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MUSIC THEORYtools for creativity & understanding

HOWARD HARRISON 2010

HH2011 \ music theory 1 \ scales \ modes \ intervals \ harmony

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If it sounds right, it is right.

Music Theory isnt a set of rules about how things should be - it just

observes how music seems to work, and what it seems to be made of.

It notices what other musicians do and have done, because we have

much to learn from them - after all, it was other musicians that

inventedthe thing in the first place.

This document is a work in progress, something that started small and

that I keep patching and extending as people seem to need it - there

will subsequently be a version that includes self-testing exercises,

some subjects will be covered in greater depth & it will broaden in

scope. In the meantime it tells you much of what you ought to know

about scales, modes, intervals and harmony in western music, and

much else. I hope it is helpful.

Each stage provides information that will allow you to understand the

next, so take it in order unless you are using it for reference purposes.

Words in red are key terms or concepts.


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MUSICTHEORY

HOWARD HARRISON 2010


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CONTENTS

Page numbers might be approximate!

7 SOUND

9 THE CHROMATIC SET

10 First Intervals - octave, tone, semitone

11 SCALES

12 The Major Scale13 Tetrachords

13 Key Signatures

14 The 12 major Keys

17 Minor Scales - Natural Minor

18 Melodic & Harmonic Minor Scales

20 Relative Major & Minor keys

21 Minor Key Signatures

22 Scale Step Names

24 Key relationships25 Other Scales - Modes

27 Pentatonic Scales

28 Whole Tone & Octatonic Scales

29 Atonal Music

30 INTERVALS

Harmonic & Melodic Intervals

Integer Notation

31 Pitch Class Intervals

Intervals in tonal music

Number & Quality

32 Major & Perfect Intervals

Minor Intervals

Diminished Intervals

33 Augmented Intervals


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34 Consonance & Dissonance

Inversions

35 Interval Characters

36 Intervals & Musical Style

38 HARMONY

39 Functional Harmony

40 Diatonic Chords - naming them

41 Primary Chords - The 3-chord trick

Secondary Chords

42 Hierarchy of Chords

The Dominant Seventh

43 Modal Chord Sets

45 The Classical Minor System47 Rock & Pop Chord Sequences

48 Other Chords

And more! - CHORD PROGRESSIONS . . . . . .


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SOUNDHit a drum-skin \ force air between your

vocal folds \ pass fluctuating electrical

signals through a loudspeaker system \

squeeze a reed and blow \ twang a string

- whenever you activate a musical

instrument you make an elastic material

wobble; you make it vibrate.

When something vibrates it disturbs the

air around it and the ripples that result

spread through the air and ultimately

disturb your ear-drum. Electrical impulses

report the movements of your ear-drum

to your brain and at that point the

vibrations become sound. Sound is onlyin your head; if there's no-one there to

hear it, a falling tree really does make no

sound.

If the ripples move your ear-drum at

absolutely regular intervals, and if there

are more than 20 and less than about

20,000 of them each second, the brain

will perceive a steady note. The faster the

vibration, the higher the note.

A string that plays the A below the

middle C on a piano vibrates 440 times a

second. We say that it has a frequency of

'440 cycles per second (cps), or

'440Hz' (Hertz).

Halve the length of that string and it will

vibrate 880 times a second, exactly twice

as fast as before.

We now hear a note with a mysterious

quality; although it's obviously higher

than the 440 A and therefore different, it

is also strangely the same. Because the

new note sounds the same-but-different,

it feels reasonable to name it after the

first, so this is another, higher A.

The distance or interval between two

notes related in this way is an octave, and

the strange kinship between the two

notes is called octave equivalence, a

phenomenon that almost all human

beings experience and one of the

essential building blocks of almost allmusic.

Long ago, we started finding notes to

spread through the space within the

octave. We could have chosen any

number of notes but most cultures went

for 5, 6 or 7 and most probably chose

their sets of notes intuitively, as they

might have picked flowers - because they

liked them and the ways in which they

related to each other.

In ancient Greece, however, Pythagorus

noticed that it isn't only the simple 2:I

proportions of the octave that please the

ear. Two notes whose frequencies are

related in the proportion 3:2 are alsoparticularly pleasing and produce what

we now call a Perfect Fifth, (C & the G

above it, for instance). 4:3 is a Perfect


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Fourth (C to the F above). 5:4 is a Major

Third (C to E).

These in te rva l s a re remarkab ly

consonant. What the Greeks had noticed

was tha t s imp le ma thema t ica l

relationships between frequencies please

us, particularly when the notes are

played together.

As harmony began to interest European

musicians more and more, they tried

many ways of tuning the intervals within

the octave.

They also devised the chromatic set, a

pool of 12 notes from which a variety of

7-note scales could be extracted; many

early instruments couldnt play all the

possible scales, but an instrument that

was designed to play the chromatic set

could- in theory, at least.

A problem, however; because the 12

notes werent evenly spread through the

octave, some scales were more perfectly

tuned than others. This had its

advantages; composers could choose a

key for its particular flavour, sweet or

sour. But it had its disadvantages; keys

including more than four flats or sharps

were so sour that they were barely

usable. This hampered composers who

wanted to write music that changed keyfreely in the course of a piece, and there

was a growing interest in this possibility.

Slowly, we gravitated towards a tuning

system that had been around since

Galileo's father had advocated it in 1581;

equal temperament, twelve notes spread

at mathematically calculated, equal

intervals across the octave. Now, the

frequency relationships between any two

adjacent notes were identical. We had

str iven for intervals of pris t ine

mathematical and aural perfection but

now made a compromise, trading some

slightly iffy intervals for the possibility of

writing music that could move freely

between 12 acceptably tuned keys, each

one of them using only a selection ofnotes from the full set, and each one

tuned exactly like the others.

This was a move which liberated

composers to write ever richer and more

exotic harmonies and to take their

listeners on safari through many of the 24

available major and minor keys - and

then beyond!

The incredibly fertile but slightly sour set

of twelve notes that we have inherited is

the equally tempered chromatic scale or

chromatic set.


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the CHROMATIC SET

So - the chromatic set contains the 12 equally spaced notes available to us

on most Western instruments. Arranged in ascending or descending order

the 12 notes of the chromatic set become the chromatic scale. The distance,

or interval, between each of these notes and its nearest neighbour is called

a semitone (a frequency relationship of roughly 16:15)

As we have tended to use only seven of these 12 notes at a time, it has

made practical sense to name the 12 notes using only seven letter names.

Seven of these have simple letter names, but notice that they arent

distributed evenly through the twelve (well, they couldnt be . . . ).

A B C D E F G A

The 7 notes with simple letter names are called naturals - A natural, B

natural and so on. Most of the naturals are a tone apart (i.e. two semitones),

but notice that A & B are only a semitone apart, and so are E & F.

The 5 remaining notes are named after the naturals that they sit between and

this means that they can each have two names. The note between A & B, for

instance, can be called A# (A sharp - which simply means the note a

semitone higher than A) OR it can be called B (B flat), meaning the note

a semitone lower than B.

We say that A# is the enharmonic equivalent of B.

Similarly; F# = G, G# = A, C# = D, D# = E

Heres the full chromatic set written out twice, with sharp names on the toprow, and flats on the bottom.

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

A B B C D D E E F G G A A

And here are the two versions written in standard notation -


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The sign that you see written before the naturals () is a natural sign. As you

would expect, its used to indicate that the following note is a natural, and

its use is necessary here to cancel the flat sign on the note before it. Apart

from that, only the names are different; in every other respect these two

chromatic scales are identical.

accidentals

Sharp signs #, flat signs , and natural signs are all called accidentals

when used just before a note. They all apply to the rest of the bar that they

appear in but not beyond.

