material for creative music-makers · 2018. 11. 26. · 3-note scales 8 4-note scales 11 5-note...

1

MATERIAL FOR CREATIVE

MUSIC-MAKERS

2

Contents

Introduction 3

Index of Some Named Scales 6

Legend 1 7

3-Note Scales 8

4-Note Scales 11

5-Note Scales 19

6-Note Scales 36

On 7-Note Scales, 209 and Foreign Scales 56

7-Note Scales 57

8-Note Scales 74

9-Note Scales 96

10-Note Scales 106

11-Note Scales 109

12-Note Scale 110

Introduction 2 111

Legend 2 111

Subscales 112

Text (with track- by-track illustration and comment) 113

Symmetrical Scales 124

Translation 129

Extenses 134

Rhythm 135

Backings for Practice 136

Some Uses 140

Some Short Sequences 141

Things to Do with Strange Scales 143

The Last Track 145

P.S. Temperament 146

Table of CD Contents 147

Bibliography (By Title) 149

Many Thanks

to mathematician Dennis Parnham for proposing the altogether more

reliable procedure by which I was able to identify a number of omissions

and duplications in the original draft - and

to Clo, Mel, Lupin and Jo.

3

Introduction

5

Where known, names of scales have been written in atop

the appropriate columns of the grid. There are

six 2-note 'scale' families (not included) and six 10-note ones;

nineteen 3-note and 9-note families;

forty-three 4-note and 8-note families;

sixty-six 5-note and 7-note families;

eighty 6-note families and

one 11-note family

Three-note families go from 1 to 19

Four-note families………………20 to 62

Five-note families……………….63 to 128

Six-note families………………….129 to 208

Seven-note families…………….209 to 274

Eight-note families……………..275 to 317

Nine-note families………………318 to 336

Ten-note families………………..337 to 342

Eleven-note family……….…….343

Twelve-note family…….………344

Symmetric scales: 1, 20, 22, 51, 129, 135, 137, 151, 185, 275,

279, 296, 318 and 337.

h

Numberof notesper family

19 three and nine-note families

80 six-note families

66 f ive and seven-note

families

43 four and eight-note families

6 tw o and ten-note 'families'

1 single-noter and 1 eleven-noter

1 2 3 4 5 6 7 8 9 10 11

6

Index of Some Named Scales

7

Legend 1

8

3-Note Scales

11

4-Note Scales

19

5-Note Scales

36

6-Note Scales

56

On 7-Note Scales, 209 and Foreign Scales

57

7-Note Scales

74

8-Note Scales

96

9-Note Scales

106

10-Note Scales

109

11-Note Scales

110

12-Note Scale

111

Introduction 2 and Legend 2

113

Text

As per The Surrey with the Fringe on

top. Rogers and Hammerstein

114

As per Old Devil Moon. Lane and Harburg

131

Translations 209 scale) while the biggest jump (of five notes) is by semitone, major 7th or

tritone, e.g. an F scale to a like Gb or E or B. So moving down the grid one

row at a time, the scales change by perfect 4ths, and from a given row to

consecutive rows, the number of notes differing are: 1, 2, 3, 4, 5, 5, 5, 4, 3, 2, 1

But move to the next family, 210, and the sequence is not at all the same: from

any one row to any other, there's no difference of just a single note. The

sequence of different-note numbers, going downwards (from any one row),

now, is: 3, 2, 3, 3, 5, 3, 5, 3, 3, 2, 3. Onto Family 215, the sequence reads:

5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5 while the only one-note difference in Family 222 is

at the maximum stretch of a tritone, which means that, whereas a row-by-row

sequence of one-note changes in Family 209 will take us right through the

the 12- tone chromatic, one-note changes within 222 can only shuttle us back

and forth between two families a tritone apart.

Questions, therefore, arise. If, for example, a key change of a perfect 4th

within the familiar Family 209, say A to D, is to be translated into 210, do

you choose the same key step - A to D with its three-note difference in 210,

or do you go for a minimum difference (of two notes) within 210 - say A to G

or A to B so as to retain a comparably smooth change?..... An impracticability

of 'word-for-word translation'. (…not that there can be a huge demand for

music translations!) See the diagram on the next page.

Track 27 The first thirteen bars (in 2/2 time) of Claude Debussy's Jardins sous la pluie -

Debussy's Gardens in the Rain - from Estampes.

Jardins sous The rule here is that, in the first translation, A becomes Ab; in the second,

la pluie A becomes Ab, D becomes D# and C becomes C#.

