Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 3 | 4 | 4 | 4 | 2 |
Every set in the class holds four semitones, three whole tones, four minor thirds, four major thirds, four fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 4 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 6 | 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.
0124578
- 0124578C C# D E F G G#
- 1235689C# D D# F F# G# A
- 234679tD D# E F# G A Bb
- 34578teD# E F G G# Bb B
- 045689eE F F# G# A B C
- 015679tF F# G A Bb C C#
- 12678teF# G G# Bb B C# D
- 023789eG G# A B C D D#
- 013489tG# A Bb C C# D# E
- 12459teA Bb B C# D E F
- 02356teBb B C D D# F F#
- 013467eB C C# D# E F# G
0134678
Relations
- Complement
- 5-Z38 01258
- Z-partner
- 7-Z18, the same interval vector in another class
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×4 · 2-2 ×3 · 2-3 ×4 · 2-4 ×4 · 2-5 ×4 · 2-6 ×2
3 notes: 3-1 · 3-2 ×4 · 3-3 ×5 · 3-4 ×4 · 3-5 ×5 · 3-6 · 3-7 ×3 · 3-8 ×3 · 3-9 ×2 · 3-10 ×2 · 3-11 ×4 · 3-12
4 notes: 4-2 · 4-3 ×2 · 4-4 · 4-5 · 4-6 · 4-7 · 4-8 · 4-9 · 4-10 · 4-11 · 4-12 ×2 · 4-13 ×2 · 4-14 ×2 · 4-Z15 ×2 · 4-16 ×2 · 4-17 · 4-18 ×3 · 4-19 ×3 · 4-20 · 4-22 · 4-23 · 4-24 · 4-27 · 4-Z29 ×2
5 notes: 5-3 · 5-7 · 5-10 ×2 · 5-13 · 5-14 · 5-16 ×2 · 5-Z17 · 5-Z18 · 5-19 ×2 · 5-20 · 5-21 · 5-22 · 5-23 · 5-26 · 5-29 · 5-30 · 5-Z36 · 5-Z38
6 notes: 6-Z11 · 6-Z13 · 6-15 · 6-Z17 · 6-18 · 6-Z19 · 6-Z24
- Around it
- 8-4 · 8-5 · 8-18 · 8-20 · 8-27 · and 16 larger classes