Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 3 | 4 | 3 | 5 | 4 | 2 |
Every set in the class holds three semitones, four whole tones, three minor thirds, five major thirds, four fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 3 | 4 | 3 | 5 | 4 | 4 | 4 | 5 | 3 | 4 | 3 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 4 | 5 | 4 | 4 | 4 | 5 | 2 | 5 | 4 | 6 | 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.
0124689
- 0124689C C# D E F# G# A
- 123579tC# D D# F G A Bb
- 23468teD D# E F# G# Bb B
- 034579eD# E F G A B C
- 014568tE F F# G# Bb C C#
- 125679eF F# G A B C# D
- 023678tF# G G# Bb C D D#
- 134789eG G# A B C# D# E
- 024589tG# A Bb C D E F
- 13569teA Bb B C# D# F F#
- 02467teBb B C D E F# G
- 013578eB C C# D# F G G#
0135789
Relations
- Complement
- 5-30 01468
- 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 ×3 · 2-4 ×5 · 2-5 ×4 · 2-6 ×2
3 notes: 3-1 · 3-2 ×2 · 3-3 ×3 · 3-4 ×5 · 3-5 ×3 · 3-6 ×3 · 3-7 ×3 · 3-8 ×6 · 3-9 ×2 · 3-10 · 3-11 ×5 · 3-12
4 notes: 4-2 · 4-4 · 4-5 ×2 · 4-7 · 4-8 · 4-11 ×2 · 4-12 · 4-14 ×2 · 4-Z15 ×2 · 4-16 ×3 · 4-17 · 4-18 · 4-19 ×2 · 4-20 ×2 · 4-21 ×2 · 4-22 ×3 · 4-24 ×2 · 4-25 · 4-26 · 4-27 ×2 · 4-Z29 ×2
5 notes: 5-6 · 5-9 · 5-11 · 5-13 · 5-15 · 5-Z18 · 5-20 ×2 · 5-21 · 5-24 ×2 · 5-26 · 5-27 ×2 · 5-28 · 5-30 ×2 · 5-32 · 5-33 · 5-34 · 5-Z38
- Around it
- 8-Z15 · 8-16 · 8-19 · 8-22 · 8-24 · and 17 larger classes