Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 4 | 4 | 3 | 4 | 2 |
Every set in the class holds four semitones, four whole tones, four minor thirds, three major thirds, four fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 4 | 4 | 4 | 3 | 4 | 4 | 4 | 3 | 4 | 4 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 4 | 5 | 4 | 4 | 4 | 5 | 4 | 6 | 4 | 3 | 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.
0123568
- 0123568C C# D D# F F# G#
- 1234679C# D D# E F# G A
- 234578tD D# E F G G# Bb
- 345689eD# E F F# G# A B
- 045679tE F F# G A Bb C
- 15678teF F# G G# Bb B C#
- 026789eF# G G# A B C D
- 013789tG G# A Bb C C# D#
- 12489teG# A Bb B C# D E
- 02359teA Bb B C D D# F
- 01346teBb B C C# D# E F#
- 012457eB C C# D E F G
0235678
Relations
- Complement
- 5-Z36 01247
- Z-partner
- 7-Z12, the same interval vector in another class
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×4 · 2-2 ×4 · 2-3 ×4 · 2-4 ×3 · 2-5 ×4 · 2-6 ×2
3 notes: 3-1 ×2 · 3-2 ×5 · 3-3 ×3 · 3-4 ×4 · 3-5 ×4 · 3-6 · 3-7 ×5 · 3-8 ×4 · 3-9 ×2 · 3-10 ×2 · 3-11 ×3
4 notes: 4-1 · 4-2 · 4-3 · 4-4 ×2 · 4-5 ×2 · 4-6 · 4-7 · 4-8 · 4-10 ×2 · 4-11 ×2 · 4-12 ×2 · 4-13 ×3 · 4-14 ×2 · 4-Z15 ×2 · 4-16 ×2 · 4-18 · 4-20 · 4-22 · 4-23 · 4-25 · 4-26 · 4-27 ×2 · 4-Z29 ×2
5 notes: 5-2 · 5-3 · 5-4 · 5-5 · 5-6 · 5-10 ×2 · 5-Z12 · 5-14 · 5-15 · 5-Z18 · 5-20 · 5-23 · 5-25 ×2 · 5-27 · 5-28 ×2 · 5-29 · 5-Z36 · 5-Z38
6 notes: 6-Z3 · 6-Z11 · 6-Z23 · 6-Z25 · 6-Z40 · 6-Z41 · 6-Z43
- Around it
- 8-2 · 8-6 · 8-13 · 8-18 · 8-22 · and 17 larger classes