Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 5 | 3 | 4 | 3 | 2 |
Every set in the class holds four semitones, five whole tones, three minor thirds, four major thirds, three fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 4 | 5 | 3 | 4 | 3 | 4 | 3 | 4 | 3 | 5 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 2 | 5 | 4 | 6 | 4 | 5 | 4 | 5 | 4 | 4 | 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.
0123468
- 0123468C C# D D# E F# G#
- 1234579C# D D# E F G A
- 234568tD D# E F F# G# Bb
- 345679eD# E F F# G A B
- 045678tE F F# G G# Bb C
- 156789eF F# G G# A B C#
- 026789tF# G G# A Bb C D
- 13789teG G# A Bb B C# D#
- 02489teG# A Bb B C D E
- 01359teA Bb B C C# D# F
- 01246teBb B C C# D E F#
- 012357eB C C# D D# F G
0245678
Relations
- Complement
- 5-9 01246
- 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 ×5 · 2-3 ×3 · 2-4 ×4 · 2-5 ×3 · 2-6 ×2
3 notes: 3-1 ×3 · 3-2 ×5 · 3-3 ×3 · 3-4 ×3 · 3-5 ×3 · 3-6 ×3 · 3-7 ×3 · 3-8 ×6 · 3-9 ×2 · 3-10 · 3-11 ×2 · 3-12
4 notes: 4-1 ×2 · 4-2 ×3 · 4-3 · 4-4 · 4-5 ×3 · 4-6 · 4-10 · 4-11 ×2 · 4-12 ×2 · 4-13 · 4-14 ×2 · 4-Z15 ×2 · 4-16 ×2 · 4-19 ×2 · 4-21 ×2 · 4-22 · 4-23 · 4-24 ×2 · 4-25 · 4-27 · 4-Z29 ×2
5 notes: 5-1 · 5-2 · 5-4 · 5-5 ×2 · 5-8 · 5-9 ×2 · 5-10 · 5-13 ×2 · 5-14 · 5-15 · 5-Z17 · 5-23 · 5-24 · 5-26 · 5-28 · 5-29 · 5-30 · 5-33
- Around it
- 8-2 · 8-5 · 8-11 · 8-Z15 · 8-21 · and 16 larger classes