Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 5 | 5 | 4 | 3 | 3 | 1 |
Every set in the class holds five semitones, five whole tones, four minor thirds, three major thirds, three fourths and one tritone.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 5 | 5 | 4 | 3 | 3 | 2 | 3 | 3 | 4 | 5 | 5 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 2 | 4 | 4 | 5 | 6 | 5 | 6 | 5 | 4 | 3 | 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.
0123457
- 0123457C C# D D# E F G
- 1234568C# D D# E F F# G#
- 2345679D D# E F F# G A
- 345678tD# E F F# G G# Bb
- 456789eE F F# G G# A B
- 056789tF F# G G# A Bb C
- 16789teF# G G# A Bb B C#
- 02789teG G# A Bb B C D
- 01389teG# A Bb B C C# D#
- 01249teA Bb B C C# D E
- 01235teBb B C C# D D# F
- 012346eB C C# D D# E F#
0234567
Relations
- Complement
- 5-2 01235
- Z-partner
- none: no other class has this interval vector
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×5 · 2-2 ×5 · 2-3 ×4 · 2-4 ×3 · 2-5 ×3 · 2-6
3 notes: 3-1 ×4 · 3-2 ×7 · 3-3 ×5 · 3-4 ×3 · 3-5 ×2 · 3-6 ×3 · 3-7 ×4 · 3-8 ×2 · 3-9 ×2 · 3-10 · 3-11 ×2
4 notes: 4-1 ×3 · 4-2 ×5 · 4-3 ×2 · 4-4 ×3 · 4-5 · 4-6 · 4-7 · 4-10 ×2 · 4-11 ×3 · 4-12 ×2 · 4-13 · 4-14 ×2 · 4-Z15 · 4-16 · 4-17 · 4-18 · 4-21 · 4-22 ×2 · 4-23 · 4-Z29
5 notes: 5-1 ×2 · 5-2 ×3 · 5-3 ×2 · 5-4 · 5-5 · 5-8 · 5-9 · 5-10 · 5-11 ×2 · 5-14 · 5-16 · 5-Z18 · 5-23 ×2 · 5-24 · 5-Z36
- Around it
- 8-1 · 8-2 · 8-4 · 8-10 · 8-11 · and 13 larger classes