfasthe isgoing,howsharpthecurvesare,andhowlonghespentinthepubatlunchtime.Atypicalexampleofananalogrecordingwouldbeforyoutocopyan

image using tracing paper and a pencil. It’s quite easyto see how the

accuracy of your trace would be improved by using exactly the rightwidth of line and being extremely carefulabout it. There might besituations,however,wherethelineyouaretryingtocopywigglestoandfrotoorapidlyforyoutofollowitaccurately.

DigitalreproductionDigital reproduction takes a completely different approach. The word“digital”meansthatacomputermustreducethetaskdowntoaseriesof“yes” or “no” statements. In this case the computer will divide up thepagewiththewigglylineonitintoalotoflittlesquares.Thecomputerwillthenpointacameraattheimageandaskitself“Isthereadarklineinthissquare?” and do this for all the small squares, one at a time. Thecomputerthenstoresallthe“yes”and“no”answers.Whenthecomputeris asked to reproduce the image, it thenprints ablack square for every“yes”andablanksquareforevery“no.”Theadvantageofthissystemisthat computers can memorize zillions of “yes” or “no” answers withincredible accuracy. The information can be stored and reproducedfaultlessly at any time and there is no dependence on the accuracy ofmovingmachinery.Thedisadvantageofthismethodisthatcurvedlinesaremadeupoflittlesquares—andifyoudon’tmakeyoursquaressmallenough in the firstplaceyour reproducedimagewillnot look likeyouroriginal smooth wiggly line. I have demonstrated this by showing thedifference between a gooddigital copy and one in which the smallsquaresweretoobig.

The principle of digital reproduction. Both of these images wereproduced digitally—using a computer to divide up the curveinto acollectionofblacksquares.Ifweusemillionsoftinysquares(aswehavedone in theupper image)we seea smoothcurve. If the squaresare toolarge,astheyareinthelowerimage,welosealotofpicturequalityandthe shape of thecurve is only recorded approximately. Modern hi-fiequipment uses “squares” which are so tiny that we cannot hear theeffectofdigitization.

Now thatwe know the difference between analog technology (which isused to produce vinyl records) and digital technology(CDs), we cananswerouroriginalquestion:“Arevinylrecordsbetter thanCDs?”Andtheansweris…veryveryfewpeoplecantellthedifferencebetweenthetwo (as long as the vinyl records are in perfect condition—andwe usegoodequipment in both cases). This point was proved by a couple ofmusic psychologists (Klaus-Ernst Behne and Johannes Barkowsky)in1993.Theytook160peoplewhowereseriouslyintomusicsystemsandwhohadstrongopinionsabouttheCD/vinyldebateandmadethemlistent oboth types of music reproduction. Only four out of the 160 couldactually identify whether or not they were listening to aCD—eventhoughthevinylfansallbeganthetestthinkingthatCDssounded“shrillanddead”comparedtothe“warm”soundofvinyl.Also,don’tforgetthatthese weren’t just average listeners—they were keen, opinionatedenthusiasts.ThenumberofaveragelistenerswhocouldtellthedifferencebetweenthesoundofaCDandthatofavinylrecordwasprobablylessthan one in a hundred—and that’s back in 1993. Improvements intechnology since then have undoubtedly reduced this numberandrenderedthecomparisonirrelevant.MuchoftheCD/vinyldebatecanprobablybeattributedtotechnology

nostalgia, which dates back to cave-dwellers having heatedargumentsabout the superiority of bronze arrow heads compared with thenewfangled iron ones. Back in the 1930smusic fanswere complaining

that, because thenew recording techniques couldhandle loudandquietmusic, theymissed theexcitementof thedistortionwhich tookplace inorchestralclimaxesontheirolderrecords.Later,in1963,areviewofthelatest technology(RCADynagrooverecording)notedthatsomelistenersfound the new, smoother sound too sterile. Personally I think that thedifference between vinyl and CD sound is bound to be irrelevantcomparedtovariableslikethetickingofthecentralheating,trafficnoise,andtheplaintivevoiceinthebackgroundaskingifthisjazzisgoingtobeplayingformuchlonger….

ThedifferencebetweenCDsandMP3technology

Imagineweareataconcertwatchingourfavoriteband(thePsychedelicDeathWeasels) playing their epic rock ballad, “Ismy cocoa ready yet,luv?”During the quiet, romantic verses we can clearly hear all the

instruments, including the acoustic guitarwhich is being playedby thesinger.However,whenthebandplaystheheavyrockchorus,allwecanheararethebass,drumsandelectricguitar.Wecanseethatthesingerisstillplayinghisacousticguitarbutthesoundheismakingiscompletelydrownedoutbytheother,louderinstruments.IfthistrackwasbeingrecordedontoCD,everysoundmadebyevery

instrumentwouldbefaithfullyrecordedasdigitalinformation—eventheinaudible music produced by the acoustic guitar during the hard rockchorus.As far as the digital recording process isconcerned, the sameamountofdatawillbecollectedforthe“hidden”guitarasforthemuchlouder instruments. You wouldn’t hear these “hidden” sounds at theconcertorontheCD,sothefaithfulcollectionofthisdataispointless—but the recordingequipment does it automatically because it doesn’tknowhowtopickandchoose.This “drowningout” or hidingof one instrument by another happens

