Tone Clock · Set classes · 6 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 3 | 3 | 2 | 2 | 1 |
Every set in the class holds four semitones, three whole tones, three minor thirds, two major thirds, two fourths and one tritone.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 4 | 3 | 3 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 2 | 3 | 4 | 3 | 4 | 5 | 4 | 4 | 2 | 1 | 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.
012356
- 012356C C# D D# F F#
- 123467C# D D# E F# G
- 234578D D# E F G G#
- 345689D# E F F# G# A
- 45679tE F F# G A Bb
- 5678teF F# G G# Bb B
- 06789eF# G G# A B C
- 01789tG G# A Bb C C#
- 1289teG# A Bb B C# D
- 0239teA Bb B C D D#
- 0134teBb B C C# D# E
- 01245eB C C# D E F
013456
Relations
- Complement
- 6-Z36 012347
- Z-partner
- 6-Z36, the same interval vector in another class
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×4 · 2-2 ×3 · 2-3 ×3 · 2-4 ×2 · 2-5 ×2 · 2-6
3 notes: 3-1 ×2 · 3-2 ×4 · 3-3 ×3 · 3-4 ×3 · 3-5 ×2 · 3-6 · 3-7 ×3 · 3-8 · 3-10
4 notes: 4-1 · 4-2 · 4-3 · 4-4 ×2 · 4-5 · 4-7 · 4-8 · 4-10 · 4-11 ×2 · 4-12 · 4-13 ×2 · 4-Z15
- Around it
- 7-1 · 7-4 · 7-5 · 7-11 · 7-16 · 7-Z36 · and 32 larger classes