Track 28 The first thirty bars in 3/4 time of Erik Satie's third Gymnopédie (plus a final

Satie's chord) are all in A minor except Bar 7 where the B is flattened. The rule: in the

Gymnopédie first translation, Ab, Db, Eb and Gb replace A, D, E, and G. In the second, A

Number 3 becomes A#, D becomes Db and E becomes Ebb.

132

Number of note differences from any one row to any other.

Specimen scale family 222 etc.

222

½ ½ 1 1 ½ 1 ½ 1

1 A Bb Cb Db Eb Fb G

2 D Eb Fb Gb Ab Bbb C 4

3 F×

G#

A B C#

D E#

3 4

4 B#

C#

D E F#

G A#

3 3 4

5 E#

F#

G A B C D#

3 3 3 4

6 A#

B C D E F G#

4 3 3 3 4

7 D#

E F G A Bb C#

1 4 3 3 3 4

8 G#

A Bb C D Eb F#

4 1 4 3 3 3

9 C#

D Eb F G Ab B 3 4 1 4 3 3

10 F#

G Ab Bb C Db E 3 3 4 1 4 3

11 B C Db Eb F Gb A 3 3 3 4 1 4

12 E F Gb Ab Bb Cb D 4 3 3 3 4 1

1 A Bb

Cb

Db

Eb

Fb

G 4 3 3 3 4

2 D Eb

Fb

Gb

Ab

Bbb

C 4 3 3 3

3 F×

G#

A B C#

D E#

4 3 3

4 B#

C#

D E F#

G A#

4 3

5 E#

F#

G A B C D#

4

6 A#

B C D E F G#

etc.

7 D#

E F G A Bb

C#

8 G#

A Bb

C D Eb

F#

9 C#

D Eb

F G Ab

B

10 F#

G Ab

Bb

C Db

E

11 B C Db

Eb

F Gb

A

12 E F Gb

Ab

Bb

Cb

D

Number of notes differing from Row 1






Row

So for example, from Row 3 (222F˟) to Row 9 (222C#), there's a 1-note difference. From Row 1 (222A) to Row 4 (222B#), there's

a 3-note difference.

133

Track 29 A sixteen bar paraphrase on the chords of Look for the Silver Lining (Kern and

deSylva). The complete 32-bar sequence (2×16) in 4/4 is set out here without

An Old harmonic elaboration. It's all in Eb major except for the bars beneath the scale

Standard. boxes.

Version 1 Eb∆ C-7 F-7 Bb7 Eb∆ C-7 F-7 Bb7 Eb∆ Ab7 G-7 C-7

The original

sequence F-7 Bb7 G-7 C-7 C-7 F7 F-7 Bb7

Eb∆ C-7 F-7 Bb7 Eb∆ C-7 F-7 Bb7 Bb-7 Eb7 Ab∆ Ab∆

A˚ A˚ Eb∆ C-7 F-7 Bb7 Eb∆ (F-7 Bb7)

Track 30 The first three translations (being of the first eight bars of the song) are into

relatively familiar scales from the 209 family: the Dorian, the Lydian and the

Locrian, which is tantamount to changing the key signature from Eb major,

respectively to Db major, Bb major and E major. In the original above, the

sixth bar changes from Eb major (in 209D) by one note to Eb melodic minor

Versions in the next family 210C. Similarly, in……

2, 3 and 4 the Eb Dorian version (in Db major), bar 6 is in Db melodic minor - 210C

Dorian, the Eb Lydian version (in Bb major), bar 6 is in Bb melodic minor - 210A, and

Lydian, the Eb Locrian version (in E major), bar 6 is in E melodic minor - 210D#.

Locrian

The next version is a translation of the first sixteen bars into a strange scale,

Version 5 219F#, G, Ab, Bb, C, D, Eb - root Eb. As before, bar 6 switches to the next

219F# family, in this case, to 220E#, a difference of two notes, the smallest possible

change here. In the original, bars 13 and 14 are up a 5th from Eb to Bb

major; in this version, likewise, they are up a 5th from 219 F# to 219C#.

Version 6 Just the first eight bars in 227C# and 228 C#. Same scale shift as before, i.e.

227C# moving to the next family with minimum note-

change.

Version 7 Same procedure.

236C#

Backing chords - Track 41

Bb major

Ab major

210D (Eb melodic

minor)

275D (double diminished)

219C#, D, Eb, F, G, A, Bb.

