8/11/2019 Octatonic. Scale Usage Notes Very Useful for Composition

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The Octatonic Scale

0

The octatonic scale, which consists of alternating half and whole steps, can be constructed from any two non-intersectingdiminished seventh chords. Since there are three diminished seventh chords (discounting enharmonic spelling), three distinctoctatonic scales result. These are identified by the pitch-class numbers of the first half-step on or above C (0). Also note thatthe octatonic scale always alternates two even pcs and two odd pcs.

A. Brinkman Class Notes

X

3

6

9

1

Y

4

7

a

2

Z

5

8

b

0

Oct. (X !

Y)0,1

1

3

4

6

7

9

a

1

Oct. (Y !

Z)

2

1,2

4

5

7

8

a

b

0

Oct. (X !

Z)

2

2,3

3

5

6

8

9

b

0

There are four tritones in the each octatonic scale, (2 even, and two odd):

2

3

5

6

8

9

b

1. 4-10(0235) [minor] tetrachords at the tritone (tritone betweensets)

Besides the diminished seventh chord model shown above, there are a number of other ways to partition the octatonic scaleinto equivalent sets. Some of these are shown below: (Oct. shown here)

2,3

2. 4-3(0134) tetrachords at the tritone (tritone betweensets)

3. 4-26(0358) tetrachords (minor-minor 7th chords) at the tritone (tritone betweensets)

4. 4-25(0268) tetrachords (French 6th chords) (tritone withinsets, even vs. odd)

5. 4-9(0167) tetrachords at the minor third (one even and one odd tritone withineach set)

0

Other common sonorities also occur in the scale. Locate all of the major triads, minor triads, and Dominant 7th chords in theOct. scale below (enharmonic spelling permitted).0,1

1

3

4

6

7

9

a

8/11/2019 Octatonic. Scale Usage Notes Very Useful for Composition

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8/11/2019 Octatonic. Scale Usage Notes Very Useful for Composition

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A. Brinkman Trichordal Subsets of the Octatonic Scale Page 1 of 2

localhost:41> partition 8-28

*** Row/Set-Class Partition Table ***

subject: 0134679a= 8-28 {0134679a} z0 m28 ic:[448444] inv:(44440000) cycle:

partition size = 3

3-2 {013} z0 m7 ic:[111000] inv:(10005655) cycle:========================0134679a position

========================013 012

01 a 0170 9a 067134 123

346 234467 345679 456

79a 567------------------------ 8

3-3 {014} z0 m11 ic:[101100] inv:(10005655) cycle:========================

0134679a position========================

01 4 01301 9 0160 34 023

1 9a 16734 7 2353 67 245

67 a 4576 9a 467

------------------------ 8

3-5 {016} z0 m5 ic:[100011] inv:(10016776) cycle:

========================0134679a position

========================01 6 01401 7 015

0 67 045

1 67 14534 9 236

34 a 2373 9a 2674 9a 367

------------------------ 8

8/11/2019 Octatonic. Scale Usage Notes Very Useful for Composition

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A. Brinkman Trichordal Subsets of the Octatonic Scale Page 2 of 2

3-7 {025} z0 m2 ic:[011010] inv:(10005655) cycle:========================

0134679a position========================0 3 a 027

0 79 0560 7 a 057

13 6 12413 a 1271 46 134

46 9 346

4 79 356------------------------ 8

3-8 {026} z0 m8 ic:[010101] inv:(10016776) cycle:========================

0134679a position========================0 46 034

0 4 a 0370 6 a 04713 7 125

13 9 1261 79 1563 79 256

46 a 347------------------------ 8

3-10 {036} z0 m10 ic:[002001] inv:(11118888) cycle:========================

0134679a position========================0 3 6 024

0 3 9 0260 6 9 0461 4 7 135

1 4 a 1371 7 a 1573 6 9 246

4 7 a 357------------------------ 8

3-11 {037} z0 m3 ic:[001110] inv:(10005655) cycle:========================

0134679a position========================0 3 7 025

0 4 7 035

0 4 9 0361 4 9 136

1 6 9 1461 6 a 1473 6 a 247

3 7 a 257------------------------ 8

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A. Brinkman Tetrachordal Subsets of the Octatonic Scale Page 1 of 3

