Tone Clock · Set classes · 6 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 3 | 3 | 3 | 3 | 2 | 1 |
Every set in the class holds three semitones, three whole tones, three minor thirds, three major thirds, two fourths and one tritone.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 3 | 3 | 3 | 3 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 2 | 2 | 2 | 4 | 4 | 3 | 4 | 5 | 2 | 3 | 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.
023458
- 023458C D D# E F G#
- 134569C# D# E F F# A
- 24567tD E F F# G Bb
- 35678eD# F F# G G# B
- 046789E F# G G# A C
- 15789tF G G# A Bb C#
- 2689teF# G# A Bb B D
- 0379teG A Bb B C D#
- 0148teG# Bb B C C# E
- 01259eA B C C# D F
- 01236tBb C C# D D# F#
- 12347eB C# D D# E G
034568
Relations
- Complement
- 6-Z10 013457
- Z-partner
- 6-Z10, the same interval vector in another class
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×3 · 2-2 ×3 · 2-3 ×3 · 2-4 ×3 · 2-5 ×2 · 2-6
3 notes: 3-1 ×2 · 3-2 ×3 · 3-3 ×2 · 3-4 ×2 · 3-5 · 3-6 · 3-7 ×3 · 3-8 ×2 · 3-10 · 3-11 ×2 · 3-12
4 notes: 4-1 · 4-2 · 4-4 ×2 · 4-5 · 4-10 · 4-11 · 4-12 · 4-13 · 4-19 ×2 · 4-24 · 4-26 · 4-27 · 4-Z29
- Around it
- 7-3 · 7-8 · 7-11 · 7-16 · 7-Z18 · 7-24 · and 32 larger classes