allthetimeduringtheperformanceofanytypeofmusic.Sometimes(asin the example above) one instrument is hidden for several seconds or

evenminutes.Inmanycases,however,instrumentsareonlyhiddenforafractionofasecond—forexample,alouddrumnotemightdrownoutawholebandororchestra.Apart from these hidden sounds, a CD also contains a lot of

informationthatwesimplycannothear—frequencieswhicharetoohighortoolowforthehumanear.Aswesawinearlierchapters,musicalnotesare made up of a family of related frequencies:the fundamentalfrequency, twice that frequency, three times that frequency, four times,fivetimes,etc.Ifweplaythehighestnotesoncertaininstruments,someof their harmonics will be out of our hearing range. Similarly, somecombinationsoflownotesproducesubsonicwaveswhicharetoolowforhuman ears (although you can sometimes feel them). On a CD theseinaudiblepartsofthenotesareallstoredandplayedback—eventhoughwecan’thearthem.Inthe1980sand’90sabunchofridiculouslyintelligentscientistsand

engineers developed a method of using computers toidentify all thehiddenandinaudibleinformationonmusicCDs.Onceitwasidentified,itcould be discarded and the musiccould be rerecorded without all thatredundantinformation.Approximately90percentoftheinformationonaCDcanbediscardedinthiswaytoproduceanMP3file.This,ofcourse,means that you could record ten CDs’ worth of music on one CD.Alternativelyyou can store and play back the music as digitalinformationonacomputerorpersonalstereo(iPods,etc.).AlthoughMP3technologydiscardsmostoftheinformationthatcameoutoftheoriginalmusical performance, the average listener cannottell the differencebetweenaCDandanMP3playback.

Homemusicsystems

Music system enthusiasts, or “audiophiles,” can spend over a year’ssalaryon their systems—and if that’swhat theywant todo it’s finebyme. On the other hand, you can buy a music system which willapproximately match the performance of your earsfor about $1,000. I

would advise you to go to a specialist music system shop whichspecificallyadvertisestheirgoodsasbeinghighqualitybutcheap.Ialsorecommend buying stuff second-hand from an enthusiast (enthusiaststend to upgrade everycouple of years and the equipment they buy andsellisalwayshighquality).Uptoaboutthe$1,000level,newequipmentgenerallyincreasesinqualityasthepricegoesup—butit’sbesttohaveahi-fi enthusiast giving you advice or refer to hi-fi magazinesfor their“bestunder$1,000”choices.Between$1,000and$3,000theincreasesinsoundqualitycanbedifficulttospotandabove$3,000themoney/sound-qualitycorrelationdisappearsaltogether,asfarasIcantell.Thedifferentsystemsmightsounddifferent—butit’sverydifficulttoidentifywhetheroneisactuallybetterthananother.(Itispossibletospendover$1,500peryardforaudiocablesandIwouldbeveryinterestedtomeetanyonewhocouldtellthemusicaldifferencebetweensuchcablesandoneswhichcostonlyafewdollarsperyard.)Havingboughtyourequipmentyounowhavetwochoices:

1.Youcanemployanacoustic technicianandanarchitect.For$75,000theywillbuildyouaspeciallisteningroomand,whentheyhavefinished,theywillmakethebiggestdifferencetothesoundbytryingthespeakersindifferentplacesandmovingthefurnitureabout;or2.You can save yourself $75,000 by taking the equipment home to anormal room, trying the speakers in different places and movingthefurnitureabout.

Themaindifferencebetween“pop”and“serious”music

Mostmelodiesareonlyafewsecondslongandwhatyoudowiththistinybitofmaterialisthesourceofthemaindifferencebetweenso-calledpopandseriousmusic.Thefollowingcommentsarenotintendedtomakeonegenresoundbetterthantheother—Ilovethemboth.Also,Iamgoingto

make some disgracefully broad generalizations in order to make mypoint.Apopmusiccomposerwill taketwoorthreeshortmusicalideasand

make them intoa three-minute songbyplaying themoneafter another.Theywill, for example, take tune“A”andmake it into the chorusof asong,andtune“B”willbemadeintotheverse.Thesongwill thentakethe form: introduction—verse—chorus—verse—chorus—guitar solo—verse—chorus—finale.This technique of continuously repeating the two tunes has several

effectsonthelistener(assumingthatthetunesaregoodones):

1.It’seasytorememberthetunes.2.It’seasytogetrapidlyaddictedtothetunes.3.It’seasytogetboredwiththewholethingafterit’sbeenplayedthirtyorfortytimes.

