Acoustical Properties of the Alto Saxophone

7/27/2019 Acoustical Properties of the Alto Saxophone

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AcousticalPropertiesoftheAltoSaxophone

BenMeyerandCraigRiccardo

UIUCPhysics193POM,Fall2010

HistoryoftheAltoSaxophone

ThealtosaxophonewasinventedbyAdolpheSaxofBelgianin1845. Afterstudyingtheclarinet

andtheflute,Saxdecidedtoattempttoconstructaninstrumentthatwouldcovermoreofthemiddle

rangeofsoundformilitarybands. Hisinitialgoalwastocombinethetoneoftheclarinetwiththe

brassy,brightersoundofthetrumpet. ThealtosaxophonewasfirstusedinFrenchorchestrasand

militarybandsduringthe1800s,butitdidnotgaingreatpopularityuntilthejazzmovementofthe

1920s. Thefirstaltosaxophonewasrelativelysimplecomparedtomodernsaxophones. Notonlywere

therelesskeys,buttheoriginalaltosaxhadtwotothreeoctavekeys,ratherthantheoneoctavekey

associatedwithsaxophonestoday. Theadditionsmadetothesaxophoneovertimemadeiteasierto

playandgavethemusicianmorerange.

MechanicsoftheInstrument

Thealtosaxophoneissimilartotheclarinetinthatitisareedinstrument. Thereed,whichis

usuallymade

of

aspringy

piece

of

cane

and

has

vibrational

tendencies,

is

secured

to

the

mouthpiece

andisforcedtovibratebytheairstreamofthemusician. Thevibrationintheairwithintheinstrument

causesthesaxophonetoresonate.Resonancereferstothecreationoflargeamplitudevibrationsasa

systemwhichvibrateswithacertainfrequencyisactedonbyaperiodicdisturbancewiththesame

frequency. Thismeansthattheinstrumentvibratesatthesamefrequencyastheairflowingthroughit.

Dependingonthekeycombination,differenttoneswillbeproducedasthelengthoftheinstrumentis

shortenedor

lengthened.

The

longer

the

instrument,

the

longer

it

takes

for

the

wave

to

travel

through

it,resultinginalowerfrequency. Lowerfrequenciescorrespondtoalowerpitch,whichisthesubjective

evaluationofthefrequencyofasound,andhigherfrequenciescorrespondtohigherpitch. Thisexplains

whyalowernoteisproducedwhenallofthevalvesonthesaxophoneareclosed. Thefrequencyofthe


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notecanalsobechangedbytheembouchure,ortheshapeofthemusicianslipsaroundthe

mouthpiece.

Asthesoundtravelsthroughtheinstrument,

thewavesorparticlesexperiencecompressionsand

rarefactionsasdemonstratedbythepictureonthe

right. Thesaxophoneissimilartotheclarinetinthatit

isopenononeendandclosedontheother,however,

itactsmoreasaconicaltubeandthereforeplaysall

harmonics,ortheintegermultiplesofthefundamental

frequency,ratherthanjusttheoddharmonics. The

bellofthesaxophonehelpsthesoundwavesradiate

moreintotheairandtraveltotheaudience.TestingtheInstrument

InordertocollectdatatoexaminetheacousticalqualitiesofmyYamahaaltosaxophone,the

instrument

was

placed

in

the

box

and

extremely

small

microphones

were

placed

at

the

mouthpiece

and

bellendoftheinstrument[1]. Themicrophonesmeasuredtheparticlevelocityandparticlepressure

thatwentintotheinstrumentandthatexitedtheinstrumentfromthebellend. Asinewavefunction

generatorwasusedalongwithapiezoelectrictransducer,whichactedasasmallspeaker,toexcitethe

airwithinthecolumnofthealtosaxophone. Thisprocesswasusedwiththreedifferentvalve

combinationssothatwecouldcomparetheinharmoncitiesbetweennotesandofthesaxophonein

general.The

combinations

tested

were

all

valves

up

(C#/Concert

E),

three

valves

closed

(G/Concert

B

flat),andonevalvedown(B/ConcertD). Thesoundpressureandparticlevelocitydatawasalsousedto

calculateacousticalimpedancetoidentifythefrequencyvaluesatwhichdifferentnotescanbeplayed.