(Ive never met anybody who knows why they are called accidentals, which

they clearly arent.)

first INTERVALSOCTAVE, SEMITONE & TONE

Just to recap - the differing distances between notes are called intervals, and

each interval has a name. We will describe all of these possibilities later, butfor now you need to know about the following three:

octave the interval between two notes whose frequencies are

related in the ratio 2: I - two As or two C#s for instance.

semitone the interval between any two adjacent notes in the

chromatic set, (E & F, for instance, or F and F#), and

tone two semitones, the interval between A & B or E & F#.


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SCALESA Scale is a collection of notes written or played in ascending or descending

order, starting and finishing on the tonic, the home note for the piece. Itprovides the basic raw materials from which the melody and chords of a

piece can be made.

There are hundreds of different scales in use around the world and each one

has its own flavour and offers certain musical possibilities. Some scales offer

exquisite melodic possibilities, for instance; others are a source of interesting

chords and allow us to create complex harmonic systems.

Most western scales and modes are heptatonic, meaning that they use only

seven notes. Its possible to have scales with more or less than seven notes

and pentatonic scales (five-note scales) are particularly common.

Here are some scales from various cultures, with the chromatic scale at the

top and the other scales all starting on the same note so that you can

compare them easily.


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In reality, Indonesian, Middle Eastern and many other scales use notes that

simply aren't available in equal temperament, so some of the scales written

above are approximations.

In almost all Western classical, popular & folk music, however, the contents

of almost all scales are now selected from the equally tempered chromatic

set.

the MAJOR SCALEThe Major Scale is undoubtedly the best-known and probably the most used

of all heptatonic scales. Its crucial to understand how the major scale is

built, if only because we define all other scales by comparing them with the

Major Scale.

A major scale can start on any note, but then follows this fixed, defining

sequence of intervals -

tone - tone - semitone - tone - tone - tone - semitone

Here, for instance, is the C major scale.

and here is an A flat major scale - the sequence of intervals is the same.


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TETRACHORDSIn common with other Heptatonic (seven note) scales, the Major scale has a

lower tetrachord and an upper tetrachord, its first and last four notes. Notice

that the two tetrachords of a major scale have identical tone-tone-semitone

structures, with a gap of one tone between the two tetrachords.

Notice, too, that the Upper Tetrachord starts on the fifth step of the scale. This

will become very significant . . . . .

KEY SIGNATURESThere are only 12 major scales, one starting on each step of the chromatic

scale. Each one of them uses a unique selection of notes. To indicate which

scale you should use, notated music almost always includes a key signature,

a bunch of up to 7 sharps or flats placed at the beginning of a piece and thenat the beginning of every subsequent line.

Some key signatures contain sharps, some contain flats. No major or minor

key signatures contain both. Some examples -

The last key signature above includes just one flat on the middle B line. In

practice, this means that you should play B every time you see a B,

regardless of which B it is. The third key signature tells you to play F#, C#,

G# & D# and the same rule applies - play these notes every time you see an

F, C, G or D. Notes not mentioned in the key signature are assumed to be

naturals.

This is a really helpful system. It saves a lot of pointless repetition of flat and

sharp signs in the notation. More importantly, it forwarns the experienced

player that they will be using a familiar collection of notes - a G major scale,

for instance.


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the 12 MAJOR KEYSTo understand how the key-signature system works, and how the 12 major

keys are related, it's worth looking again at the diagram showing the two

matching tetrachords of the major scale - (in passing, notice that, as the C

major scale is made up entirely of naturals, there is no need for a keysignature.)

As the Upper Tetrachord of this C major scale has the same structure as theLower Tetrachord, it is possible to use it as the Lower Tetrachord of a new

major scale starting on G - a G major scale -

In order to keep the tone - tone - semitone structure in the new Upper

Tetrachord, the seventh step of this new scale needs to be an F# rather than

an F -The F# is the only note in this scale that isnt a natural, so we simply write a

key signature with one sharp - F# - and this tells the player to play F# when

they see any F in this piece (not just the F on the top line of the stave).

The new Upper Tetrachord that this process has produced can be used to

begin yet another major scale. It starts on D, so its D major -


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The F# in the Lower Tetrachord is still needed, of course, but, as before, the

new 7th step (C) now has to be sharpened to maintain the major-scale

structure, and the new key signature has to have an F# anda C# -

We can carry on this process until we run out of sharps. Each new scale will

start a fifth higher than the last and will include one new sharp at the end of

its key signature.

Here are the major keys with sharps in their key signatures. Notice that the

sharps are always written in the order in which they have been added.

You may have noticed that, as you create each new scale, the sharp that is

added at the end of the key signature always refers to the new 7th step. It

follows that: -

The last sharp in a major key-signature is always a semitone below the

tonic.

The order in which the sharps appear and are written is -

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

(Father Charles Goes Down And Ends Battle)

Notice also that each new sharp is 5 steps above the last.

* E# is an alternative name for F, and B# the alternative name for C. If this is a

surprise, remember that sharp simply means a semitone higher than, and then

it makes sense.


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MAJOR KEY SIGNATURES WITH FLATSSharp key signatures can only be used for seven of the twelve keys. Flats are

needed for the rest.

Key signatures with flats work in a similar fashion to sharp signatures, buteach key starting a fifth belowthe last, and each one adding one more flat to

the key signature. Here are the 'flat' major key signatures starting from C

major again -

Usefully (and logically) -

the order of key signature flats is the reverse of the order of sharps -

B E A D G C F

(Battle Ends And Down Goes Charles Father)

Notice also that each new flat is 5 steps below the last, and that the first fourflats conveniently spell BEAD.

In flat key signatures, the next-to-the-Iast flat names the tonic;

For instance, if the key signature shows B, E & A, its the Eb that

appears next to last, so you're in E major. Look at the flat key signatures

above to check this out.

Youll spot that F major doesnt have a next-to-the-last flat - youre just going

to have to remember that one.

You may also have noticed that there are now apparently 15 key signatures -

this is because F# major has appeared twice - once as F# major, and once as

Gb major, which contains exactly the same notes by different names. B

major has also appeared as Cb, and C# as Db.


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MINOR SCALES

the NATURAL MINOR ScaleThe second best known scale is the minor scale. There are in fact various

versions of the minor scale and the simplest is theNatural Minor.

Starting on C, it goes like this:

You'll notice that the first, second, fourth and fifth notes are the same as inthe C major scale but that steps 3, 6 & 7 are flattened - a semitone lower

than their Major scale equivalents. So, as we define all scales by comparing

them with the major that would start on the same note, we can say that -

the Natural Minor scale has a flat 3, 6 & 7.

You may have also noticed that C natural minor contains the same notes as E

flat major. It will therefore have the same key signature -

Natural Minor scales can start on any note, of course -


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MELODIC & HARMONIC MINOR SCALESIn practice, many pieces in the minor dont simply use the seven notes of

the natural minor scale. Greensleeves is a perfect example of this. Here it

is in A minor, which has no key signature -

Notice that the sixth and seventh steps of the scale (F and G naturals) often

appear as predicted by the key signature, but that sometimes accidentals are

used to indicate that F# and G# should be used instead, despite the fact that

F# and G# are the sixth and seventh steps you would expect to find in A

major.

This is absolutely typical of a huge number of minor key pieces; the major

and minor sixth and seventh steps are used interchangeably, the major

versions being indicated with accidentals.

This may have arisen because musicians found it effective to accompany

minor key melodies using a couple of chords which also include the major

sixth and, more particularly, the major seventh steps. In order not to clash

with these chords, the melody sometimes has to include a major six and

seven, too. In Greensleeves, for instance, the G#s (the major 7s) are almostalways used at a point where an E major chord (E - G# - B) is sounding; a

melodic G would clash.

So why is the sixth step also altered? Sometimes to accommodate a chord

with a sharp 6 in it, but, as often as not, its altered in combination with the

seventh step, simply to avoid large leaps in what would otherwise be a

smoothly flowing phrase.