Onecommonaspectofpoporrocksongsistheiruseofahook—ashort,repeated musical phrase which is easily remembered. These can bemelodicorrhythmicandusuallylastbetweensevenandtwelveseconds.Sometimes the song beginswith the hook, as in the first five notes of“WholeLottaLove”byLedZeppelinorthefirstlineof“BabyLove”byTheSupremes. Inothercasesyouhave towait awhilebeforeyouhearthehook,whichiswhathappensin“MommaToldMeNottoCome”byThreeDogNight,or“TeenageDirtbag”byWheatus.Inallthesecasesthetitlewordsformpartofthehook.Composers of “serious” music are not averse to hooks either—just

lookatBeethoven’sFifthSymphony,withits“DaDaDaDaah”opening.On the whole, though, “serious” music composers are a little morecautiousandmiserlywiththeirmaterialthanpopcomposers.Theiraimistotaketwoorthreetunesandusethemasthebasisforapieceofmusicwhich might last betweenten and a hundred minutes. This is done byusing techniques such as breaking the tunes up and playing with the

fragments;merging one tune into the other; playing one tune as theaccompaniment to the other; and hinting that the tune is on itsway.Acomposerofalongpieceofmusicmightusefragmentsofthemaintuneas landmarks to build up expectation—and expectationis much moreimportantinlongpiecesthanitisinshortpopsongs.Manypeople,particularlyclassicalmusicprofessionals,thinkthatthe

listener retains some sort of appreciation of thekey inwhich thepiecebeginsandcansense the“homecoming”whenwe return to thatkey,asthemusicoftendoestowardtheendofapieceofclassicalmusic.Ithinkthisisabitfar-fetched.It’sexpectingtoomuchofthelistener’smemoryunless she has perfectpitch. Some studies have indicated that ourmemoryofwhat’sgoingonharmonicallyonlystretchesbackaminuteorso, andthis seemsmuchmore realistic.Peoplewill remembermelodiesor effects such as drum motifs from earlier in the music and will bepleased if they hear fragments ofthings they recognize.As far as theharmonygoes,however,myanalogyaboutdifferentkeysbeing like therungsofahamsterwheelcomesbackintoplay.Howarewesupposedtoknowifthefinalrungistherungwestartedon?I think the experience of listening to a long piece of music can be

likened to walking on a decorative carpet which is beingrolled out infrontofyouandisbeingrolledbackupacoupleofyardsbehindyou.Asyouwalkforwardnewpatternsandimagesappearandsomeofthesewillstickinyourmind.Let’ssayyousawanimageofatigerafewminutesago and you cansee the beginnings of a tiger tail coming up. Thecomposer could choose to satisfy your expectation by showing youanotherviewofthetiger.Orhecoulddecidetosurpriseyou—that“tigertail”might actually be the rear end of a snake. If youlisten to a pieceseveral timesandbegintoknowitbetter,yougetfewersurprisesandabetterviewofthewholecarpet.Youcanalsotakealotofpleasurefromrecognizingvariouslandmarksasyougo.A skillful composer’s job is to create expectations and theneither to

satisfy or frustrate them.But the composer cannotandmustnot try for

continuous excitement. As in any storytelling, or even a fireworksdisplay,youdeliberatelyaddsomecalmerpassages,sothattheimportantmomentsmakeagreaterimpact.Thesetechniquesforlongerpiecesresultinmusicwhichislesseasyto

loveatfirsthearing,butwhichseemstoimproveeachtimeyouhearit.

Andfinally…Whetheryoulikepopmusic,heavymetalorclassical,youmightfinditinterestingtolistentoyourfavoritepiecesandfollowjustoneinstrumentatatime.Tryplayingyourfavoritepopsongafewtimeswhileyoulistenonly to what the bassguitar is doing; then do the same for the otherinstruments.Youcan learn a lot abouthowapiece isorganized in thiswayandyouwillbereallylisteningtothemusicratherthanjusthearingit.Iwouldlike tofinishwith thebestbitofadvice thatonelistenercan

givetoanother.Whateveryourpresenttastes,thereareprobablyseveralothertypesofmusicouttherewhichwouldbringyoualotofpleasureifyoubecamemorefamiliarwiththem.Myadviceisthis:tryaddingabitofrandomnesstoyourlisteningpattern,andgiveeachnewtypeofmusicafairtrial.Ifyouareintoheavymetal,trysomefolkmusic;ifyouloveMozart,tryDollyParton.Musicalgenresarenotexclusive,andoneeasywaytoincreasetheamountoffuninyourlifeistoexpandtherangeofyourlistening.

FiddlyDetails

A.NamingandidentifyingintervalsAt various points in the book I havementioned that the jump in pitchbetween any two notes is called an interval. The intervalwe havediscussed most is the octave—the jump in pitch that corresponds to adoublingofthefrequencyofvibrationofthenote.Alltheotherintervalsalso have names, some of which I have referred to already. The tableopposite presents a listof interval names along with the size of theintervalinsemitones.Youcanalsoseethreephotosofapianistplayingtwonotes afourth apart. In each case we start on any lower note andcount up to the notewhich is five semitone steps higher (counting theblacknotesaswellasthewhiteones).Ihaveincludedthreeillustrationshereinordertomakeitclearthatitdoesn’tmatterwhichnoteyoustarton—theone five semitone stepsupwill alwaysbe a fourthhigher, andsimilarlytheoneninesemitonesupwillalwaysbeamajorsixthhigher.After years of musical training you get to recognize each of these

intervals andyoucanwritedownany tunewhichcomes intoyour head(startonanynote,upafifth,downamajorthird,etc.).Butthereisawayofidentifyingmusicalintervalswhichanyonecanmanage.Allyouhavetodoislearnthenamesoftheintervalswhichoccuratthebeginningofseveralsongs.Ihavemadealistofsuitablesongsinthetablebelow.Thefirsttwonotesofthesongsidentifiedinthislistgiveyoutheinterval inits risingform(unless Ihave statedotherwise).Most tunes startwith arisinginterval,soexamplesareplentifulandyoumightwanttosubstituteother songs for your own list. You might also want to collect twelvedescendingintervalsfromothersongs.Sonow,whenyou’rebored,sittingatanairport,youcanidentify the

interval of whichever annoying “bing bong” noise theyare using by

matchingittooneofthesesongs.

