Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 4 | 4 | 4 | 4 | 1 |
Every set in the class holds four semitones, four whole tones, four minor thirds, four major thirds, four fourths and one tritone.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 4 | 4 | 4 | 4 | 4 | 2 | 4 | 4 | 4 | 4 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 4 | 3 | 2 | 5 | 4 | 5 | 4 | 5 | 6 | 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.
0134568
- 0134568C C# D# E F F# G#
- 1245679C# D E F F# G A
- 235678tD D# F F# G G# Bb
- 346789eD# E F# G G# A B
- 045789tE F G G# A Bb C
- 15689teF F# G# A Bb B C#
- 02679teF# G A Bb B C D
- 01378teG G# Bb B C C# D#
- 012489eG# A B C C# D E
- 012359tA Bb C C# D D# F
- 12346teBb B C# D D# E F#
- 023457eB C D D# E F G
0234578
Relations
- Complement
- 5-11 02347
- 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 ×4 · 2-3 ×4 · 2-4 ×4 · 2-5 ×4 · 2-6
3 notes: 3-1 ×2 · 3-2 ×5 · 3-3 ×4 · 3-4 ×5 · 3-5 ×2 · 3-6 ×2 · 3-7 ×5 · 3-8 ×2 · 3-9 ×2 · 3-10 · 3-11 ×4 · 3-12
4 notes: 4-1 · 4-2 ×2 · 4-3 · 4-4 ×3 · 4-5 · 4-7 · 4-8 · 4-10 ×2 · 4-11 ×3 · 4-12 · 4-13 ×2 · 4-14 ×3 · 4-Z15 · 4-16 · 4-17 · 4-19 ×3 · 4-20 · 4-22 ×2 · 4-23 · 4-24 · 4-26 · 4-27 · 4-Z29
5 notes: 5-2 ×2 · 5-3 · 5-4 · 5-6 · 5-10 · 5-11 ×2 · 5-Z12 · 5-13 · 5-Z17 · 5-20 · 5-21 · 5-23 ×2 · 5-25 · 5-26 · 5-27 · 5-29 · 5-30 · 5-Z37
- Around it
- 8-2 · 8-4 · 8-14 · 8-17 · 8-22 · and 15 larger classes