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In an attempt to rationalise this rather fluid situation, theorists have

constructed the rigid harmonicandmelodic minor scales -

The Harmonic Minorscale is notated with a sharpened seventh step. This scale is regarded as

being the source of the chords used in minor key pieces. In contemporary

use, this isnt quite true. Nevertheless, for reference, here is A harmonic

minor.

(As this scale really only has a theoretical function, why do players of

melody instruments practice it so diligently, except to pass exams?)

The Melodic Minor

scale is notated with the major sixth and seventh steps in the rising version ofthe scale and the flattened sixth and seventh steps indicated by the key

signature in the descending version. Accidentals are needed in both

directions to introduce and then cancel the major 6 & 7.

There is a myth that the major 6 & 7 steps are generally used when melodies

are rising, and that the flat 6 & 7 are used when melodies are falling, andthat this justifies the way that the melodic minor is both notated and

practised.

In reality, the different sixth and seventh steps are used equally in rising and

falling melodies, and for the harmony-related reasons given above. Practising

the melodic minor as it is usually notated is valuable, but it would surely be

more realistic to practice both versions in both directions.


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RELATIVE MAJOR & MINOR KEYSHere are the key signatures for all twelve possible minor keys, each one

starting five scale steps above the last, but leaving out A# minor, Eb minor &

Ab minor, for which there are already enharmonic equivalents. It should look

familiar.

You may have identified that this sequence of minor key signatures is

essentially the same as the sequence of major key signatures that you came

across earlier. Theres nothing obscure about the reason for this: every major

scale contains the same basic set of notes as one minor scale. As these these

pairs of scales use the same notes, they use the same key signatures and they

are considered to have an especially close relationship -

C major and A minor form one such pair, so we can say that C major is the

relative major of A minor, and that A minor is the relative minor of C

major.

Notice that A is the sixth step of the C major scale.

This is true of all pairs of related scales -

The tonic of the relative minor is found on the sixth step of the major

scale (or three semitones below the tonic).

The tonic of the relative major is on the third step of the minor scale

(three semitones above).


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For reference, here's a set of key signatures with relative minors above and

relative majors below. .

MINOR KEY SIGNATURESIts really useful to be able to work out key signatures. Its even better just to

know them - there are, after all, only 12 major and 12 minor keys. At the

very least, learn all those up to four sharps and flats.

There are some handy rules, however, that can be used in various situations.

In Parallel major and minor scales (pairs of scales which start on the

same note, like C major & C minor) the minor scale has three more flats

than the major (& it follows that the relative major has three more sharps

than the minor).

(This may need a little explanation. If the major key has sharps in it, the

extra three flats in the parallel minor will effectively cancel three of the

sharps. If there were four sharps, for instance, three will be cancelled and

you will be left with one. If there was only one sharp, one of the new flats

will cancel it and the remaining two flats will appear in the key signature.

Have a look at the chart of relative majors and minor key signatures if you

need to clarify this to yourself.)

Also -

The tonic of a minor scale is two tones above the last flat or one tone

below the last sharp of the key signature.


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SCALE STEP NAMESBefore moving on to talk about key relationships, we need to give new

names to the steps of the scale. These names will be useful when you come

to read about chords in part two, as well.

ABSOLUTE & RELATIVE NAMESThere are various ways of naming notes. Some of them are absolute; a C is

always a C, for instance. In most kinds of music, however, there is also a way

of naming notes which we can think of as being relative, a way of

identifying the position of a note within the scale and its relationship to the

other members.

For instance, each scale note has a relationship to the tonic and a position in

the scale. It follows that the second step of a scale can be called just that -

step two. The rest of the notes could be similarly named steps three, four,

five and so on.

Another relative set of names that you may have come across is doh-re-mi-

fah-so-la-te-doh. In this sol-fa system, the first step of the scale is doh

regardless of what key you are in, and re is the second step, and so on.

(Unless youre French . . . . . . . )

Indian music uses a similar set of names -

Sa - re - ga - ma - pa - dha - ni - sa.

These names are fine in many situations but Western musicians have found it

useful to use both an absolute name (C, F# etc.) and a relative name for

each note, and have favoured a set of names that recognises the significance

of each scale step; in many ways, western music has a hierarchical structure,

and these names recognise that -

STEP NAMESThe first step of the scale, the most significant of all, to which all the others

relate, is the TONIC.

I have already hinted that the fifth step of the scale has particular importance

and a particularly strong 3:2 frequency relationship with the tonic. It is

called the DOMINANT.


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The fourth step (which could also be thought of as the note 5 steps belowthe

tonic) has a similar but slightly weaker relationship to the tonic. It is called

the SUB-DOMINANT.

The third step of scale is halfway between the two poles of the scale, the

tonic and the dominant, and it is called the MEDIANT. Combined with the

tonic and dominant, it completes the tonic chord of the key.

The sixth step of the scale is halfway between the tonic and the sub

dominant below it. It is called the SUBMEDIANT. Combined with the tonic

and sub-dominant, it completes the subdominant chord.

That leaves just two more steps --

Step two is tthe note just above the tonic and is called the SUPERTONIC.

Step seven often creates a desire for the tonic in the listener and is called the

LEADING-NOTE.

Here are the names applied to the notes of a C major scale, but remember

that they can apply to the steps of all major & minor scales, and the modes

that we will discuss later.

Step No. Name Sol-fa Indian

1 tonic Doh Sa

2 supertonic Re Re

3 mediant Mi Ga

4 subdominant Fa Pa

5 dominant Soh Ma

6 submediant La Da

7 leading note Ti Ni

8 upper tonic Doh Sa


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KEY RELATIONSHIPS

Relative major & minorYouve already seen that pairs of major and minor scales which share the

same note-content are are considered to be closely related - we say that C

major is the relative major of A minor and that D minor is the relative

minor of F major, and so on.

Parallel keysOther pairs of scales are also considered as being related. Major and minor

keys starting on the same tonic, for instance, are called parallel keys. Wesay that C Minor is the parallel minor of C major. Similarly, D major is the

parallel major of D minor. If a piece modulates (changes key) from A major

to A minor, we can say that it has moved to the parallel minor. It is also

common to talk about moving to the tonic minor or the tonic major - it

means the same thing.

Dominant - subdominant etc. . . . .If a piece modulates from C major to G major, we say that it has modulated

to the dominant, because G major is the scale / key built on the dominant of

C major.

Similarly, a shift from C to F major would be a modulation to the sub-

dominant. A shift from C to E would be a modulation to the mediant . . . .

and so on.

Close & distant relationships

Some keys are more closely related than others. On the whole, keys areconsidered to be mostly closely related when the two scales share a tonic or

key-signature. Moving to the dominant involves changing only one note, so

that relationship is also considered to be a close one. The less that scales

have in common, the more distantly related they will be.


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THE CIRCLE OF FIFTHSIf you move from any key to its dominant, and then from the new key to its

dominant, and so on, you will eventually find that you have moved through

all twelve possibly keys and returned to the one you started on. This

sequence of keys is called the Circle of Fifths because each new tonic is a

fifth above the last (a fifth being the interval between the tonic and fifth step

of a major or minor scale).

This concept has been very important in tonal music, and can be applied to

key relationships and to chord sequences (which well look at in much more

detail later).

Here is the Circle of Fifths for reference -


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OTHER SCALES

the CHURCH MODESWe have discussed the two best-known Western scales, and these are the

ones that most theory courses restrict themselves to.

However, many other scales used to be used in Europe, including a set of

modes. They were used less and less as harmony became the driving force

behind our music but they came back into use in many twentieth and

twenty-first century genres. Their use in folk music never declined.

The modes in this set have something in common; they each contain 5 tones

and 2 semitones, and the 2 semitones are in every case a fifth apart.