Size ofinterval Nameofinterval Song to identify rising

interval

1semitone minorsecondorsemitone

“IleftmyheartinSanFrancisco”

2semitones majorsecondortone “FrèreJacques”or“Silentnight”

3semitones minorthird“Greensleeves”or“SmokeontheWater”(byDeepPurple)—firsttwoguitarnotes

4semitones majorthird“Whileshepherdswatchedtheirflocksbynight”or“Kumbayah”

5semitones fourth “Herecomesthebride”or“WewishyouamerryChristmas”

6semitones diminishedfifth(oraugmentedfourth) “Maria”fromWestSideStory

7semitones fifth(orperfectfifth)“Twinkletwinklelittlestar…”(thejumpbetweenthetwotwinkles)

8semitones minorsixth(oraugmentedfifth)

ThethemefromLoveStorybeginswiththisintervalfallingthenrising

9semitones majorsixth “Mybonnieliesovertheocean…”

10semitones minorseventh “Somewhere”fromWestSideStory

11semitones majorseventh “Takeonme”(songbythebanda-ha)

12semitones octave “Somewhereovertherainbow”fromTheWizardofOz

13semitones minorninth

14semitones majorninth

15semitones minortenth

16semitones majortenth

17semitones eleventh(oranoctaveandafourth)

Three photos of a pianist playing two notes a fourth apart. It doesn’tmatterwhichnoteyoustarton—thetwonotesarealwaysseparatedbyagapoffivesemitones.

B.Usingthedecibelsystem1.Thedecibelsystemisamethodofcomparingthedifferenceinvolumebetween two sounds. These differences are measured inthe followingway:

Ifthedifferencebetweentwosoundsis10decibelsthenonesoundistwiceasloudastheother.Ifthedifferenceis20decibelsthenonesoundis4timesasloudastheother.Ifthedifferenceis30decibelsthenonesoundis8timesasloudastheother.Ifthedifferenceis40decibelsthenonesoundis16timesasloudastheother.Ifthedifferenceis50decibelsthenonesoundis32timesasloudastheother.Ifthedifferenceis60decibelsthenonesoundis64timesasloudastheother.Ifthedifferenceis70decibelsthenonesoundis128timesasloudastheother.Ifthedifferenceis80decibelsthenonesoundis256timesasloudastheother.Ifthedifferenceis90decibelsthenonesoundis512timesasloudastheother.If the difference is 100 decibels then one sound is 1,024 times asloudastheother.If the difference is 110 decibels then one sound is 2,048 times asloudastheother.If the difference is 120 decibels then one sound is 4,096 times asloudastheother.

2.Whenusingrule1(above)itdoesn’tmatterwhichdecibelnumberyou

starton.Forexample,thedifferencebetween10decibelsand20decibelsis 10 decibels so 20 decibels is twice as loud as 10 decibels. But thedifferencebetween83decibelsand93decibelsisalso10decibels—so93decibelsistwiceasloudas83decibels.Similarly,72decibelsis16timesas loudas32decibels (because thedifferencebetween72 and32 is 40decibels).3. Although the decibel system should only be used to compare therelativeloudnessoftwonoises(asinrules1and2above),manypeopleusedecibels as a definitemeasureof the loudnessof a single noise. Inthiscasetheyarenotsaying“alargebeecreatesanoiseof20decibels”;what theyareactuallysayingis“alargebeecreatesanoisewhichis20decibels louder than thequietestnoisewecanhear.”Thequietestnoisewecanheariscalledthe“thresholdofhearing,”sowearereallysaying“alargebeecreatesanoisewhichis20decibelslouderthanthethresholdof hearing.” When people appear to be using decibels in a non-comparative way (e.g., “The loudness of that motorbikeis 90dB”) it’sjustbecausetheyhaven’tbotheredtoincludethephrase“louderthanthethresholdofhearing”—it’stakenforgranted.