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ImageofAltoSaxophoneintheBox:

ImageofPCBasedDataAcquisitionSystem:


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GeneralResults

Impedance:

UsingthisprocesswiththeDAQsystemsupplieduswithalargequantityofdata,suchasthe

complexparticlepressureandcomplexparticlevelocityputintothesaxophone. Themainconcernto

us,however,wastheratioofthetwo,ortheacoustic impedance. Acousticimpedanceisdefinedasthe

soundpressuredividedbytheparticlevelocity,anditisdependentuponfrequency. Impedance,

definedinadifferentway,istheresistancetheinstrumenthastoblowingairthroughit.

Acousticimpedancecanalsobereferredtoasacousticalohms,whichmakessensesinceohms

measureselectricalresistance.Whenplayingthesaxophone,themusicianputspressureintothe

instrumentbyblowingairintothemouthpiece. Thepressuretravelsthroughtheinstrumentasawave

butisreflectedbacktowardsthereedandmouthpiecewhenitreachesthebellendoftheinstrument.

Thisreturnofthepressurewavetothemusicianslipscausesthemouthpiecetovibrate,informingthe

playerabout

which

frequency

they

must

play

to

achieve

the

desired

note.

This

process

helps

to

explain

whyoneoftenfeelsavibrationfromthemouthpiecetotheirlipsastheyplaycertainnotes. Towrapup

thisidea,thegreatertheimpedance,thegreaterthenumberofwavesthatarereflectedbacktowards

themusicianslipstosignalwhatfrequencyshouldbeplayed. Thus,thehighertheimpedance,the

easieritwillbeforamusiciantoplaythatnoteorinotherwords,theplayablenotesontheinstrument

willoccurattheimpedancepeaksormaximumsonthegraphs.

ImpedanceoftheYamahaAltoSaxophone:

Wewillusethefollowinggraph,whichmeasuresthemagnitudeoftheinputimpedanceofthe

saxophoneasavariableoffrequency,inordertomakeconnectionstothedifferentnotesthatcanbe

playedonourspecificaltosaxophone.


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InputImpedanceMaxima&Minima,allvalvesopen(C#5)

The

first

impedance

maximum

that

is

easily

seen

occurs

at

around

400

Hertz.

As

stated

before,

the

maximaoftheimpedancegraphsshouldshowtheplayablenotesontheinstrument. However,the

fundamentalfrequencyorfirstharmonicofthealtosaxophone,orthepedalnote,isextremelydifficult

toplaybecauseitispulleddownsoloworflat. Thesecondimpedancepeak,whichoccursat851.5

Hertz,wouldthenrepresentthelowestplayablenoteontheinstrumentforthefingeringcombination

ofC#5. Thesubsequentpeaksthatoccurathigherfrequenciesrepresenttheoctavesofthisnote.

Therefore,it

seems

to

appear

from

this

graph

and

the

maxima

of

the

impedance

that

there

are

four

playablenoteswhenallthekeysonthealtosaxophoneareup. Thisseemstoexplainourunderstanding

ofhowonoursaxophonesweareabletoplayalowC#belowthestaff,C#inthestaff,ahighC#above

thestaff,andthealtissimonote,eventhoughitisextremelydifficulttoplay,whichcanbeproducedby


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changingtheembouchureorthestreamofair. Thesehighernotesareoftenmoredifficulttoplayon

thealtosaxophone,whichisalsorepresentedbythegraphabovebythelowervaluesoftheimpedance

peaksathigherfrequencies. Thisalsohelpstoexplainwhytheadditionoftheoctavekeywasnecessary

toallowthemusiciantoplaythesehigherpitchednotes.

InputImpedanceMaxima&Minima,1valveclosed(B4)

Similarly,theimpedanceoftheothernotestestedwereexaminedtodeterminethevariousplayable

noteswithonevalveclosed,orB4onthealtosaxophone,andthreevalvesclosed,orG4onthealtosax.

Theabovegraphshowstheimpedancemaxima,andaccordinglytheplayablenoteswiththeB4

fingering,andthefollowinggraphshowsthesamethingfortheG4fingering.