Apart from the Ionian and Aeolian (which are the same as the Major &

Natural Minor), the Dorian, Mixolydianand Phrygian modes are themost

frequently encountered.

Here is the full set -


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As with all other scales, these modes can start on any note. There is an all-

naturals version of each of these modes, and you might like to experiment

with them all -

Name Content all-naturals version starts on . .

IONIAN C

MIXOLYDIAN 7 G

DORIAN 3 & 7 D

AEOLIAN 3, 6 & 7 A

PHRYGIAN 2,3,6 & 7 E

LOCRIAN 2, 3, 5, 6 & 7 B

LYDIAN #4 F

These modes are associated with (and help to characterise) different styles

and have been heavily used in recent music. The Mixolydian, Dorian and

Aeolian, for instance, are heavily associated with folk and popular styles, but

also modal jazz. The Phrygian is instantly recognised as the Flamenco scale

and gets heavily used in Heavy Metal. The Lydian is beautiful but quite rare

and associated mainly with East European folk styles. The Locrian is so

strange and unstable its rarely used at all.

MODAL KEY SIGNATURESKey signatures for these modes are no different from major and minor key

signatures and simply recognise the pitch content of the piece.

Having applied the key signature, there is sometimes confusion about how

to name the tonality of modal pieces.

The first step is to identify the tonic by listening to and examining the piece -

the closing chord and note are a fairly reliable guide. If the tonic is E, then

the piece is in 'E something'.

The second step is to ask which mode the rest of the notes in the piece make

when arranged above E - when you've identified the unique structure of the

Dorian or the Phrygian, then you can say that the piece is in 'E Dorian' or 'EPhrygian'.


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PENTATONIC SCALESFive-note (pentatonic) scales are common and two of them have become so

well known that we tend refer to them as The Major Pentatonic and The

Minor Pentatonic.

The Major Pentatoniccontains steps 1, 2, 3, 5 & 6 of the major scale.

Here is C Major Pentatonic -

This scale crops up in music from Scotland to China, Africa to the Andes. You

can play F# Major Pentatonic entirely on the black notes of any keyboard.

The Minor Pentatonic & The Blues Scale

is also very common, and it contains a 1, b3, 4, 5 & b7.

Here is A Minor Pentatonic

Notice that it contains the same notes as C Major Pentatonic.

Many musicians think of this as The Blues Scale, but a fuller version of the

Blues Scale will include a chromatic link between the 4th & 5th -


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WHOLE TONE & OCTATONIC / DIMINISHED SCALES

There are too many other scales to mention them all. As far as Western music

goes, the following two have been much used both in 20th century classical

music and jazz improvisation. The first is the

Whole-tone scale,most famously used by Claude Debussy. Every interval in the scale is a tone,

and it has a curiously centreless, floating quality. This is rarely notated with

the key signature - just use accidentals as necessary.

The other is the

Octatonic /diminished scalean eight-note scale made up of alternating tones and semitones. This appears

in the work of many composers (Messiaen, for instance), and is often used by

jazz players as the basis of improvisation against diminished chords. Again, a

key signature is not appropriate (or possible).

KEY SIGNATURES WITH SHARPS & FLATS COMBINEDSome scales from other musical cultures can only be notated with key

signatures that combine sharps and flats. Heres an Indian scale -

ATONAL MUSIC

Much 20th-century music is atonal, meaning that it is not in any key and

usually indicating that all 12 notes of the chromatic set are used freely orequally in the music. A key signature makes no sense in this situation, so

accidentals must be used throughout the music.


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In tonal music, accidentals only apply for the remainder of the bar that they

first appear in. This convention also applies in some atonal music, but most

atonal composers notate their music on the understanding that accidentals

only apply to the note that they precede. Its usually clear from the context

which of these conventions applies.


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INTERVALSYou have already come across the octave, tone & semitone. There are other

intervals, of course, and it would be easy enough to list their sizes andnames, but its important to recognise that intervals are much more than

spaces between notes. Each one has its own character, value and

psychological and emotional impact; styles are defined by the use of certain

intervals, forward motion is achieved by the shifting between dissonant and

consonant intervals, harmonic systems are constructed around them, the

emotional value of each one has been explored across time and disparate

cultures. Intervals are really important - well come back to some of their

more interesting qualities later..

Harmonic & Melodic Intervals

Intervals can be harmonic or melodic, depending on whether the two notes

are heard simultaneously (as part of a harmony) or one-after-the-other (as

part of a melody). Harmonic and melodic intervals of the same size have the

same names.

INTEGER NOTATION

The simplest way to name intervals is simply to say how many semitoneseach interval spans. In this system,

C to C# is a 1

C to D is a 2

and so on . . . . . . .

Falling melodic intervals can be notated with a minus sign, so

C up to E = 4

C down to E = - 8

This system of naming is particularly appropriate for

atonal or post-tonal music - it makes no sense to talk

about minor thirds, major sixths and so on when

describing music which is neither major nor minor.

This is also the way that MIDI programs such as

LOGIC identify intervals; if you want to transpose

some midi information youll be invited to say howmany semitones you want to raise or lower what you

have recorded.


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Youll find a chart comparing numeric intervals with their tonal equivalents

on page 00.

PITCH CLASS INTERVALSIn music the term pitch is used to identify a unique note - middle C, for

instance, but not the one above it. By contrast, a pitch-class identifies all

notes of the same name - the pitch-class C means allCs, G# means allG#s

and so on.

Pitch-class Intervals measure the shortestdistance between two pitch-classes,

rather than the actual distance between specific pitches. It follows that 6 is

the largest pitch-class interval that is needed.

The most appropriate application for this system is to serial music.

INTERVALS IN TONAL MUSIC / Diatonic IntervalsThe above makes perfect sense in certain music, but is still true that most of

the music that we listen to and perform is tonal, and there is an established

system for naming intervals embedded in that system.

Number & Quality

Each interval is named in part after the number of scale steps that it spans,

always counting from the lowestnote.

An interval between C and E, for instance, is a third because it

spans three letter-names - C, D & E.

A to E spans A, B, C, D & E so it is a fifth.

A to G is a seventh.

This is a simple rule but you may have already spotted a problem. C/E is athird because it spans C, D & E. However, C to E is also a third, because it

too spans three scale steps. The two intervals are clearly different, so we


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need to say what kind of thirds these are to avoid confusion; we have to

identify the qualityof each interval.

Here are some straightforward and then increasingly obscure rules about the

full naming of intervals.

MAJOR & PERFECT INTERVALSIf the upper note of an interval can be found in the major scale built on the

lower note, the interval is either a Major interval or a Perfect interval. Here

are all the possible intervals in C major. Notice that, where you might have

expected to find a major fourth and a major fifth you find a Perfect Fourth

and a Perfect Fifth.

MINOR INTERVALSIf you flatten the upper note of any of the four major intervals, you produce a

minor interval. This means that we can have a 'minor second', even though it

never actually occurs in a minor scale. (The minor third, sixth and seventh

do appear in the minor scale.)

DIMINISHED INTERVALSIf you flatten a minor interval or a perfect interval, the result is a diminished

interval. It's been necessary to notate some of these with 'double flats' and

these do what it says on the can so A!, for instance, turns out to be another

way of naming a G.


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AUGMENTED INTERVALSIf you sharpen the upper note of a major or perfect interval, the result is an

augmented interval. As with some of the diminished intervals, some of these

are very uncommon.

You'll have noticed that what is essentially the same interval can have two or

more names - compare a Minor 3rd and Augmented 2nd, for instance.

