Tone Clock · Set classes · 6 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 3 | 2 | 2 | 4 | 3 | 1 |
Every set in the class holds three semitones, two whole tones, two minor thirds, four major thirds, three fourths and one tritone.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 3 | 2 | 2 | 4 | 3 | 2 | 3 | 4 | 2 | 2 | 3 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 4 | 3 | 0 | 3 | 4 | 4 | 2 | 3 | 4 | 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.
014568
- 014568C C# E F F# G#
- 125679C# D F F# G A
- 23678tD D# F# G G# Bb
- 34789eD# E G G# A B
- 04589tE F G# A Bb C
- 1569teF F# A Bb B C#
- 0267teF# G Bb B C D
- 01378eG G# B C C# D#
- 012489G# A C C# D E
- 12359tA Bb C# D D# F
- 2346teBb B D D# E F#
- 03457eB C D# E F G
023478
Relations
- Complement
- 6-16 014568
- Z-partner
- none: no other class has this interval vector
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×3 · 2-2 ×2 · 2-3 ×2 · 2-4 ×4 · 2-5 ×3 · 2-6
3 notes: 3-1 · 3-2 · 3-3 ×3 · 3-4 ×4 · 3-5 ×2 · 3-6 · 3-7 · 3-8 ×2 · 3-9 · 3-11 ×3 · 3-12
4 notes: 4-2 · 4-4 · 4-5 · 4-7 · 4-8 · 4-14 · 4-Z15 · 4-16 · 4-17 · 4-19 ×2 · 4-20 · 4-22 · 4-24 · 4-Z29
- Around it
- 7-6 · 7-11 · 7-13 · 7-20 · 7-21 · 7-30 · and 33 larger classes