Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 3 | 5 | 4 | 3 | 5 | 1 |
Every set in the class holds three semitones, five whole tones, four minor thirds, three major thirds, five fourths and one tritone.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 3 | 5 | 4 | 3 | 5 | 2 | 5 | 3 | 4 | 5 | 3 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 | 2 | 5 | 2 | 5 | 4 | 4 | 6 | 3 | 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.
0234579
- 0234579C D D# E F G A
- 134568tC# D# E F F# G# Bb
- 245679eD E F F# G A B
- 035678tD# F F# G G# Bb C
- 146789eE F# G G# A B C#
- 025789tF G G# A Bb C D
- 13689teF# G# A Bb B C# D#
- 02479teG A Bb B C D E
- 01358teG# Bb B C C# D# F
- 012469eA B C C# D E F#
- 012357tBb C C# D D# F G
- 123468eB C# D D# E F# G#
0245679
Relations
- Complement
- 5-23 02357
- Z-partner
- none: no other class has this interval vector
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×3 · 2-2 ×5 · 2-3 ×4 · 2-4 ×3 · 2-5 ×5 · 2-6
3 notes: 3-1 ×2 · 3-2 ×4 · 3-3 ×2 · 3-4 ×3 · 3-5 ×2 · 3-6 ×3 · 3-7 ×7 · 3-8 ×2 · 3-9 ×4 · 3-10 · 3-11 ×5
4 notes: 4-1 · 4-2 ×2 · 4-4 ×2 · 4-5 · 4-6 · 4-10 ×2 · 4-11 ×3 · 4-13 · 4-14 ×3 · 4-Z15 · 4-16 · 4-17 · 4-18 · 4-20 · 4-21 · 4-22 ×5 · 4-23 ×3 · 4-26 ×2 · 4-27 ×2 · 4-Z29
5 notes: 5-2 ×2 · 5-5 · 5-9 · 5-11 ×2 · 5-14 · 5-23 ×3 · 5-24 · 5-25 · 5-27 ×2 · 5-29 · 5-32 · 5-34 · 5-35 ×2 · 5-Z36 · 5-Z38
- Around it
- 8-10 · 8-11 · 8-14 · 8-22 · 8-23 · and 13 larger classes