COMPARISON CHARTFor reference, here is a chart comparing some ways of naming intervals -

No. ofsemitones

Pitch-classintervals

Diatonic name

0 0 Unison / Perfect Unison

1 1 Minor Second

2 2 Major Second

3 3 Minor Third

4 4 Major Third

5 5 Perfect Fourth

6 6 Augmented Fourth / Diminished Fifth

7 5 Perfect Fifth

8 4 Minor Sixth

9 3 Major Sixth

10 2 Minor Seventh

11 1 Major Seventh

12 0 Octave / Perfect Octave


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CONSONANCE & DISSONANCESome intervals are noticeably more consonant than others - easier on he ear,

if you like. By contrast, some intervals are dissonant - harder on the ear.

These terms are relative; some people have a lower dissonance threshold

than others, and feelings about what intervals are consonant have changedover time.

The octave is regarded as being the most consonant interval and, if you

remember from the very beginning of this document, it is the interval with

the simplest mathematical relationship between its two frequencies (2:1). The

perfect fifth and perfect fourth come next with frequency relationships of 3:2

and 4:3.

Different authorities apply different criteria when evaluating the relative

consonance and dissonance of some of the remaining intervals. Few,

however, disagree that the next group still sound relatively consonant

major third (5:4)

minor third (6:5)

major sixth (5:3)

minor sixth (8:5),

and that the most dissonant intervals are -

major second (9:8)

minor seventh (16:9)

minor second (16:15)

major seventh (15:8)

diminished fifth (45:32)

Notice that the more consonant intervals feature frequency relationships

containing lower numbers.

INVERSIONSIf you take the lower note of any interval and move it up an octave, you have

inverted the interval.

If you invert a second, the result is the seventh. If you invert a third, the result

is a sixth. Similarly, a fourth becomes a fifth, a fifth a fourth, a sixth a third

and, finally, a seventh becomes a second.


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That was a very general statement. What about minor thirds, major thirds,minorsevenths etc? The rule is very simple;

When you invert intervals -

The numbers add up to 9, and

Perfect intervals remain Perfect. (P)

Major intervals (M) become Minor (m)

Minor intervals become Major.

Augmented intervals (+) become Diminished (d)

Diminished intervals become Augmented.

INTERVALS - THEIR CHARACTERSEach interval has certain qualities in common with its inversion -

HARMONIC INTERVALS (when two notes are played simultaneously)

Perfect fifths and fourths, for instance, are generally thought to sound stable,

spacious, clear, even noble.

Thirds and sixths are also thought to be stable, but less stable than fifths and

fourths, also thicker, sweeter and richer.

Seconds and sevenths are considered to sound unstable and relatively

dissonant. Minor seconds & major sevenths are considered to be the most

dissonant.

A special mention for the diminished fifth / augmented fourth, which is so

unstable and dissonant it used to be known as the devils interval and was

even forbidden at one time. This interval famously characterised what most

people regard as the most dissonant, least tonally stable music of the 20thand 21st centuries.


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MELODIC INTERVALS

It isnt far-fetched to suggest that when we hear the two consecutive notes of

a melodic interval, we nevertheless relate them harmonically in our minds,

and its certainly true that melodic intervals have the same qualities as their

harmonic equivalents; melodic perfect fifths still suggest solidity and

boldness; diminished fifths stillfeel strange, spiky, in need of resolution.

Some intervals seem to inspire particular expressive associations; a falling

minor third is usually considered sad, while a rising major sixth is generally

thought to sound optimistic and aspiring (the opening notes of If I ruled the

world . . . make an obvious example).

. . . . large & small

Its also possible to generalise about the size of melodic intervals. A melody

consisting entirely of small intervals will inevitably have a more flowing andless abrasive character than one made out of relatively large leaps. Large

leaps can be very striking, underline moments of high emotion and markedly

raise the energy level - a lot of conjunct motion will produce the opposite

effects. Many composers successfully exploit and contrast these two kinds of

motion, even within one phrase.

HARMONIC INTERVALS & MUSICAL STYLEDifferent harmonic intervals have characterised the music of different periods

and its interesting that, in Europe at least, we have gradually accommodated

and at times favoured the more dissonant intervals.

Heres an excerpt from a little mediaeval piece for two instruments or voices.

Harmonically, it is typical of its period. The numbers show what intervals

occur between the parts, and a quick glance will tell you how favoured

octaves, fifths and fourths are, particularly if you look at the intervals which

are rhythmically stressed.


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Heres part of a baroque duet by Telemann, historys most prolific composer.

There is now a very marked shift to a texture saturated with thirds. Thirds, of

course, are the building blocks of major and minor chords, and Telemanns

music was conceived in terms of chord progressions, so this is no

surprise . . . .

Finally, heres some early 20th-century music by Schoenberg.

Now the picture is not so clear. Schoenberg still uses thirds, but the less

stable minor thirds, and he freely uses and emphasises more dissonant,

unstable intervals like seconds, sevenths and augmented fourths.

While the textures of popular music were to remain saturated with the

sweetness and harmonic stability of thirds, a huge amount of 20th Century

classical music was to be flavoured with the peppery, unstable intervals that

Schoenberg had favoured.

Its clear that the use of different harmonic intervals lends markedly differentflavours and helps to characterise different styles, even different periods of

music. It also partly determines what is possible in each periods music.


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TRANSPOSITIONIf you start singing a favourite tune now, the chances are that you will pitch

it higher or lower than the last time you sang it. Even though you start thetune on a different note, the melody remains recognisable because the

intervallic structure of the piece is retained; you still move down a major

third, up a tone, down a perfect fifth etc. regardless of which note you started

on. This, for example -

is the same tune as this -

Youll note that the second version of the tune starts a perfect fourth higher

than the first - in fact, everynote in the second version is a perfect fourth

higher than the corresponding note in the first.

We say that the tune has been transposed up a perfect fourth.

The act and technique of moving music in this way is called transposition

and whole pieces of music can be transposed; so long as every note in

Beethovens 5th Symphony is raised by a semitone, most listeners wont

notice the difference. (This has actually happened; in Beethovens time

instruments were tuned considerable lower than they are now.)

The ability to transpose music is an essential skill for any arranger or

composer. You may have a vocalist who can sing a piece more effectively in a

different part of his or her range, for instance - the instrumentalists need to

transpose their parts to suit. In another situation, you may want to repeat a

section of a piece but in a new key. If you are writing or arranging for

transposing instruments such as clarinets, saxes and French Horns, you need

to know how to transpose their parts so that they sound at the right pitch.

There are various ways you can approach this problem -


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TRANSPOSITION TECHNIQUES

1 Interval by interval

This is perhaps the most laborious transposition method, but sometimesnecessary, particularly in music without a key signature. When you have

decided how far you need to transpose the music, move every note up or

down by the same interval. Here, for example, the first melody is transposed

up a tone, and then down a major third.

Another approach is to decide on the new first note and then copy the

interval sequence from the source melody. In this case, thats down a dim5,

up a m3, down a dim5 and so on. Using both approaches allows you to

double check that you havent slipped up at any point. And - of course -

check the results by ear.

2 Transposing from one key to another.

The most likely transposing job will involve moving material from one key to

another: D major might suit your vocalist better than C major, for instance, or

a piece might simply be easier to play in C rather than C#. This process israther easier than the previous one -

1) Work out what your new key needs to be. Insert the appropriate

key signature in your new score.

2) Work out how many scale steps up or down you need to move

from the original version to the transposed version. (E up to G

would be a third, and so would Eb to G#).

3) Move every note that number of steps. The new key signature

takes care of the intervallic structure . . . Job almostdone -


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Heres an example, a tune in E minor thats needs transposing up into G

minor:

After inserting the new key-signature (two flats), simply compare the two

tonics, in this case E & G. They are a third apart (and it doesnt matter what

kind of third). Now slide all the music up a third, (from any space to the

space above, or from any line to the line above). The original piece included

some accidentals. If you simply copy them across -

it might or might not sound right, and the E# in this example doesnt.

