Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 3 | 4 | 4 | 4 | 3 | 3 |
Every set in the class holds three semitones, four whole tones, four minor thirds, four major thirds, three fourths and three tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 3 | 4 | 4 | 4 | 3 | 6 | 3 | 4 | 4 | 4 | 3 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 4 | 4 | 4 | 4 | 2 | 6 | 4 | 4 | 4 | 5 | 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.
0135679
- 0135679C C# D# F F# G A
- 124678tC# D E F# G G# Bb
- 235789eD D# F G G# A B
- 034689tD# E F# G# A Bb C
- 14579teE F G A Bb B C#
- 02568teF F# G# Bb B C D
- 013679eF# G A B C C# D#
- 012478tG G# Bb C C# D E
- 123589eG# A B C# D D# F
- 023469tA Bb C D D# E F#
- 13457teBb B C# D# E F G
- 024568eB C D E F F# G#
0234689
Relations
- Complement
- 5-28 02368
- 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 ×4 · 2-3 ×4 · 2-4 ×4 · 2-5 ×3 · 2-6 ×3
3 notes: 3-1 · 3-2 ×3 · 3-3 ×3 · 3-4 ×2 · 3-5 ×5 · 3-6 ×3 · 3-7 ×3 · 3-8 ×6 · 3-9 · 3-10 ×4 · 3-11 ×3 · 3-12
4 notes: 4-2 ×2 · 4-5 · 4-6 · 4-8 · 4-9 · 4-11 ×2 · 4-12 ×3 · 4-13 ×3 · 4-Z15 ×2 · 4-16 · 4-18 ×3 · 4-19 ×2 · 4-21 ×2 · 4-22 ×2 · 4-24 ×2 · 4-25 · 4-27 ×3 · 4-28 · 4-Z29 ×2
5 notes: 5-7 · 5-8 · 5-9 · 5-Z12 · 5-13 · 5-19 ×2 · 5-22 · 5-24 · 5-26 ×2 · 5-28 ×2 · 5-30 · 5-31 ×3 · 5-33 · 5-34 · 5-Z36 ×2
- Around it
- 8-12 · 8-Z15 · 8-25 · 8-27 · 8-Z29 · and 15 larger classes