219F#, G, Ab, Bb, C, D, Eb.

220E#, F#, G, A#, B#,

C#, D#. 219F#

219F#219F#

227C#, D, Eb, F, Gb, Ab, Bb.

228C#, D, Eb, F×, G#,

A#, B. 227C#

236C#, D, Eb, F#, G, Ab, Bb.236C#

237C#, D, Eb, F, Gb,

Abb, B.

136

Backings for Practice

137

Track 34 A 3/4 vamp in 252E rooted on Gb. Keyboard drops out for a stretch to allow

Scale 252 for chord practice.

From sample

Track 4.

Track 35 is 217A# throughout but the changes within the scale effect a sort of 12-bar

Scale 217 blues. Though the ostinato starts on E# (=F), the initial tonality is F× (=G).

Hear sample

Track 6

Track 36 A pizzicato backing on three folk scales scales: sixteen bars of each scale × 2.

Scales 217

220 & 224

Sample at

Track 7

Track 37 Chord backing for melodic line in 276Eb.

Scale 276

From sample

Track 8.

Accidental chords are entered above the top of each three staves.

Root

Root

16 bars in 217F#

16 bars in 220G#

16 bars in 224G#

F(M) Bb- Bbo A- Ao Eb(M)

Go A+ F(M) C(M) Eo Perfect 4ths F7 No 5th

A(M) Dbo C- F7 No 3rd Bb-

138

Track 38 Scale 276Eb (see above). Rising chords with accelerando.

Scale 276

Six clicks

count-in

Track 39 Chords descending stepwise in the nonatonic 325G.

Scale 325

Hear sample at

Track 9.

Track 40

Scale 318 Here, the sections are continuous. The first eight bars are played twice. (TryHear playing the first eight bars of the tune of de Paul and Rae's Star Eyes over them.)

Track 23 Eb∆ B+∆ G#-∆ E∆ Eb∆ B∆ Bb-∆ Gb∆ D+∆ Db∆ Bb-∆ Gb∆ F∆ A-∆ G#-∆E∆

The third and fourth eights bring in the upper extensions:

Upper chords F#-∆ D∆ Bb+∆ G-∆ F#-∆ D-∆ C+∆ A-∆ F∆ E-∆ C+∆ A-∆ G#-∆ B+∆ Bb+∆G-∆

Lower chords Eb∆ B+∆ G#-∆ E∆ Eb∆ B∆ Bb-∆ Gb∆ D+∆ Db∆ Bb-∆ Gb∆ F∆ A-∆ G#-∆E∆

all accidental The last four eights use the 318 scales in a freer modal approach:

318 scales: G/B/Eb Gb/Bb/D F/A/C# C/E/G#

ie:

3 bars

3 bars

1 bar

and

139

Track 40

ctd 1bar

Hear Track 23

Track 41 Chord sequence of Look for the Silver Lining translated from Eb

From Tracks major into 219F# -two 32-bar choruses.

29 & 30

Translation

of a

standard

sequence

Track 42 This is a backing track on the extense by perfect 5ths. Despite the click count-

From in, it's really without rhythm; just an atmosphere.

Track 31

Extense by

5ths.

Track 43 Extense by perfect 4ths. The backing here is bass and keyboard. The passage

From is repeated with drums.

Extense by

4ths.

From

Track 32

Track 44 A 12/8 backing in the extense by 7ths.

Extense by

7ths.

From

Track 33

219F#, G, Ab, Bb, C, D, Eb.

220E#, F#, G, A#, B#,

C#, D#. 219F#

219F# 219C#, D, Eb, F, G, A, Bb. 219F#

219B, C, Db, Eb, F, G, Ab.219F#

219F#275D, Eb, F, Gb, G#, A, B, C.

-7th -7th ∆ ∆

-7th Ø 7th

-∆ +∆-∆+∆

∆∆

140

Some Uses

Two ways of making new music:

1/ from within by drawing on one’s knowledge, memory and aesthetic sense

2/ from without by exploring the potentials of unfamiliar tools and material.

Through familiarity, the music is likely to be more comprehensible. Sadness, say,

may be suggested by the conventions of minor key and slow tempo. This, though,

can sound stale and run-of-the-mill.The unfamiliar, on the other hand, may sound

chaotic – incomprehensible, or alternatively, it may open up fresh experience (maybe

not yet named).

Overall, this latter is our orientation.

