Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 3 | 4 | 3 | 4 | 3 |
Every set in the class holds four semitones, three whole tones, four minor thirds, three major thirds, four fourths and three tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 4 | 3 | 4 | 3 | 4 | 6 | 4 | 3 | 4 | 3 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 4 | 4 | 6 | 5 | 2 | 4 | 4 | 4 | 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.
0123679
- 0123679C C# D D# F# G A
- 123478tC# D D# E G G# Bb
- 234589eD D# E F G# A B
- 034569tD# E F F# A Bb C
- 14567teE F F# G Bb B C#
- 025678eF F# G G# B C D
- 0136789F# G G# A C C# D#
- 124789tG G# A Bb C# D E
- 23589teG# A Bb B D D# F
- 03469teA Bb B C D# E F#
- 01457teBb B C C# E F G
- 012568eB C C# D F F# G#
0123689
Relations
- Complement
- 5-19 01367
- 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 ×4 · 2-4 ×3 · 2-5 ×4 · 2-6 ×3
3 notes: 3-1 ×2 · 3-2 ×3 · 3-3 ×3 · 3-4 ×4 · 3-5 ×6 · 3-7 ×3 · 3-8 ×5 · 3-9 ×2 · 3-10 ×4 · 3-11 ×3
4 notes: 4-1 · 4-4 ×2 · 4-5 ×3 · 4-6 · 4-7 · 4-8 · 4-9 · 4-12 ×3 · 4-13 ×3 · 4-14 ×2 · 4-Z15 ×2 · 4-16 ×3 · 4-18 ×3 · 4-20 · 4-23 · 4-25 · 4-27 ×3 · 4-28 · 4-Z29 ×2
5 notes: 5-4 ×2 · 5-5 · 5-6 · 5-7 · 5-14 · 5-15 · 5-Z18 ×2 · 5-19 ×2 · 5-20 · 5-28 ×2 · 5-29 ×2 · 5-31 ×3 · 5-Z38 ×2
- Around it
- 8-9 · 8-13 · 8-Z15 · 8-18 · 8-Z29 · and 15 larger classes