C.TuninganinstrumenttoapentatonicscaleIf you are doing this as an experiment itwould be convenient to use aguitar, as it’s the commonest six-string instrument.On a guitar, thestringsaretraditionallynumbered1to6with6beingthethickestoneandthe lowest note. Unfortunately,this is the opposite of the numberingsystemIusedinchapter8.Itriedreversingthenumbersinthechaptertomatch theguitarsystem,butitspoiledtheclarityofthechapter.SoI’mgoing to give you instructions twice—once following the numberingsysteminchapter8,andonceusingthetraditionalguitarnumberingforthestrings.Youcanuseeithersetofinstructions—they bothgiveexactlythesameresult.If you tune a guitar to a pentatonic scale, you will change the

differencebetweenthethickeststringandthethinnestfromtwooctavestooneoctave. Ifyoumake the thickeststringgive itsusualnotebeforeyoustart,thiswillmeanthatthethinnerstringswillbeveryslackbythetimeyouhave finished.Thisdoesn’tmattermuch ifyouaredoing thisoutofcuriosityandyouaregoingtoreturntheguitartoitsnormaltuninginafewminutes.If,ontheotherhand,youaredoingthisasalong-termplanorasademonstrationforstudents,I’drecommendthatyoutightenthethickeststringtogiveahighernotebeforeyoustartand/orchangethethinnerstringsforthickerones.Retuning like this takes a while if you start with a normally tuned

guitar,becausethestringsresentbeingde-tunedsomuchandtakealongtimetosettledowntotheirnewtighterorslackertensions.Ialsosuspectthat theunbalanced tensionofthestringswillcause theneck tobend ifyouleaveaguitartunedlikethisforseveraldays.So,herewego.Onefingerofonehandwillbeusedtopluckthestrings

individually, andone fingerof theotherhand (calledthe“non-pluckingfinger,”below)shouldgentlyrestonthestring—asshowninthephotoinchapter8.Eachstringcanproducefournoteseasily:

•thenaturalnoteoftheopenstring(whichwewillcall“open”)• the “octave above” pinged note—created by pinging the string withyour non-plucking finger on themiddle of the string (ona guitar, themiddleofthestringisdirectlyabovethetwelfthfret)

• the “double octave above” note—created by pinging the string withyour non-plucking finger one quarter of its length fromeither end—directlyabovethefifthfret

• the“new”note—createdbypingingthestringwithyournon-pluckingfinger one third of its length from either end—directlyabove theseventhfret.

Ifwecallthethickeststringnumber1

Firstofallwetunethethickeststring(string1)toahigherthannormalnote(tostopthethinnerstringsbeingtooslackwhenwehavefinished).Thenthe“octaveabove”noteofstring1shouldmatchthe“open”note

ofstring6.The “new”note of string 1 shouldmatch the “octave above” note of

string4.The “new” note of string 4 shouldmatch the “double octave above”

noteofstring2.The “new”note of string 2 shouldmatch the “octave above” note of

string5.The “new” note of string 5 shouldmatch the “double octave above”

noteofstring3.Alldone—instantOrientalsound.

Ifwecallthethickeststringnumber6(normalguitarnumbering)

Firstofallwetunethethickeststring(string6)toahigherthannormalnote(tostopthethinnerstringsbeingtooslackwhenwehavefinished).Thenthe“octaveabove”noteofstring6shouldmatchthe“open”note

ofstring1.The “new”note of string 6 shouldmatch the “octave above” note of

string3.The “new” note of string 3 shouldmatch the “double octave above”

noteofstring5.The “new”note of string 5 shouldmatch the “octave above” note of

string2.The “new” note of string 2 shouldmatch the “double octave above”

noteofstring4.Alldone—instantOrientalsound.

D.Calculatingequaltemperament

AsIsaidinchapter8,GalileiandChuTsai-Yufoundthatcalculatingtheequal temperament system is pretty easy once youhave presented theproblemclearlyandlogically:

1.Anoteanoctaveaboveanothermusthavetwicethefrequencyofthelowerone.(Thisisthesameassayingthatifyouusetwoidenticalstringsone must be half the length of the other—the frequency of the noteproducedbyastringgoesupasthestringgetsshorterandhalfthelengthgivesdoublethefrequency.)2.Theoctavemustbedividedupintotwelvesteps.3.Allthetwelvestepsmustbeequal.(Ifyoutakeanytwonotesonestepapart,thenthefrequencyratiobetweenthemmustalwaysbethesame.)

Let’slookatanexampletomakethecalculationclearer.Inthisexamplewewillmakeeverystring90percentaslongasitslongerneighbor—andallstringsaremadeofthesamematerialandareunderthesameamountoftension.

1.Let’smakeourlongeststring24incheslong.2.Stringnumber2is90percentofthelengthofstring1(i.e.,21.6incheslong).

3.Stringnumber3is90percentofthelengthofstring2(i.e.,19.4incheslong).

4.Stringnumber4is90percentofthelengthofstring3(i.e.,17.5incheslong).

5.Continueuntilyoureachstring13.