JAZZ

Aside from the case of free jazz, a performance will be based on conventions

including harmonic sequences. (Since bop, a greater degree of freedom has

developed especially in modal jazz, but also within standard changes, where free-

flying chords leap and swirl off from the basic tonality and usually land back on it

some bars later). Any strange scales can be used either as material for creating new

music, allowing a pretty free rein of selection, whereas subscales (see Page 111) are

playable – mainly as melodic lines or bass figures - within standard changes without

the need to modify those changes. Between these two extremes, strange scales can

work as substitutes for standard changes with greater or lesser departure from the

familiar, and with some adjustment to the standard harmony. As an example, the

chords in the two bars (repeated) from the middle of My Funny Valentine (Rodgers &

Hart) in Eb: Eb∆ │ F-7 Bb7 │ or: Eb∆ │ Ab (Lydian)│ are all in Eb major Ionian – i.e.

family 209D which includes fifteen 3-noters, twenty 4-noters, fourteen 5-noters and

six 6-noters. A 5-noter will be more distinctive than a 6-noter but will offer more

choice than a sparser subscale. We might choose 63FGBbCD or 63BbCEbFG or

63EbFAbBbC ( be a bit gingerly with the Ab in the Eb chord.) All can be used in the

short sequence. But 91DEbGAbBb has more character and can be played

throughout. (see p112) The passage is sometimes played as Eb∆ │ FØ │ or Eb │

Ab-∆ │. Here, 210GAbBbCbDbEbF is likely to be chosen for the second bar.

However, the passage could be played entirely in 211GAbBbCbDEbF, i.e. Eb

harmonic major, as substitute for Eb major, with the same chord spelling; it’s to be

understood beforehand that the C is replaced by Cb. Note that the subscale

91DEbGAbBb also fits here. Note, too, that these latter chords often occur as in the

opening bars of Those Little White Lies (Walter Donaldson) and Bud Powell’s Celia.

Appendix 1 USES

141

Some 7-note substitutes with major 3rd and major 7th other than 211 (above) that

might be used with some preparedness as substitutes for standard major scales. (All

suggested chords, for now, will be tetrads i.e. 1,3,5,7 chords.)

212 e.g. BbC#DEFGA in 212A, which also contains D harmonic minor. A short

sequence in 212A: Bb∆ G-7 EØ A7 D-∆.

219 e.g. BbCDEFG#A and FG#ABbCDE in 219G#. A sequence:

Bb∆ G#[o3][o5][o7](=notes G#,Bb,D,F.) A-∆ and F∆.

223 e.g. BbCDEbFG#A in G#223. An alternative turnaround: Bb∆ D-7 C-7+5(=notes

C,Eb,G#,Bb) Ao∆(=notes A,C,Eb,G#) and Bb∆..

224 e.g. BbCbDEbFGA and EbFGABbCbD both in 224A. Workable turnarounds:

Bb∆ G-7 Eb∆ Cb[+5]∆(=notes Cb,Eb,G,Bb) and Bb∆; and Eb∆ Cb[+5]∆

A[o3][o5]7(=notes A,Cb,Eb,G) F[o5]7 and Eb∆.

229 e.g. BbC#DEFGbA in 229E. A turnaround: Bb∆ Gb+∆ F+∆ D-∆.

230 e.g. BbC#DEFG#A and ABbC#DEFG# both in 230G# which also includes the

Hungarian minor in D. See p.118 and Track 15. A turnaround Bb∆ A∆ F+∆ D-∆.

232 e.g. BbC#DEbFGbA in 232C#. Turnaround Bb∆ Gb+∆ Eb-∆

C#[o3][bb5][o7](=notes C#,Eb,Gb and Bb).

Some minor scales with major 7ths other than melodic minor in 210. Minors with

dominant 7ths – the Dorian, Aeolian and Phrygian are all included in 209.

212 e.g. BbCDbEbFGbA (the harmonic minor) in 212F. See 212 in major scales

above. This is a standard scale, the usual modulation being CØ F7(b9) Bb-∆ or Gb∆

F7(b9) Bb-∆. The F chord often has a + sign after it but it should properly be a flat

6th rather than an augmented 5th.

219 e.g. BbCbDbEbFGbA in 219A. Note that this scale also contains Cb∆ and Gb∆

See 219 above in the major scales. Turnaround: Bb-∆ Gb∆ Cb∆ F7[o5] Bb-∆.

