Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 2 | 4 | 6 | 4 | 1 |
Every set in the class holds four semitones, two whole tones, four minor thirds, six major thirds, four fourths and one tritone.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 4 | 2 | 4 | 6 | 4 | 2 | 4 | 6 | 4 | 2 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 6 | 5 | 2 | 4 | 6 | 5 | 2 | 3 | 6 | 5 | 2 |
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.
0124589
- 0124589C C# D E F G# A
- 123569tC# D D# F F# A Bb
- 23467teD D# E F# G Bb B
- 034578eD# E F G G# B C
- 0145689E F F# G# A C C#
- 125679tF F# G A Bb C# D
- 23678teF# G G# Bb B D D#
- 034789eG G# A B C D# E
- 014589tG# A Bb C C# E F
- 12569teA Bb B C# D F F#
- 02367teBb B C D D# F# G
- 013478eB C C# D# E G G#
0134589
Relations
- Complement
- 5-21 01458
- Z-partner
- none: no other class has this interval vector
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×4 · 2-2 ×2 · 2-3 ×4 · 2-4 ×6 · 2-5 ×4 · 2-6
3 notes: 3-1 · 3-2 ×2 · 3-3 ×7 · 3-4 ×7 · 3-5 ×2 · 3-6 · 3-7 ×2 · 3-8 ×2 · 3-9 · 3-10 · 3-11 ×7 · 3-12 ×2
4 notes: 4-2 · 4-3 · 4-4 ×2 · 4-5 · 4-7 ×3 · 4-8 · 4-11 · 4-12 · 4-14 ×2 · 4-Z15 · 4-16 · 4-17 ×3 · 4-18 ×2 · 4-19 ×7 · 4-20 ×3 · 4-22 · 4-24 · 4-26 · 4-27 · 4-Z29
5 notes: 5-3 · 5-6 · 5-11 · 5-13 · 5-16 · 5-Z17 · 5-Z18 · 5-20 · 5-21 ×6 · 5-22 · 5-26 · 5-27 · 5-30 · 5-32 · 5-Z37 · 5-Z38
- Around it
- 8-7 · 8-17 · 8-19 ×2 · 8-20 · and 10 larger classes