Tone Clock · Set classes · 6 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 2 | 3 | 3 | 2 | 4 | 1 |
Every set in the class holds two semitones, three whole tones, three minor thirds, two major thirds, four fourths and one tritone.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 2 | 3 | 3 | 2 | 4 | 2 | 4 | 2 | 3 | 3 | 2 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 4 | 3 | 2 | 3 | 2 | 5 | 2 | 4 | 4 | 1 | 4 |
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.
013568
- 013568C C# D# F F# G#
- 124679C# D E F# G A
- 23578tD D# F G G# Bb
- 34689eD# E F# G# A B
- 04579tE F G A Bb C
- 1568teF F# G# Bb B C#
- 02679eF# G A B C D
- 01378tG G# Bb C C# D#
- 12489eG# A B C# D E
- 02359tA Bb C D D# F
- 1346teBb B C# D# E F#
- 02457eB C D E F G
023578
Relations
- Complement
- 6-Z47 012479
- Z-partner
- 6-Z47, the same interval vector in another class
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×2 · 2-2 ×3 · 2-3 ×3 · 2-4 ×2 · 2-5 ×4 · 2-6
3 notes: 3-2 ×3 · 3-4 ×3 · 3-5 ×2 · 3-6 · 3-7 ×4 · 3-8 · 3-9 ×2 · 3-10 · 3-11 ×3
4 notes: 4-8 · 4-10 · 4-11 ×2 · 4-13 ×2 · 4-14 ×2 · 4-16 · 4-20 · 4-22 · 4-23 · 4-26 · 4-27 · 4-Z29
- Around it
- 7-11 · 7-14 · 7-29 · 7-32 · 7-35 · 7-Z36 · and 32 larger classes