Tone Clock · Set classes · 6 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 3 | 3 | 2 | 2 | 3 | 2 |
Every set in the class holds three semitones, three 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 | 3 | 3 | 2 | 2 | 3 | 4 | 3 | 2 | 2 | 3 | 3 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 4 | 4 | 2 | 3 | 2 | 4 | 4 | 5 | 2 | 2 | 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.
012467
- 012467C C# D E F# G
- 123578C# D D# F G G#
- 234689D D# E F# G# A
- 34579tD# E F G A Bb
- 4568teE F F# G# Bb B
- 05679eF F# G A B C
- 01678tF# G G# Bb C C#
- 12789eG G# A B C# D
- 02389tG# A Bb C D D#
- 1349teA Bb B C# D# E
- 0245teBb B C D E F
- 01356eB C C# D# F F#
013567
Relations
- Complement
- 6-Z41 012368
- Z-partner
- 6-Z41, 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 ×2 · 2-4 ×2 · 2-5 ×3 · 2-6 ×2
3 notes: 3-1 · 3-2 ×2 · 3-3 · 3-4 ×2 · 3-5 ×5 · 3-6 ×2 · 3-7 ×2 · 3-8 ×2 · 3-9 · 3-10 · 3-11
4 notes: 4-2 · 4-5 · 4-6 · 4-8 · 4-9 · 4-11 ×2 · 4-13 ×2 · 4-Z15 · 4-16 · 4-18 · 4-21 · 4-22 · 4-Z29
- Around it
- 7-4 · 7-5 · 7-14 · 7-15 · 7-28 · 7-29 · and 31 larger classes