Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 4 | 3 | 3 | 5 | 2 |
Every set in the class holds four semitones, four whole tones, three minor thirds, three major thirds, five fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 4 | 4 | 3 | 3 | 5 | 4 | 5 | 3 | 3 | 4 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 4 | 4 | 6 | 4 | 4 | 3 | 4 | 6 | 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.
0123578
- 0123578C C# D D# F G G#
- 1234689C# D D# E F# G# A
- 234579tD D# E F G A Bb
- 34568teD# E F F# G# Bb B
- 045679eE F F# G A B C
- 015678tF F# G G# Bb C C#
- 126789eF# G G# A B C# D
- 023789tG G# A Bb C D D#
- 13489teG# A Bb B C# D# E
- 02459teA Bb B C D E F
- 01356teBb B C C# D# F F#
- 012467eB C C# D E F# G
0135678
Relations
- Complement
- 5-14 01257
- 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 ×4 · 2-3 ×3 · 2-4 ×3 · 2-5 ×5 · 2-6 ×2
3 notes: 3-1 ×2 · 3-2 ×4 · 3-3 · 3-4 ×5 · 3-5 ×6 · 3-6 ×2 · 3-7 ×4 · 3-8 ×3 · 3-9 ×3 · 3-10 · 3-11 ×4
4 notes: 4-1 · 4-2 · 4-4 · 4-5 ×2 · 4-6 ×2 · 4-8 ×2 · 4-9 · 4-10 · 4-11 ×3 · 4-13 ×2 · 4-14 ×3 · 4-Z15 · 4-16 ×3 · 4-18 · 4-20 ×2 · 4-21 · 4-22 ×2 · 4-23 · 4-26 · 4-27 · 4-Z29 ×3
5 notes: 5-2 · 5-5 ×2 · 5-7 ×2 · 5-9 · 5-Z12 · 5-14 · 5-19 · 5-20 ×3 · 5-23 · 5-24 ×2 · 5-25 · 5-27 ×2 · 5-29 · 5-Z36 · 5-Z38
- Around it
- 8-4 · 8-6 · 8-Z15 · 8-16 · 8-23 · and 15 larger classes