You clearly need to think of the accidentals in a different way in this context.

In the original tune, the accidentals told you that the C and two Ds should be

played a semitone higher than the notes implied by the key signature (i.e. that

you should play a C# & D# instead of C & D). When you make the

transposition, you need to make sure that the same is still true. In the G minor

version, the key signature implies an Eb and an F natural, and as the notes asemitone higher than those are E natural and F#, those are the notes that you

now need to notate. The correct transposition is therefore -

Notes for computer users:

In Logic etc. you can ask the program to transpose your midi

recordings up or down by a specified number of semitones - refer to

the comparison chart a few pages back to translate interval names

into numbers.

In dedicated notation packages like Sibelius, transposition works in

a number of ways and you need to be careful which method you

use. For instance, if you select a group of notes in Sibelius and then

use the arrow keys to raise or lower them, the notes will be moved

up or down a space or line at a time, but are unlikely to retain theirintervallic structure unless you are transposing by an octave.


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Alternatively, you can select notes and then use the Transpose

function. At this point you will be offered the choice to 1) transpose

your material up or down by an interval that you specify, or 2)

transpose the material to a new key of your choice (assuming that

you are creating a score in a key). Both of these methods will retain

the intervallic structure correctly, but the notation might or might not

be grammatically correct (particularly as regards accidentals) so you

will still need to check and edit the music.

Transposing chord symbols

Easy. Transpose the roots of the chord symbols consistently. The suffixes

remain unchanged.

For instance:

Cmaj7 | Fm9 |E |D7 ||

when transposed up a perfect fourth, becomes -

Fmaj7 | Bbm9 |A |G7 ||

Transposing Instruments

For reasons to do with the historical development of various wind

instruments, we have a strange situation where an alto saxophone player

might finger and play a written C, but produce the sounding Eb a major sixth

below. On a tenor sax, the same fingering and notation will produce a Bb

and octave and a tone below.

This isnt quite as crazy as it may sound, but it is a situation were stuck withso . . . . .

There are a number of transposing instruments, nowadays mostly in

Bb (meaning that a written & fingered C produces a sounding Bb) or in

Eb (meaning that a written and fingered C produces a sounding Eb).

The commonest transposing instruments are -

Clarinet (Bb - sounds a tone lower than written)

Bass clarinet (Bb - sounds an octave + tone lower than written)


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Soprano sax (Bb - sounds a tone lower than written)

Alto sax (Eb - sounds a major sixth lower than written)

Tenor sax (Bb - sounds an octave + tone lower than written)

Baritone sax (Eb - sounds an octave + major sixth lower than written)

Trumpet and Cornet (Bb - sounds a tone lower than written)

French Horn (in F - sounds a perfect fifth lower than written)

Cor anglais (in F - sounds a perfect fifth lower than written)

I should also mention that some instruments transpose at the octave -

the guitar, for instance, sounds an octave lower then written, while

the glockenspiel sounds an octave higher.

In order to cope with this situation, the arranger / composer has to transpose

the players parts to compensate for this discrepancy. For instance, a Bb

clarinet sounds a tone lower than written, so you need to compensate by

notating its music a tone higherthan you want to hear.Write a D if you want

to hear a C, a G# if you want to hear an F#.

Just as importantly, youll need to give the transposing instrument its own key

signature - write the clarinets music in the key of D major if you want to hear

C major, and so on.

Played by a clarinet, soprano sax, trumpet or cornet, this E major scale -

sounds like this, a D major scale -

Notes for computer users

If you set up your program correctly, you will find that parts are

automatically transposed, along with their appropriate key signatures

etc.


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MECHANICAL TRANSPOSITION

Guitars + Capos . . . .The guitarists capo is a clamp placed on the guitar neck which effectively

shortens the fingerboard; a capo placed in the second fret will raise the pitchof the guitar by two semitones. If you now finger and play a C major chord

on your shorter, higher pitched instrument, it will sound as a D major chord.

The guitar has effectively become a transposing instrument in D. By placing

the capo in the third fret, youll make it a transposing instrument in Eb, and

so on.

This is very useful if youve learned a piece in one key and want to transpose

it quickly into another. There will also be situations where you want to use

the capo to improve or change the sonority of the guitar, or to allow you to

use easier or more effective voicings. If the guitar is to sound in the same key

as any other instruments, you will have to transpose its part in order to

compensate for the effect of the capo.

For instance, if your piece is in Eb major, an awkward key for a guitarist, you

can put the capo on the third fret. This raises the pitch of the guitar by three

semitones / a minor third. If you then transpose the guitar music down a

minor third to compensate for this, you find yourself reading & playing in the

friendlier key of C major, but still sounding in Eb. So -

CAPO 3 || C | G | F ||

sounds -

|| Eb | Bb | Ab ||

. . . . and Digital KeyboardsAlmost all digital keyboards have a transpose function which is even more

flexible than the guitarists capo because it will transpose down as well as up.

Control of this varies, but typically you need to work out how many

semitones you want to raise or lower the music by and then, in combination

with a transpose button, press the key positioned the same number of

semitones above or below middle C. (Refer to the keyboard instructions).


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HARMONYMusic can be conceived as having a horizontal axis and a vertical axis.

Melody and rhythm take place in the horizontal dimension. Harmony is whathappens in the vertical axis.

Any vertical slice of music containing more than one note is considered to

contain harmony, and there is no limit to the number of pitches that might be

present in such a slice. The resulting chords will have a variety of

characteristics, and these characteristics will help to define the style, period

and genre of the piece. Jazz, for instance, is typically saturated with more

complex and more ambiguous chords than would be typical of Mozart or

recent rock music; Stockhausens music is typically more dissonant than

Debussys.

Most styles of music, then, have distinctive vertical characteristics. While the

kinds of harmonies permitted or favoured in a particular style might help to

define it and might indeed be crucial to its overall effect on the listener, they

are not, however, necessarily structural elements. . . . .

Between about 1650 and 1900, however, European musicians developed a

number of styles in which the harmonic aspects were of primary structural

importance. This Period of Common Practice was, if you like, the period ofthe chord progression, of major and minor keys, of chords used in a

hierarchical relationship, of harmonic journeys to and from the tonic chord

and from one key centre and another, so creating a sense of movement and a

defining shape for each piece. This very specific kind of harmony is called

tonal harmony, or functional harmony, and is Europes greatest gift to the

Worlds music..

From the perspective of a Western Classical Music historian, the period of

Common Practice is now over, but this kind of harmony still provides the

back-bone for most of our popular music, and a good deal else. It has alsospread to musical cultures which were untouched by it when the period was

supposedly ending.

Well discuss other non-functional harmonic possibilities later, but for now

well look at the kind of harmony we have been surrounded by all our

lives . . . . .


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FUNCTIONAL HARMONYTwo kinds of chord are fundamental to functional / tonal harmony - major &

minor chords.

MAJOR & MINOR CHORDS

The 1st, 3rd & 5th notes of any major scale constitute its tonic chord.

The 1st, 3rd & 5th notes of any minorscale constitute its tonic chord.

For example;

C, E & G are the 1st, 3rd & 5th notes of a C major scale, so they are a C

major chord when played together.

C, Eb & G are the 1st, 3rd & 5th notes of a C minor scale, so they are a C

minor chord when played together.

(Note that major chords are named without a suffix, but that minor chords

need a lower case m).

The three notes of every major or minor chord are called the root, third and

fifth.

All major chords incorporate a major third between the root and the third,

and a minor third between the third and the fifth.

All minor chords incorporate a minor third between the root and the third),

and a major third between the third and the fifth.

(A major third spans 4 semitones, and a minor third spans 3, so you

can also calculate the contents of major and minor chords by taking

any starting note and then ascending 4 + 3 semitones for a major

chord, and 3 + 4 semitones for a minor chord.)