This example shows how the percentage shortening system works, butunfortunately we picked the wrong percentage. There istoomuch of ajumpbetweenstrings.Wewantthethirteenthstringtobehalfaslongasthe original string so that it willproduce a note an octave above it.However, if you make every string 90 percent of the length of the

previousone,yourthirteenthstringwillbefarshorterthanyouwantittobe.Sowhatpercentageshouldweuseforshorteningourstrings?This is where Galilei and Chu Tsai-Yu come in handy. They

calculated* exactly the correct percentage to make string 13 half thelength of string 1.And the answer is… 94.38744 percent. Or, toput itanotherway, you need to remove 5.61256 percent of the length of anystringtofindthelengthofitsshorterneighbor.Sonowlet’sdothecalculationusingthiscorrectpercentage:

1.String1is24incheslong.2.String2is94.38744percentaslongasstring1—i.e.,22.65inches.3.String3is94.38744percentaslongasstring2—i.e.,21.38inches.4.String4is94.38744percentaslongasstring3—i.e.,20.18inches.5.String5is94.38744percentaslongasstring4—i.e.,19.05inches.6.String6is94.38744percentaslongasstring5—i.e.,17.98inches.7.String7is94.38744percentaslongasstring6—i.e.,16.97inches.8.String8is94.38744percentaslongasstring7—i.e.,16.02inches.9.String9is94.38744percentaslongasstring8—i.e.,15.12inches.10.String10is94.38744percentaslongasstring9—i.e.,14.27inches.11.String11is94.38744percentaslongasstring10—i.e.,13.47inches.12.String12is94.38744percentaslongasstring11—i.e.,12.71inches.13.String13is94.38744percentaslongasstring12—i.e.,12.00inches.

Nowthethirteenthstringishalfaslongasthefirststring,whichiswhatwe wanted. Also, the relative length of any stringcompared to itsneighborisalwaysthesame—soitdoesn’tmatterwhichstringyoustartyourtuneon,thesamesequenceofupanddownjumpswillgiveyouthesametune(butthewholetunewillbehigherorlowerinpitch).

E.Thenotesofthemajorkeys

Inthefollowinglist,“ ”means“flat”and“#”means“sharp.”

Amajor:A,B,C#,D,E,F#,G#B major:B ,D,E ,G,ABmajor:B,C#,D#,E,F#,G#,A#Cmajor:C,D,E,F,G,A,BD major:Db,E ,G ,A ,B ,CDmajor:D,E,F#,G,A,B,C#E major:E ,G,A ,B ,C,DEmajor:E,F#,G#,A,B,C#,D#Fmajor:F,G,A,B ,D,EF#major:F#,G#,A#,B,C#,D#,E#(orG major:G ,A ,B ,C ,D ,E

,F)Gmajor:G,A,B,C,D,E,F#A major:A ,B ,C,D ,E ,F,G

Note:F#isthesameasG —sowecouldhaveeitherkeyinthiscase.Ineveryothercasewherethekeycouldhaveoneoftwonames(e.g.,D andC#),wegenerallychoosetheonewiththeleastsharpsorflatsinthekeysignature.D involvesfiveflatsbutitsalternative,C#,wouldhavesevensharps—sowegenerallyuseD .ThereisnosuchclearchoiceinthecaseofF#/G becauseF#hassixsharpsandG hassixflats.

AcknowledgmentsIwould,ofcourse,liketotakeallthecreditforthegoodbitsofthisbook,andblameallthebadbitsonsomeoneelse—preferablysomeoneIdon’tlike who lives miles away. Unfortunately, this sort of behavior isgenerallyfrownedupon,soIhadbettercomecleanandadmitthatIhadalotofhelp.Myeditor,HelenConford,wasendlesslyhelpfulinkeepingmeonthe

straightandnarrowand trying togetme toproduceareadablepieceofwork. Without the enthusiasm of my agent, Patrick Walsh, the wholethingwouldhavefallenatthefirstfence.IwouldalsoliketothankSarahHunt-Cooke for her impressive wheeler-dealing work on the project.Also, thanks toJaneRobertsonforhercopy-editingandtoRebeccaLeeforhereditorialcoordination.ManythankstoTracyBeharandMichaelPietschofLittle,Brownfor

lots of useful ideas and guidance, and to their colleaguesChristinaRodriguez and Peggy Freudenthal for all their editorial and productionwork.Thanks also to my friends and family who read through the shabby

initial drafts and gave lots of useful feedback and ideas,especiallyDr.Nikki Dibben, Utkarsha Joshi, Libby Grimshaw,AngelaMelamed, Dr.SteveDance,TonyLangtry,MiniGrey(andHerbie),RodO’Connor,Dr.DonalMcNally,Mike Smeeton, ClemYoung,Dr. JohnDowden,Whit,ArthurJurgensand,ofcourse,Queenie(mymother).Thanksarealsoduetomycompositiontutor,Dr.GeorgeNicholson.SpecialthankstoJoGreyforthephotographs.Agold-medal-order-of-merit isdue tomygirlfriendKimJurgens for

herexcellentproof-reading,encouragementandhelpwiththeartwork—andforpreventingmefromthrowingmylaptopand/orprinteroutofthedining-roomwindowonnumerousoccasions.Finally, the platinum award for suggestions, corrections and back-up

information is awarded to my unfeasibly well-informedfriend John

Wykes.Having handed out these justifiable honors, I see no reason why I

should go the whole hog and admit responsibility for anyerrors,omissionsorotherbadstuff.Ithinkanyblameinvolvedshouldbeborneby my secondary school geography teacher,Mr. Nigel Jones, of 14bMontebank Close, Eccles, Lancashire. Please send any negativecomments, lawsuitsordemands forcompensationdirectly tohimat theaboveaddress.