227 e.g. BbCDbEbFG#A in 227G#. A sequence: Bb-∆ Db+∆ C-[+5]7 Ao∆

G#[o3][bb5][o7](=notes G#,Bb,Db,F)

230 e.g. BbCDbEFGbA in 230E. See 230 above in the major scales and p118.

Turnaround: Bb-∆ Gb∆ F∆ Db+∆ Bb-∆

Dominant 7th chords. Just about anything with a major 3rd and a dominant 7th will do

here.

The (double) diminished scales – see Footnote 2 on Page 6, Scale 275 Page 74,

and Symmetric Scales Pages 124 → 126 – each contain four such dominant 7th

chords. So using such a scale, in principle, we can modulate, say, from G-7 by the

C7 or the A7, or the Gb7(F#7) or the Eb7 to the F∆. Usually, this would be written as

either C7 or Gb7. (In Scale 210, the dominant 7th chord would be either a Gb7(#11)

or a C alt.). Combining the Gb7 and the C7 tetrads, we get a symmetric hexatonic

subscale 135 C/F#(Gb)....C,Db,E,F#,G,Bb.

211 e.g. CDbEFGABb in 211A.

212 e.g. CDbEFGAbBb in 212C. A Spanish sound.. Note the scale also includes

Db∆. See 212 in major and minor scales above too.

Scales 213 and 214 are both subscales of the (double) diminished 275.

Track 45

Track 46

Just 4-beat count-ins here

SOME SHORT SEQUENCES

142

213F#GABbCDbE and 214D#EF#GABbC both contain a C7 quadrad.

215 e.g. CDEF#GAbBb in 215F#, a whole tone scale plus G.

See also 217(C=B#), 218, 220 etc. (not to forget the denser scales.)

Voicings other than the root position tetrads above may give more colour- by

inversion or spreading a chord out, or by doubling a note or two.

212 changes in in-scale 4ths: BbEA. GC#F. EAD. C#FBb. ADG.

233 changes spread out in intervals 5,2 and 4: BbFAD. DACF. CG#BbEb. AEbG#C.

230 changes in intervals 4,3 and 4: BbEGbC. GbCEA. FBbDbGb. DbGbBbE.

(N.B. Some in-scale intervals differ from perfect ones. See Page 111.)

As well as sequences of chord changes, many tunes contain (potentially) modal

passages. See Pages 113 and 114 re Track 2 of the CD: The Surrey With The

Fringe on Top (Rogers and Hammerstein) and Old Devil Moon (Lane and Harburg).

Subscales can function as pedals or ostinati for, say, bass or tuned percussion in

modal passages or backing passages of changes that contain them - so Scale 1:

AC#F is common to all changes in the familiar scales 210A, E#, C# and 212A, F, C#.

Scale 25ABDE is a subscale of 209G#, C#, F#, B 210G# and C# so would be

more or less consonant with a sequence like:

│A-7D7│B-7E7│A∆ │D7[#11]│D-7G7│E-7A7│D∆ │G7[#11]│

Cycling a subscale figure, with its permutations, maybe repeating one or two of its

notes per cycle, combining with other repeating figures of different durations, these

will produce cross rhythms and phasing, perhaps through different keys. A minimalist

piece or backdrop for soloists might result. John Coltrane would use a short figure as

a theme as in Jupiter from Interstellar Space – a 3-note figure transposed and played

occasionally and variously, free-flying, throughout as a launchpad for new excursions

– and with permutations as in Sunship, the album’s title track. (both are up-tempo.)

To use strange scales in sequences parallel to conventional ones isn’t

straightforward. In the standard scales of 209, minimum, and therefore, smoothest

change is by perfect 4ths and 5ths through a cycle of all twelve keys. By contrast,

the minimum change of one note in 222 is not by 4ths and 5ths but by tritone which

means that there is no cycle of twelve keys but rather a shuttling between two keys

(see Modulation, Pages 130 to 132). In fact, each grid has a different set of intervals

each with its own music grammar. All this poses problems, or preferably,

opportunities for new composition. The developments of jazz, compared to those of

contemporary classical music, have been quite conservative and steady; so

Jupiter

Sunship

Track 47

143

suggesting to most orthodox jazz musicians that they use strange scales might seem

like inviting a poet to present a new work in Volapük - examples of strange scales

being used by jazz musicians are pretty rare.. For my part though, I rather relish

imagining how to make sense of these resources.

In improvised group music (apart from some free jazz) there will be some agreed

course of action. This is not the case with other ways of composing where there are

no such constraints. Whether it’s a drone plus melodic line (Page 113 re CD Track

1), a strange scale analogue of a classical sonata; a commercial jingle, a four-chord

pop song, a film score, it’s up to the music maker’s imagination.

