Tone Clock · Set classes · 6 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 2 | 2 | 2 | 3 | 2 |
Every set in the class holds four semitones, two whole tones, two minor thirds, two major thirds, three fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 4 | 2 | 2 | 2 | 3 | 4 | 3 | 2 | 2 | 2 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 4 | 4 | 4 | 3 | 2 | 3 | 4 | 4 | 4 | 2 | 0 |
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.
012367
- 012367C C# D D# F# G
- 123478C# D D# E G G#
- 234589D D# E F G# A
- 34569tD# E F F# A Bb
- 4567teE F F# G Bb B
- 05678eF F# G G# B C
- 016789F# G G# A C C#
- 12789tG G# A Bb C# D
- 2389teG# A Bb B D D#
- 0349teA Bb B C D# E
- 0145teBb B C C# E F
- 01256eB C C# D F F#
014567
Relations
- Complement
- 6-5 012367
- 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 ×2 · 2-3 ×2 · 2-4 ×2 · 2-5 ×3 · 2-6 ×2
3 notes: 3-1 ×2 · 3-2 ×2 · 3-3 ×2 · 3-4 ×3 · 3-5 ×5 · 3-7 · 3-8 ×2 · 3-9 · 3-10 · 3-11
4 notes: 4-1 · 4-4 · 4-5 ×2 · 4-6 · 4-7 · 4-8 · 4-9 · 4-12 · 4-13 · 4-14 · 4-Z15 · 4-16 · 4-18 · 4-Z29
- Around it
- 7-4 · 7-5 · 7-6 · 7-7 · 7-Z18 · 7-19 · and 32 larger classes