Tone Clock · Set classes · 8 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 6 | 5 | 5 | 5 | 5 | 2 |
Every set in the class holds six semitones, five whole tones, five minor thirds, five major thirds, five fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 6 | 5 | 5 | 5 | 5 | 4 | 5 | 5 | 5 | 5 | 6 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 | 4 | 4 | 6 | 6 | 6 | 5 | 6 | 7 | 6 | 5 | 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.
01234578
- 01234578C C# D D# E F G G#
- 12345689C# D D# E F F# G# A
- 2345679tD D# E F F# G A Bb
- 345678teD# E F F# G G# Bb B
- 0456789eE F F# G G# A B C
- 0156789tF F# G G# A Bb C C#
- 126789teF# G G# A Bb B C# D
- 023789teG G# A Bb B C D D#
- 013489teG# A Bb B C C# D# E
- 012459teA Bb B C C# D E F
- 012356teBb B C C# D D# F F#
- 0123467eB C C# D D# E F# G
01345678
- 01345678C C# D# E F F# G G#
- 12456789C# D E F F# G G# A
- 2356789tD D# F F# G G# A Bb
- 346789teD# E F# G G# A Bb B
- 045789teE F G G# A Bb B C
- 015689teF F# G# A Bb B C C#
- 012679teF# G A Bb B C C# D
- 012378teG G# Bb B C C# D D#
- 0123489eG# A B C C# D D# E
- 0123459tA Bb C C# D D# E F
- 123456teBb B C# D D# E F F#
- 0234567eB C D D# E F F# G
Relations
- Complement
- 4-4 0125
- 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 ×5 · 2-4 ×5 · 2-5 ×5 · 2-6 ×2
3 notes: 3-1 ×4 · 3-2 ×8 · 3-3 ×7 · 3-4 ×7 · 3-5 ×6 · 3-6 ×3 · 3-7 ×5 · 3-8 ×4 · 3-9 ×3 · 3-10 ×2 · 3-11 ×6 · 3-12
4 notes: 4-1 ×3 · 4-2 ×5 · 4-3 ×3 · 4-4 ×4 · 4-5 ×3 · 4-6 ×2 · 4-7 ×2 · 4-8 ×2 · 4-9 · 4-10 ×2 · 4-11 ×4 · 4-12 ×3 · 4-13 ×3 · 4-14 ×5 · 4-Z15 ×2 · 4-16 ×3 · 4-17 ×2 · 4-18 ×3 · 4-19 ×4 · 4-20 ×2 · 4-21 · 4-22 ×3 · 4-23 · 4-24 · 4-26 · 4-27 · 4-Z29 ×4
5 notes: 5-1 ×2 · 5-2 ×3 · 5-3 ×3 · 5-4 ×2 · 5-5 ×3 · 5-6 · 5-7 ×2 · 5-8 · 5-9 · 5-10 ×2 · 5-11 ×3 · 5-Z12 · 5-13 ×2 · 5-14 · 5-16 ×3 · 5-Z17 ×2 · 5-Z18 ×2 · 5-19 ×2 · 5-20 ×3 · 5-21 ×2 · 5-22 · 5-23 ×2 · 5-24 ×2 · 5-25 · 5-26 · 5-27 ×2 · 5-29 · 5-30 · 5-Z36 ×2 · 5-Z37 · 5-Z38
6 notes: 6-1 · 6-2 · 6-Z3 · 6-5 · 6-8 · 6-9 · 6-Z10 ×2 · 6-Z11 · 6-Z12 · 6-Z13 · 6-14 ×2 · 6-15 · 6-16 · 6-Z17 · 6-18 · 6-Z19 ×2 · 6-Z24 · 6-Z25 · 6-Z26 · 6-Z36 ×2 · 6-Z37 · 6-Z38 · 6-Z39 · 6-Z40
7 notes: 7-2 · 7-3 · 7-4 · 7-6 · 7-11 · 7-14 · 7-Z37 · 7-Z38
- Around it
- 9-1 · 9-3 · 9-4 · 9-7 · and 7 larger classes