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InputImpedanceMaxima&Minima,3valvesclosed(G4)

TheincreasednumberofimpedancepeaksfortheB4andG4fingeringsasdemonstratedbythegraphs

indicatesthatthereareanincreasednumberofplayablenoteswhenusingthesefingering

combinations. Asasaxophonist,onemaynotactuallyuseallofthesenoteswhenplayingmusic,butby

changingonesembouchuretovarythefrequencyofthenoteplayed,onecouldtheoreticallyproduceall

ofthesepitcheswithbothfingerings. Theoutputimpedance,whichwasalsomeasuredandgraphed,

hasusefulimplicationsinthatitprovidesinformationaboutwhatsoundsorpitchesareheardbythe

audience.


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InharmonicitiesoftheAltoSaxophone

Oneofthemaingoalsintakingallofthisdatawastodeterminetheharmonicvalueofthealto

saxophone. Toachievethis,thegraphsoftheimpedanceforeachnotewereused,andthefrequencyof

thesecondinputimpedancepeak,orthesecondharmonic,wascomparedtotheclosestnoteonthe

piano[2].

Asdepictedbytheinharmonicitygraphabove,theC#5,whichhadasecondharmonicwiththe

frequencyof851.5Hertz,wasclosesttoAb5onthepiano,whichhasafrequencyof830.61Hertz.

Likewise,B4hadasecondharmonicfrequencyof729.5HertzandwascomparedtoGb5witha

frequencyof739.99Hertz. Finally,G4onthealtosax,withameasuredfrequencyof551.5Hertz,was

comparedtotheclosetnoteonthepianoofDb5,withafrequencyof554.37Hertz. Aspredicted,the

firstharmonicofeachnoteispulledextremelylow,sincethepedalnoteisveryflatandrarelyabletobe

played. Thegraphcomparestheharmonicnumberofeachnotetotheinharmonicityvalueincents.


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Centsreferstothelogarithmicunitusedtodivideintervals. Theoctaveisdividedintotwelvedifferent

semitones;therefore,thereare100centsinasemitone. Asemitonecanalsobedefinedasahalfstep.

Usingthisconceptandthedatafromthegraph,wecanstarttomakeconnectionstowhatthismeans

forourspecificinstrument. Forinstance,wecanlookatthethirdharmonicofAb5,orC#onthealto

sax,andnoticethatitisoffbyapproximately90cents,ornearlyafullsemitoneortwelfthofanoctave

sharp. ThefourthharmonicofC#isalsopulledhigh,whichhelpsustounderstandwhywhenplaying

thisspecificsax,thepitchofC#isusuallytoosharpandmustoftenbeadjustedbyusingthe

embouchure. B4onthealtosaxophonealsoappearedtobepulledhigh,withthefourthharmonicbeing

overafullsemitonegreaterthanwhatitshouldbe. Finally,G4,whichisoftenoneoftheeasiernotesto

playonthealtosax,seemedtobelessinharmonic,withtheinharmonicityincentsvaryingslightlylow

andhighforthevariousharmonics. Thismayexplainwhysaxophonistswilloftentunetothisnoteas

well.

Conclusions

Inconclusion,theintendedpurposeofanalyzingthedataobtainedinclasswastodetermine

the

harmonic

content

and

acoustical

properties

of

our

Yamaha

alto

saxophone.

Through

the

data

obtainedbythePCbaseddataacquisitionsystem,wewerenotonlyabletoexaminetheinput

impedancetodeterminethefrequenciesoftheplayablenotesfordifferentkeycombinations,butwe

werealsoabletodeterminetheinharmonicityoftheinstrumentandmakeconnectionstowhatthis

meansintermsofactuallyplayingthesaxophone.

References

[1]Acoustic

Impedance

of

aBb

Trumpet,

David

Pignotti

UIUC

Physics

Senior

Thesis,

2007,

http://online.physics.uiuc.edu/courses/phys193/193_reu.html

[2]CalculatingMusicalInstrumentInharmonicities,Prof.S.Errede,UIUCPhysics193LabHandout,

http://online.physics.uiuc.edu/courses/phys193/193_labs.html

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Acoustical Properties of the Alto Saxophone