Musical Set Theory

Chromatic

Index

Set classes with chromatic clusters have runs of two (or more) consecutive semitone intervals (i.e. three notes or more). Chromatic-cluster-containing scales and chords have limited voice-leading possibilities. More

These chromatic runs are designated by filled gray circles on clock diagrams. These 212 set classes are very close to being degenerate since they are always one voice-leading step away from chords with a cardinality differing by one.

Less

Cohemitonic chromatic-cluster-containing

3 Notes

3-1

(012)
Chromatic-3

4 Notes

4-6

4-5

4-4

4-2

4-1

(0123)
Chromatic-4

5 Notes

5-15

5-Z38

5-14

5-7

5-Z37

5-13

5-Z36

5-11

5-6

5-9

5-5

5-8

5-4

5-3

5-2

5-1

(01234)
Chromatic-5

6 Notes

6-Z48

6-18

6-Z44

6-Z47

6-Z17

(012478)
All-Trichord

(014678)
All-Trichord

6-Z43

6-Z46

6-22

6-16

6-7

6-Z45

6-21

6-15

6-Z12

6-Z41

6-14

6-Z38

6-Z42

6-Z6

6-5

6-Z11

6-Z40

6-Z10

6-Z39

6-9

6-8

6-Z37

6-Z4

6-Z3

6-Z36

6-2

6-1

(012345)
Chromatic-6

7 Notes

7-30

7-33

(012468t)
Melodic Minor ♭2

7-22

(0125689)
Hungarian Minor

7-29

7-28

7-20

7-21

7-27

7-26

7-19

7-25

7-15

7-24

7-Z18

7-Z38

7-14

7-23

7-7

7-Z17

7-Z37

7-16

7-13

7-Z12

7-Z36

7-11

7-6

7-10

7-9

7-5

7-8

7-4

7-3

7-2

7-1

(0123456)
Chromatic-7

8 Notes

8-27

8-25

8-26

8-20

8-23

(0123578t)
Quartal-8

8-24

8-16

8-19

8-22

8-18

8-17

8-9

8-Z15

8-Z29

8-14

8-21

8-8

8-13

8-12

8-6

8-7

8-11

8-5

8-10

8-4

8-3

8-2

8-1

(01234567)
Chromatic-8

9 Notes

9-12

(01245689t)
Enneatonic

9-11

9-10

9-9

(01235678t)
Quartal-9

9-8

9-5

9-7

9-4

9-6

9-3

9-2

9-1

(012345678)
Chromatic-9