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DIATONIC CHORDS

Every major scale will yield a number of triads (three-note chords). C major,

for instance, yields three major chords, three minor chords and one other - a

diminished chord (which will be discussed later).

We can extract these chords from the scale without making any chromatic or

other alterations and can therefore say that these chords are diatonic in the

key of C major.

Naming major & minor diatonic chords -

1. Jazz & Pop notation

Each chord in a key set such as the one above is named after its root. It is

assumed that the chord will be a major chord unless you put a lower-case m

after it to indicate a minor chord. This system of notation is now very

widespread.

2. Roman numerals

You can also name chords after the scale steps that they are built on, and, to

avoid confusion, Roman Numerals are used. Note that upper-case numerals

indicate major chords, and that lower-case numerals indicate minor chords.

3. Functional names

The chord built on the tonic is called the tonic chord. Similarly, the chordbuilt on the dominant (fifth step) can be called the dominant chord (or simply

the dominant), the chord built on the sub-dominant is called the sub-

dominant chord, and so on . . . . . in C major, then, the following chords are

named -

System 1 is excellent in playing situations. Systems 2 & 3 have advantages

when it comes to analysing and understanding chord sequences.


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MAJOR KEY PRIMARY CHORDS - THE THREE-CHORD TRICK

Of the six major & minor chords above, chords I, IV & V are called the

Primary Chords. Thousands, possibly millions of tunes and songs are built

around these three chords alone and any musician armed with this

knowledge can quickly work out an accompaniment to an unfamiliar song -

hence the Three Chord Trick.

This is a pun on Three Card Trick, of course, and this set of chords is indeed

a powerful hand - (see what I did there?) - it contains

the tonic - the home chord to which all others must lead and

on which the piece will come to rest.

the dominant - the chord that we feel creates the strongestsensation of a need for the tonic, and

the sub-dominant - which creates the same sensation,

perhaps not quite so strongly.

SECONDARY CHORDS

The three minor chords are known as the Secondary Chords. They are ii, iii &

vi, or the supertonic, mediant and sub-mediant. We feel that these lead less

directly and powerfully back to the tonic.

Notice, however, that the roots of these three chords are related to each other

in the same way that the roots of the primary chords are. Here are the

primary & secondary chords in C major.

Youll see that the three secondary chords are built on A, D, & E. Taken on

their own, these couldbe I, IV & V - the 3-chord trick - in A minor.

This can be very useful, and many chord progressions employ this fact,

shifting the emphasis to the Secondary chords and then back to the Primary

chords, all to create that satisfying sense of going away from and then back

towards the tonic.


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Here are the Primary & Secondary chords in three different major keys -

HIERARCHY OF CHORDS

We are beginning to build a picture, I hope, of a hierarchy of chords, some

with a more powerful and close relationship to the tonic than others.

THE DOMINANT SEVENTH

It is, of course, possible to extract more than 7 chords from a major scale.

Some of these may be interesting and beautiful but might not have a clear

tonal function (well return to the idea of non-functional harmony later) -

One particular extra chord is, however, verypowerful. By adding a seventh

to the dominant chord, you create the dominant seventh, and we feel that

this chord creates an even greater desire and expectation of the tonic than the

simple dominant.

In C major, the dominant seventh chord will contain G, B, D & F, the F being

7 steps (specifically a minor 7th) above the root of the chord. This would be

notated as G7.

In any key the dominant seventh chord can be notated as V7, and is oftencalled the 5-7 chord.


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Here, then, is a fuller set of diatonic chords, in a range of keys - notice the

dominant sevenths in each key -

MODAL CHORD SETS

Although the Major scale came to have enormous importance, there was a

time when it was just the Ionian Mode, only one of a set of modes that are

actually still in use.

Chord sets can be extracted from these modes in exactly the same way that

they were extracted from the major scale. For comparison, here are the

Ionian (major) and the four other commonest modes (the Dorian, Phrygian,

Mixolydian & Aeolian (Natural Minor)), and the chords built on each step -


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The contents of these five chord-sets are identical, but the chords change

their positions and functions in each new mode. In one key, C is the tonic,

but it then takes up position as the sub-tonic, sub-mediant, subdominant and

finally the mediant.

So how and why does C feel like home in one piece, but not in a piece with

identical chord-content? How does the chord of Em, a relatively weak chord

in C major, then get promoted to the position of dominant in A Aeolian?

It is clear that the way in which chords are deployed in actual music is

crucial. Chords acquire their status in each new hierarchy partly by being

being placed in significant positions (beginnings and endings of phrases, for

instance), and partly by being approached in ways that point up their

importance. If the right things arent emphasisedat the right times, the chords

lose their functionality, progressions lose their dynamic qualities - and themusic is less moving.

It is also true that, from mode to mode, the relationships between the roots of

the chords remain pretty much the same; tonic, dominant and subdominant

are still separated by perfect fifths, for instance. The new secondary chords

might now be found on different steps and might be a mixture of major and

minor chords (the Mixolydian) or all major chords (the Aeolian), but they still

form sets whose roots are fifth-related.

These root relationships to some extent override changes and additions to the

chord contents. In other words, a D - G - C sequence tends to work whether

the individual chords are minor ormajor because the movement of roots is so

clear and powerful. Try these - they all work -

Here are the same modes that you saw above, now transposed to start on the

same tonic -


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Now you can see more easily what these harmonised modes have in

common, where they differ, and where they have significant and unique

features.

Only the Ionian (the Major), for instance, includes a major dominant, more

powerful than the minor dominant because it includes a leading note only a

semitone below the tonic. (In some of the other modes, the chord on the sub-

tonic / leading note works almost as well as the dominant when leading back

to the tonic).

The Phrygian has a unique supertonic chord built on a flat 2; this I - II chord

relationship immediately identifies the music as Flamenco (or perhaps HeavyMetal ).

And so on . . . . . .


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THE CLASSICAL MINOR SYSTEM

So far, so simple. The classical minor is more complex.

It is more complex than the major and other modes because it includes a

number of melodic and harmonic alternatives. If you look back to the section

dealing with the Harmonic & Melodic minor scales, youll see that users of

these scales have the option of both a major and a minor 6th, and both a

major and minor seventh. In the Melodic Minor, the major 6 & 7 are

conventionally notated in the ascending version of the scale, and the minor 6

& 7 are written in the descending version -

This is a set of notes that ironically yields far more chords than the so-called

Harmonic Minor, and the reality is that, in one style or another, all of them

get used. Omitting the three possible diminished chords, we now have a set

of 10 chords -

This set includes all six of the chords from the relative major key as well as

the chords associated with the natural minor, anda major dominant 7th, of

course.

ROCK & POP CHORD SEQUENCES

I should mention here that, in a number of rock & pop styles, its common forpieces in major keys to incorporate some of the chords usually associated

with the parallel / tonic minor, particularly the major chords built on the flat

sixth and flat seventh steps.

A piece in C major, for instance, might well include Ab and Bb chords.

There are other ways in which rock practice differs from that so far described,

and Ill deal with this later.


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OTHER CHORDS

The chord sets described above may be regarded as basic sets; you will

certainly use some or all of the chords from each set in a piece, and these

will provide the essential framework of your chord progressions. However,

you will have noticed that, in practice, chords from outside these sets do get

used.

First, some chord-types apart from major and minor that can be extracted

from the parent scales -

Open \ Power Chords (5)

Major or minor chords with the third missing. Much used in folk music and,of course, rock music, particularly Heavy Metal.

Diminished chords ( / dim / m5)

You have already seen that each of the scales and modes discussed above

contains a diminished chord. A diminished chord may be described as a

minor chord with flattened fifth, or as two superimposed minor thirds.

