Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 3 | 5 | 4 | 3 | 2 |
Every set in the class holds four semitones, three whole tones, five minor thirds, four major thirds, three fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 4 | 3 | 5 | 4 | 3 | 4 | 3 | 4 | 5 | 3 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 2 | 5 | 6 | 3 | 4 | 6 | 4 | 4 | 4 | 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.
0123569
- 0123569C C# D D# F F# A
- 123467tC# D D# E F# G Bb
- 234578eD D# E F G G# B
- 0345689D# E F F# G# A C
- 145679tE F F# G A Bb C#
- 25678teF F# G G# Bb B D
- 036789eF# G G# A B C D#
- 014789tG G# A Bb C C# E
- 12589teG# A Bb B C# D F
- 02369teA Bb B C D D# F#
- 01347teBb B C C# D# E G
- 012458eB C C# D E F G#
0134569
Relations
- Complement
- 5-16 01347
- 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 ×3 · 2-3 ×5 · 2-4 ×4 · 2-5 ×3 · 2-6 ×2
3 notes: 3-1 ×2 · 3-2 ×4 · 3-3 ×5 · 3-4 ×4 · 3-5 ×3 · 3-6 · 3-7 ×4 · 3-8 ×3 · 3-10 ×4 · 3-11 ×4 · 3-12
4 notes: 4-1 · 4-2 · 4-3 · 4-4 ×3 · 4-5 ×2 · 4-7 · 4-8 · 4-10 · 4-11 ×2 · 4-12 ×3 · 4-13 ×3 · 4-Z15 · 4-17 · 4-18 ×3 · 4-19 ×3 · 4-20 · 4-24 · 4-26 · 4-27 ×3 · 4-28 · 4-Z29
5 notes: 5-2 · 5-3 · 5-4 ×2 · 5-6 · 5-10 · 5-Z12 · 5-13 · 5-16 · 5-21 · 5-22 · 5-25 · 5-26 ×2 · 5-31 ×3 · 5-32 · 5-Z37 · 5-Z38 ×2
- Around it
- 8-3 · 8-12 · 8-17 · 8-18 · 8-Z29 · and 14 larger classes