Bibliography

Books

ThephysicsofmusicJ.Backus,TheAcousticalFoundationsofMusic,2ndedn,W.W.Norton,1977

W.Bragg,TheWorldofSound,G.BellandSons,1927M. Campbell and C. Greated,TheMusician’sGuide to Acoustics , newedn,OxfordUniversityPress,1998

H. Helmholtz,On theSensationsofTone , 2nd edn,DoverPublications,Inc.,1954

D. M. Howard and J. Angus,Acoustics and Psychoacoustics, 2nd edn,FocalPress,2000

I. Johnston,MeasuredTones—The InterplayofPhysics andMusic , 2ndedn,Taylor&Francis,2002

S. Levarie and E. Levy,Tone—A Study inMusical Acoustics , 2nd edn,KentStateUniversityPress,1980

J. R. Pierce,The Science of Musical Sound, 2nd revised edn, W. H.FreemanandCo.,1992

J. G. Roederer,The Physics and Psychophysics of Music—AnIntroduction,3rdedn,Springer-Verlag,1995

C. Taylor,ExploringMusic—TheScienceandTechnologyofTonesandTunes,Taylor&Francis,1992

ThepsychologyofmusicJ. Dowling andD. L. Harwood,MusicCognition,Academic Press Inc.,1986

D.Huron,SweetAnticipation—MusicandthePsychologyofAnticipation,MITPress,2006

P. N. Juslin and J.A. Sloboda (eds),Music and Emotion—Theory andResearch,OxfordUniversityPress,2001

D. L. Levitin,This Is Your Brain on Music: The Science of a HumanObsession,DuttonBooks,2006

B. C. J.Moore,AnIntroduction to thePsychologyofHearing, 3rd edn,AcademicPress,1989

O.Sacks,Musicophilia—TalesofMusicandtheBrain,Picador,2007J.A. Sloboda,TheMusicalMind—TheCognitivePsychology ofMusic,ClarendonPress,1985

GeneralG. Abraham (ed.),The Concise Oxford History of Music, OxfordUniversityPress,1985

F. Corder,TheOrchestraandHow toWrite for It , J.CurwenandSons,1894

R.W.Duffin,HowEqualTemperamentRuinedHarmony ,W.W.NortonandCo.,2007

A.Einstein,AShortHistoryofMusic,3rdedn,DorsetPress,1986H. Goodall,Big Bangs: The Story of Five Discoveries that ChangedMusicalHistory,ChattoandWindus,2000

G.Hindley(ed.),TheLarousseEncyclopediaofMusic,Hamlyn,1971B.McElheran,ConductingTechnique:ForBeginnersandProfessionals ,3rdedn,OxfordUniversityPress,2004

R.andJ.Massey,TheMusicofIndia,KahnandAverill,1976W. Piston,Orchestration, Victor Gollancz, 1978 (originally published,1955)

A. Ross,TheRest IsNoise: Listening to the TwentiethCentury, FourthEstate,2008

C.Sachs,AShortHistoryofWorldMusic,DobsonBooks,1956

S. Sadie (ed.),Collins Classical Music Encyclopedia, HarperCollins,2000

P.A. Scholes (ed.),TheOxfordCompanion toMusic, 2nd edn,OxfordUniversityPress,1939

R.SmithBrindle,MusicalComposition,OxfordUniversityPress,1986E.Taylor,TheABGuidetoMusicTheory,Parts1and2,TheAssociatedBoardoftheRoyalSchoolsofMusic,1989/1991

H.H.Touma,TheMusicoftheArabs,AmadeusPress,1996H.J.Wood,MyLifeofMusic,VictorGollancz,1938

JournalPapersD. Deutsch and K. Dooley, “Absolute pitch among students in anAmerican music conservatory: Association with tone languagefluency,”J.Acoust.Soc.Am.125(4),April2009,pp.2398–2403

R. W. Duffin, “Just Intonation in Renaissance Theory and Practice,”MusicTheoryOnline,Vol.12,No.3,October2006

J. Powell andN.Dibben, “Key–MoodAssociation:ASelf-PerpetuatingMyth,”MusicaeScientiae,Vol.IX,No.2,Fall2005,pp.289–312

Contents

FrontCoverImageWelcomeDedication1.So,WhatIsMusic,Anyway?2.WhatIsPerfectPitchandDoIHaveIt?3.NotesandNoises4.XylophonesandSaxophones:SameNotesbutDifferentSounds5.InstrumentalBreak6.HowLoudIsLoud?7.HarmonyandCacophony8.WeighingUpScales9.TheSelf-ConfidentMajorandtheEmotionalMinor10.IGotRhythm11.MakingMusic12.ListeningtoMusicFiddlyDetailsA.NamingandidentifyingintervalsB.UsingthedecibelsystemC.TuninganinstrumenttoapentatonicscaleD.CalculatingequaltemperamentE.ThenotesofthemajorkeysAcknowledgments

BibliographyAbouttheAuthorCopyrightPage

AbouttheAuthor

Dr. John Powell is a physicist and a classically trainedmusician, withnaturally curly hair. He has given lectures at internationallaserconferencesandplayedguitarinpubsinreturnforfreebeer.Heprefersthe latter activity. Dr. Powell decided towrite this engaging andaccessibleintroductiontothescienceandpsychologybehindmusicwhenhe discovered that all theexisting books on the subject gave him aheadache.Heholdsamaster’sdegreeinmusiccompositionandaPhDinphysics, andhas taught physics at the Universities of Nottingham andLulea(Sweden)andmusicalacousticsatSheffieldUniversity.He livesinNottingham,England.