localhost:41> partition -s4 8-28

*** Row/Set-Class Partition Table ***

subject: 0134679a= 8-28 {0134679a} z0 m28 ic:[448444] inv:(44440000) cycle:

partition size = 4

4-3 {0134} z0 m26 ic:[212100] inv:(11003322) cycle:========================0134679a position

========================0134 0123

01 9a 01673467 2345

679a 4567

------------------------ 4

4-9 {0167} z0 m9 ic:[200022] inv:(22226666) cycle:========================0134679a position

========================01 67 0145

34 9a 2367

------------------------ 2

4-10 {0235} z0 m10 ic:[122010] inv:(11113333) cycle:========================

0134679a position========================013 a 0127

0 79a 05671346 1234

4679 3456

------------------------ 4

4-12 {0236} z0 m27 ic:[112101] inv:(10002432) cycle:========================

0134679a position========================013 9 0126

01 4 a 0137

0 346 02340 6 9a 0467

134 7 12351 79a 15673 679 2456

467 a 3457------------------------ 8

8/11/2019 Octatonic. Scale Usage Notes Very Useful for Composition

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A. Brinkman Tetrachordal Subsets of the Octatonic Scale Page 2 of 3

4-13 {0136} z0 m13 ic:[112011] inv:(10012442) cycle:========================

0134679a position========================013 6 0124

01 7 a 01570 3 9a 0267

0 679 0456134 a 12371 467 1345346 9 2346

4 79a 3567------------------------ 8

4-15 {0146} z29 m29 ic:[111111] inv:(10000331) cycle:

========================0134679a position========================

01 46 013401 79 01560 34 a 0237

0 67 a 045713 67 124513 9a 1267

34 79 235646 9a 3467

------------------------ 8

4-17 {0347} z0 m17 ic:[102210] inv:(11113333) cycle:========================0134679a position

========================01 4 9 01360 34 7 0235

1 6 9a 14673 67 a 2457

------------------------ 4

4-18 {0147} z0 m18 ic:[102111] inv:(10012442) cycle:

========================0134679a position

========================01 4 7 013501 6 9 0146

0 34 9 02360 3 67 0245

1 4 9a 13671 67 a 145734 7 a 2357

3 6 9a 2467------------------------ 8

8/11/2019 Octatonic. Scale Usage Notes Very Useful for Composition

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A. Brinkman Tetrachordal Subsets of the Octatonic Scale Page 3 of 3

4-25 {0268} z0 m25 ic:[020202] inv:(22226666) cycle:========================

0134679a position========================0 46 a 0347

13 79 1256------------------------ 2

4-26 {0358} z0 m3 ic:[012120] inv:(11003322) cycle:========================

0134679a position========================0 3 7 a 0257

0 4 79 035613 6 a 1247

1 46 9 1346------------------------ 4

4-27 {0258} z0 m12 ic:[012111] inv:(10002432) cycle:========================

0134679a position========================0 3 6 a 0247

0 3 79 02560 46 9 03460 4 7 a 0357

13 6 9 124613 7 a 1257

1 46 a 13471 4 79 1356

------------------------ 8

4-28 {0369} z0 m28 ic:[004002] inv:(44448888) cycle:

========================0134679a position========================

0 3 6 9 02461 4 7 a 1357

------------------------ 2

4-29 {0137} z15 m15 ic:[111111] inv:(10000331) cycle:========================0134679a position

========================

013 7 012501 6 a 0147

0 467 03450 4 9a 0367134 9 1236

1 679 1456346 a 23473 79a 2567

------------------------ 8