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.
013457
- 013457C C# D# E F G
- 124568C# D E F F# G#
- 235679D D# F F# G A
- 34678tD# E F# G G# Bb
- 45789eE F G G# A B
- 05689tF F# G# A Bb C
- 1679teF# G A Bb B C#
- 0278teG G# Bb B C D
- 01389eG# A B C C# D#
- 01249tA Bb C C# D E
- 1235teBb B C# D D# F
- 02346eB C D D# E F#
023467
Relations
- Complement
- 6-Z39 023458
- Z-partner
- 6-Z39, 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 · 3-2 ×3 · 3-3 ×4 · 3-4 ×2 · 3-5 · 3-6 ×2 · 3-7 · 3-8 ×2 · 3-9 · 3-10 · 3-11 ×2
4 notes: 4-2 ×2 · 4-3 · 4-4 · 4-7 · 4-11 · 4-12 ×2 · 4-14 · 4-16 · 4-17 · 4-18 · 4-21 · 4-22 · 4-Z29
- Around it
- 7-2 · 7-4 · 7-13 · 7-25 · 7-26 · 7-Z37 · and 32 larger classes