*A tuning fork is a specially shaped piece ofmetalwhich produces aspecificnotewhenyouhitit.

*Ifyoulookbacktothephotoofthepianokeyboardinchapter1,youwill see that theword“adjacent” isa littlecomplicatedforapiano.Allthewhitekeyslookadjacenttoeachotherbecausetheblackkeysarenotlongenough to separate themproperly.The fact that theblackkeysareshortismerelytohelpwiththeergonomicsoftheinstrument.Asfarasthe sound is concerned,the white notes B and C are adjacent to eachother,butFandG,forexample,arenot—theyareseparatedbyF#.

*Wecouldfindoutwhattheactualrippleshapeforaclosingdoorlookslikebyattachingamicrophonetoacomputerandaskingthecomputertodraw the changes in pressure experienced by the microphone (amicrophone acts rather like an ear—it has asmall part inside whichmovesinandoutasthepressureoftheairgoesupanddown).Theactualripple patternwould probablybeevenmorecomplicated than theone Ihavedrawnhere.

*Whenwesay“cyclespersecond,”wemeanhowmanytimesthestringmoved throughacompletecycleinonesecond.Acompletecyclewouldbe,forexample,startinginthemiddle,movingovertotheright,backtothemiddle,overtotheleftandthenbacktothemiddle.

*Theuseoffretstoshortenguitarstringsisdiscussedhere.

*Traditionallytheorganisreferredtoasakeyboardinstrumentandthethought-police will take you away in handcuffs ifyou call it a windinstrument. So I’m calling the second three instruments “wind intubes”—let’sallhopeIgetawaywithit.

*Actually,eachhammerhitstwoorthreestrings—alltunedtothesamenote—forextraloudness,butIwillreferto“astring”asiftherewasonlyoneineachcase.

*The first two notes of “Somewhere over theRainbow” are an octaveapart.

*Guitaristscall“pinging”“playingharmonics.”

*Iwillcallthisthekeynote,orteamleader,butitistraditionallycalledthetonic , which is based on theAncient Greek and Latin words for“tone.”

* Even though the sharp/flat notes have two names, it would beconsideredverypeculiartonamethenotesofthe“A”majorscaleusing“flat”nameslikethis:

A—B—D —D—E—G —A —A

This way of naming notes in a key is not used because some lettersappeartwice(“A”and“A ”“D”and“D Ý),whichisconfusing.Weuseonlyeither“flat”or“sharp”namesforeachkey—andchoosewhicheversystemusesalltheletters,likethis:

EMajor:E,F#,G#,A,B,C#,D#,E

B Major:B ,C,D,E ,F,G,A,B

*Muscularmemoryisexplainedhere.

* I say this here because that’s what is supposed to happen. In manycases, however, I have seen professional conductors simplymakingpointlessdramaticgestureswhich indicatenothing to themusiciansbutlookgoodtotheaudience.

*GalileiandChuTsaiYuprobablystartedbycalculatingtheincreaseinfrequencybetween twoadjacentnotes.Fromthisyoucanworkouthowmuch shorter thehigher string shouldbe. Ihaveused the shorteningofstrings because it makes the discussioneasier to follow. Our twowisemencalculatedthatweneededanincreaseinfrequencyof5.9463percentbetween two adjacentstrings: for example, ifGhasa frequencyof392Hz,thenthenoteonesemitoneup(Gsharp)hasafrequencyof105.9463percent of 392 , which is 415.3 Hz. To achieve this, if the strings areotherwise identical, theGsharp stringwillhavetobe94.38744percentthelengthoftheGstring.

HowMusicWorks

TheScienceandPsychologyofBeautifulSounds,

fromBeethoventotheBeatlesandBeyond

JOHNPOWELL

LITTLE,BROWNANDCOMPANY

NEWYORKBOSTONLONDON

Copyright

Copyright©2010byJohnPowellAllrightsreserved.ExceptaspermittedundertheU.S.CopyrightActof1976,nopartofthispublicationmaybereproduced,distributed,ortransmittedinanyformorbyanymeans,orstoredinadatabaseor

retrievalsystem,withoutthepriorwrittenpermissionofthepublisher.

Little,BrownandCompanyHachetteBookGroup

237ParkAvenue,NewYork,NY10017Visitourwebsiteatwww.HachetteBookGroup.com.

www.twitter.com/littlebrown.

FirsteBookEdition:November2010OriginallypublishedinGreatBritainbyParticularBooks,adivisionof

thePenguinGroup,August2010

Little,BrownandCompanyisadivisionofHachetteBookGroup,Inc.TheLittle,BrownnameandlogoaretrademarksofHachetteBook

Group,Inc.

Thepublisherisnotresponsibleforwebsites(ortheircontent)thatarenotownedbythepublisher.

ISBN:978-0-316-18367-3