Note that there is some confusion about the notation of this chord, and the

suffix is often used interchangeably with 7 and dim7. This means that there is

no way to distinguish between this three-note chord and the four-note 7 as

described below. For clarity, it seems worth keeping the notation as described

here, then, but be ready for some inconsistency in practice.


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Minor 7th Chords (m7)

A minor chord with an added minor 7th. This chord is tonally ambiguous,

effectively containing the notes of a minor chord andan overlapping major

chord.

Note that the suffix m refers to the basic chord. The 7 is assumed to be a

minor 7.

Major 7th Chords (maj7 / M7)

A Major chord with an added major 7th. Similarly ambiguous.

Here the maj or M refers to the seventh - in the absence of a lower-case

m, the basic chord is assumed to be a major chord.

Major 6th Chords (6)

A major chord with an added 6th. More ambiguity!

Minor 6th chords (m6)

A minor chord with an added major sixth.


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9th Chords (9)

A major chord with an added minor seventh and a major 9th. (A 9th is

effectively the second step of the scale.) Note that the added 7th is assumed

here, even though it isnt named.

Major 9th Chords (maj9 /M9)

A Major chord with an added major seventh and major 9th. Note that the

maj or M refers to the seventh - the fundamental chord and the 9th areassumed to be major.

Suspended 4th Chords ((sus4) / sus4 / sus)

A major or minor chord in which the third is replaced by the fourth.

Now a couple of important chords that cant be derived directly from major

or minor scales, or any of the modes.

Augmented Chords (+)

A major chord with an augmented (sharpened) fifth. This can also be thought

of as two superimposed major thirds.

In effect, a C+ contains the same notes as an E+ and a G#+ so your choice

of name indicates which note you want to be in the bass. Only four

distinctly different augmented chords are possible.


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Diminished 7th Chords (7)

A minor chord with a diminished fifth and an added diminished 7th. You can

also think of this as a pile of minor thirds.

The silent-movie suspense chordpar excellence.

Only four transpositions of this chord are possible so, as with augmented

chords, name the chord after the note that you want in the bass.

The above are the chords you are most likely to come across, but many

others are possible. After the next couple of paragraphs, you will find a chart

summarising the above (including major and minor and dominant seventh

chords), and introducing some other chords, too.

You might, of course, come across or create chords not in this chart. To name

them, follow these rules, some of which have been covered above -

CHORD NAMING RULES

1. It is assumed -

that the underlying chord is major unless you say so

that a 7th is a minor 7th unless you say so.

It follows that an m suffix applies to the fundamental chord, andthat maj or M will apply to the 7th.

2. It is also assumed that

If you specify an added 9th, you mean as well as a

seventh.

If you specify an added 11th (11), you mean as well as a seventh

and a ninth. Extend the rule for 13ths etc. 9ths, 11ths, 13ths and 15ths are major unless you say so.


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3. Other numbers (most likely 6) also imply notes to be added to thefundamental chord.

4. Sus implies that a chord note is to be replaced. The commonest sus

chord is a sus4, where the fourth step replaces the third, so assumethis is what is meant if the suffix is simply sus. The only other likely

sus chord is a sus 2, and here the third is replaced by the second.

COMMON CHORD TYPES / SUMMARY

Name Suffix Example DescriptionMajor none 1st, 3rd, & 5th notes of

major scale.

Minor m 1st, 3rd, & 5th notes of minor scale.

Open /Power Chord 5 1st & 5th notes of major orminor scale.

Dominant 7th 7 Major chord with addedminor 7th

Major 7th maj7 / M7 Major chord with addedmajor 7th

Minor 7th m7 Minor chord with addedminor 7th

Minor withmajor7

mmaj7 Minor chord with added major7th


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Sixth 6 Major chord with addedmajor 6th

Minor 6th m6 Minor chord with addedmajor 6th

Suspended4th

sus / sus4 Major or minor chord with thirdreplaced by fourth.

Seventh withsus4

7sus4 Dominant 7th chord with 3rdreplaced by fourth

Suspended2nd

sus2 Major or minor chord with thirdreplaced by second.

Added second 2 / add2 Major chord with added second

9th 9 Major chord with added minor7th & major 9th

Flat 9th b9 / 7b9 Dominant 7th chord with addedflattened 9th. If not using the 7 inthe suffix, make sure the flat signis raised - otherwise youreimplying a c-flat chord.

Major 9th maj9 / M9 Major chord with added major7th & major 9th

Minor 9th m9 Minor chord with added minor7th & major 9th

Diminished / dim Minor chord with flattened fifth


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Diminished7th

7 / dim7 Minor chord with flattened fifthand added diminished 7th

Augmented + / aug Major chord with sharpened fifth

Augmented7th

+7 / aug7 Augmented chord with addedminor 7th


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CHORD PROGRESSIONS

As hinted at above, the chords and even the chord-families that we have

identified are only the building blocks for something far more significant. This

is, of course, the chord progression / chord sequence / harmonic progression,the phenomenon that provided so much of the structure and the forward-

drive for almost all of the European classical music written during the Period

of Common Practice, and for the popular song from that period until the

present day.

An effective chord progression is more than a string of related chords and

interesting changes; having established a sense of home and away, it takes

the listener on a satisfying, interesting and often emotionally charged journey.

It matches and enhances the phrase-by-phrase-structure of a song melody; at

the same time, it interacts with melody in ways that enrich its expressive

content, and make it more satisfying aesthetically.

What follows is a necessarily superficial look at chord sequences, starting

with the shortest possible, and then looking at progressively more complex

examples, moving from purely diatonic sequences to those that incorporate

non-diatonic chords of one kind and another, and then to those that

modulate. In passing, well collect some of the tricks of the trade.

TWO CHORD ROCKING SEQUENCES

Many pieces have been built on a simple alternation between two chords.

One of these chords will inevitably be the tonic chord - the home chord -

and the other might be almost any other from within the diatonic set.

The following example sequences are described in numerals, and followed

by a version in the key of C. Try each one as a regularly alternating pattern,

and then explore other possibilities . . . . .

I - V \ C - G : The most obvious of all chord pairings, the tonic and thedominant. In a major key, no other chord leads so decisively back to the

tonic or establishes the tonality so clearly.

(My Lady Careys Dompe, 1551 / chorus of Yellow Submarine, 196?)

I - IV \ C - F : The next most obvious, but not quite so in your face as the

previous pair, perhaps.

I - ii \ C - Dm : The classic reggae shift.

I - iii \ C - Em : a soft change (only one note difference) but a telling one.


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I - iii \ C - Am : A similar effect to the last pairing. (Pie Jesu, Faure

Requiem / innumerable pop songs)

i - bVII \ Cm - Bb : This minor mode shift can be all you need for an Irish

jig . . .

I - bVII \ C - Bb : And this major version might be all you need for a Scots

reel, but it also features in many rock songs, particularly those in the

Mixolydian mode. Oh, and The Drunken Sailor.

There are, of course, many other possibilities, particularly when you start to

explore minor key and modal chord-sets.

From a creative point of view, it may be worth noting that such alternatingpatterns might be just one section in something grander, and that each two-

chord relationship has quite distinctive expressive and stylistic implications.

I said above that one chord in a rocking pair will inevitably be the tonic; the

other chord provides the sense of away . . . . .

Having said that, if we hear chords IV & V \ F - G repeated, we have such a

strong expectation of the unheard I chord that you coulduse this pairing to

create music that implies a tonic without you ever actually playing it. We feel

a need to hear the tonic, and the resultant tension is quite acute. Add a

seventh to the V chord to crank up the tension.

This idea that you can imply and create a desire for the tonic becomes more

usable and important in longer sequences, and its part of the reason why

short sequences almost always lack a sense of forward movement, and why

longer sequences have the potential to be more interesting and emotionally

more compelling.

MAJOR KEY - THREE CHORDS

There are disproportionately more possibilities when you allow yourselfthree

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Theory Course, 2011 - 10