Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 5 | 3 | 2 | 3 | 5 | 3 |
Every set in the class holds five semitones, three whole tones, two minor thirds, three major thirds, five fourths and three tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 5 | 3 | 2 | 3 | 5 | 6 | 5 | 3 | 2 | 3 | 5 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 4 | 6 | 6 | 4 | 2 | 3 | 4 | 6 | 6 | 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.
0123678
- 0123678C C# D D# F# G G#
- 1234789C# D D# E G G# A
- 234589tD D# E F G# A Bb
- 34569teD# E F F# A Bb B
- 04567teE F F# G Bb B C
- 015678eF F# G G# B C C#
- 0126789F# G G# A C C# D
- 123789tG G# A Bb C# D D#
- 23489teG# A Bb B D D# E
- 03459teA Bb B C D# E F
- 01456teBb B C C# E F F#
- 012567eB C C# D F F# G
0125678
Relations
- Complement
- 5-7 01267
- Z-partner
- none: no other class has this interval vector
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×5 · 2-2 ×3 · 2-3 ×2 · 2-4 ×3 · 2-5 ×5 · 2-6 ×3
3 notes: 3-1 ×3 · 3-2 ×2 · 3-3 ×2 · 3-4 ×6 · 3-5 ×9 · 3-7 ×2 · 3-8 ×5 · 3-9 ×3 · 3-10 · 3-11 ×2
4 notes: 4-1 · 4-4 ×2 · 4-5 ×5 · 4-6 ×3 · 4-7 · 4-8 ×3 · 4-9 ×2 · 4-12 · 4-13 · 4-14 ×2 · 4-Z15 ×2 · 4-16 ×5 · 4-18 · 4-20 · 4-23 · 4-25 · 4-27 · 4-Z29 ×2
5 notes: 5-4 · 5-5 ×2 · 5-6 ×2 · 5-7 ×5 · 5-14 ×2 · 5-15 ×2 · 5-Z18 · 5-19 · 5-20 ×2 · 5-28 · 5-29 · 5-Z38
- Around it
- 8-5 · 8-6 · 8-8 · 8-9 · 8-16 · and 12 larger classes