Tone Clock · Set classes · 8 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 6 | 5 | 4 | 5 | 5 | 3 |
Every set in the class holds six semitones, five whole tones, four minor thirds, five major thirds, five fourths and three tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 6 | 5 | 4 | 5 | 5 | 6 | 5 | 5 | 4 | 5 | 6 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 4 | 6 | 6 | 6 | 4 | 5 | 6 | 7 | 6 | 6 | 4 |
Notes a set keeps when inverted about n.
Its 24 sets
Set theory treats D# and Eb as one pitch class; the names under each set use one fixed spelling, sharps except Bb.
01234678
- 01234678C C# D D# E F# G G#
- 12345789C# D D# E F G G# A
- 2345689tD D# E F F# G# A Bb
- 345679teD# E F F# G A Bb B
- 045678teE F F# G G# Bb B C
- 0156789eF F# G G# A B C C#
- 0126789tF# G G# A Bb C C# D
- 123789teG G# A Bb B C# D D#
- 023489teG# A Bb B C D D# E
- 013459teA Bb B C C# D# E F
- 012456teBb B C C# D E F F#
- 0123567eB C C# D D# F F# G
01245678
- 01245678C C# D E F F# G G#
- 12356789C# D D# F F# G G# A
- 2346789tD D# E F# G G# A Bb
- 345789teD# E F G G# A Bb B
- 045689teE F F# G# A Bb B C
- 015679teF F# G A Bb B C C#
- 012678teF# G G# Bb B C C# D
- 0123789eG G# A B C C# D D#
- 0123489tG# A Bb C C# D D# E
- 123459teA Bb B C# D D# E F
- 023456teBb B C D D# E F F#
- 0134567eB C C# D# E F F# G
Relations
- Complement
- 4-5 0126
- Z-partner
- none: no other class has this interval vector
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×6 · 2-2 ×5 · 2-3 ×4 · 2-4 ×5 · 2-5 ×5 · 2-6 ×3
3 notes: 3-1 ×4 · 3-2 ×6 · 3-3 ×6 · 3-4 ×7 · 3-5 ×9 · 3-6 ×3 · 3-7 ×4 · 3-8 ×7 · 3-9 ×3 · 3-10 ×2 · 3-11 ×4 · 3-12
4 notes: 4-1 ×2 · 4-2 ×4 · 4-3 ×2 · 4-4 ×3 · 4-5 ×6 · 4-6 ×3 · 4-7 ×2 · 4-8 ×3 · 4-9 ×2 · 4-10 · 4-11 ×3 · 4-12 ×3 · 4-13 ×3 · 4-14 ×3 · 4-Z15 ×4 · 4-16 ×5 · 4-17 · 4-18 ×3 · 4-19 ×3 · 4-20 · 4-21 ×2 · 4-22 ×2 · 4-23 · 4-24 ×2 · 4-25 · 4-27 · 4-Z29 ×4
5 notes: 5-1 · 5-2 · 5-3 ×2 · 5-4 ×2 · 5-5 ×3 · 5-6 ×3 · 5-7 ×5 · 5-8 · 5-9 ×3 · 5-10 ×2 · 5-11 · 5-Z12 · 5-13 ×3 · 5-14 ×2 · 5-15 ×2 · 5-16 ×2 · 5-Z17 · 5-Z18 ×2 · 5-19 ×3 · 5-20 ×2 · 5-21 · 5-22 · 5-23 · 5-24 ×2 · 5-26 · 5-28 · 5-29 · 5-30 ×2 · 5-33 · 5-Z36 ×2 · 5-Z38
6 notes: 6-2 · 6-Z3 · 6-Z4 · 6-5 ×2 · 6-Z6 · 6-7 · 6-9 · 6-Z10 · 6-Z11 · 6-Z12 ×2 · 6-Z13 · 6-15 · 6-16 · 6-Z17 ×2 · 6-18 · 6-Z19 · 6-21 · 6-22 ×2 · 6-Z24 · 6-Z36 · 6-Z37 · 6-Z38 · 6-Z41 · 6-Z43
- Around it
- 9-1 · 9-4 · 9-5 · 9-8 · and 7 larger classes