Things to Do with Strange Scales

1. It can be tempting to zap through a lot of scales one after the other until they just

become a blur. Instead, either run a quick scan and select two or three to focus on or

pick out a few at random for condideration. The texts of the book will suggest some

approaches for dealing with them, especially pages 121 to 124. What are the chords:

the triads, the tetrads, those by in-scale 4ths and 5ths? What are the most sonorous

voicings? How do they modulate from key to key? (Remember the smoothest

modulations will be by one note through successive 4ths only within the familiar

major and minor scales of 209.) What new ‘grammars’ emerge? And what moods

do they conjure up?

2 Create melodic lines over drones, over vamps, over ostinati. (p113. Tracks 1, 4,

34).

3. Modulate chords within a scale and from one scale to another.(p115. Track 8).

4. Create a short ambient piece using two keys within one grid; and then from two

different grids. For simplicity’s sake, stick with 5-noters.

5. Create an analogue for improvisation of Miles Davis’s So What substituting

strange scales for his sixteen bars of D Dorian, eight bars of Eb Dorian, and the last

eight bars of D Dorian. Use an occasional 3- or 4-note subscale ostinato from Set 1

or 2 instead of a 4/4 walking bass, maybe in alternate 32-bar choruses.

6. Create original rhythmic figures using 3- or 4-note subscales, variously

permutating and perhaps repeating notes, varying durations of notes and rests, and

combining with notes from the same or from different 3- or 4-noters. Cycle figures of

different durations to effect a minimalist passage with a superimposed melodic line.

7. Model a strange scale analogue (with chord changes) of a tune familiar to you. (pp

129 – 134).

8. Determine whether, how and when to spice up a jazz standard with a strange

scale without disrupting the well-being of the rest of the group. .

144

9. Compose a melody line using an ethnic pentatonic with a backdrop in a rootless

(and therefore floating) triple augmented which includes that pentatonic, e.g. 89A in

318G.

10. Play a blues, maybe with ostinato, in 214 rooted on the 7th. Note that this is a

subscale of the symmetric 275 but the absence of an 8th note can lend it a more

human, less geometrical quality.

11. Have various voices playing repetitive, atmospheric backdrops within limited

pitches of an extense. Have a solo instrument play freely through the tonalities of the

extense with gradual and with disjunct intervals.

12. Note clusters will be muddy in the low register; create a piece in a 10-note scale

in the upper register with a mid-register 7-note subscale accompaniment and a 5-

note subscale bass figure. After some bars, shift the stack down, say, a minor 3rd.

13. Compose a series of short, simple, convincing pieces in strange scales and

familiar rhythms – rumba, waltz, zouk. (And not all music is in 3 or 4 time; 11/8 is a

popular dance rhythm in Bulgaria.)

146

P.S.

Equal The music in this book is based on equal temperament whereby all

tempera- semitone intervals are of equal value; unlike other music cultures, ours

ment generally doesn't make systematic use of microtones. The advantage of equal

temperament is that it allows for modulation through all twelve keys. J.S.

Bach's Well-Tempered Clavier, a set of preludes and fugues in all major and

minor keys, was written in the early 1700s to demonstrate this*. However, the

natural harmonics will not be so regimented and the compromise is that the

notes of our chromatic scale are a bit out of tune. Many synthesizers have

settings for different temperaments where you can compare, say, a pure

major 3rd with a tempered one; the former is noticeably sweeter. But then, if

you change key in that setting, the intervals will be awry. All the same, with

the music and recording technology that's now commonly available, a much

closer approximation to the natural harmonics could engender a new and

open-ended harmonic language. It's hardly surprising, though, that such

capabilities are overlooked in the avalanche of new electronic equipment.

*There is some debate as to whether the work was composed for equal temperament or

for a 'well temperament' proposed by Andreas Werckmeister.

See The Music Instinct by Philip Ball.

Temperament

147

Table of CD Contents

148

42 Extense by perfect 5ths from Track 31.

43 Extense by perfect 4ths from Track 32.

44 Extense by major 7ths from Track 33.

45 Short sequences - major

46 Short sequences - minor

47 Short sequences - dominant

48 The last track - chord cycle on 72B, 90A and 64Bb×4.

149

African Music: a People’s Art. Francis Bebey and Josephine Bennett. Lawrence Hill Books.

1975.

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