Tone Clock · Set classes · 8 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 5 | 5 | 6 | 4 | 5 | 3 |
Every set in the class holds five semitones, five whole tones, six minor thirds, four major thirds, five fourths and three tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 5 | 5 | 6 | 4 | 5 | 6 | 5 | 4 | 6 | 5 | 5 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 6 | 4 | 6 | 7 | 4 | 6 | 6 | 5 | 6 | 6 | 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.
01234679
- 01234679C C# D D# E F# G A
- 1234578tC# D D# E F G G# Bb
- 2345689eD D# E F F# G# A B
- 0345679tD# E F F# G A Bb C
- 145678teE F F# G G# Bb B C#
- 0256789eF F# G G# A B C D
- 0136789tF# G G# A Bb C C# D#
- 124789teG G# A Bb B C# D E
- 023589teG# A Bb B C D D# F
- 013469teA Bb B C C# D# E F#
- 012457teBb B C C# D E F G
- 0123568eB C C# D D# F F# G#
02356789
- 02356789C D D# F F# G G# A
- 1346789tC# D# E F# G G# A Bb
- 245789teD E F G G# A Bb B
- 035689teD# F F# G# A Bb B C
- 014679teE F# G A Bb B C C#
- 012578teF G G# Bb B C C# D
- 0123689eF# G# A B C C# D D#
- 0123479tG A Bb C C# D D# E
- 123458teG# Bb B C# D D# E F
- 0234569eA B C D D# E F F#
- 0134567tBb C C# D# E F F# G
- 1245678eB C# D E F F# G G#
Relations
- Complement
- 4-13 0136
- Z-partner
- none: no other class has this interval vector
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×5 · 2-2 ×5 · 2-3 ×6 · 2-4 ×4 · 2-5 ×5 · 2-6 ×3
3 notes: 3-1 ×3 · 3-2 ×7 · 3-3 ×6 · 3-4 ×4 · 3-5 ×7 · 3-6 ×2 · 3-7 ×7 · 3-8 ×6 · 3-9 ×3 · 3-10 ×5 · 3-11 ×6
4 notes: 4-1 ×2 · 4-2 ×3 · 4-3 ×2 · 4-4 ×3 · 4-5 ×3 · 4-6 ×2 · 4-7 · 4-8 · 4-9 · 4-10 ×2 · 4-11 ×2 · 4-12 ×5 · 4-13 ×6 · 4-14 ×3 · 4-Z15 ×4 · 4-16 ×3 · 4-17 ×2 · 4-18 ×5 · 4-20 · 4-21 · 4-22 ×3 · 4-23 ×2 · 4-25 · 4-26 ×2 · 4-27 ×5 · 4-28 · 4-Z29 ×4
5 notes: 5-1 · 5-2 · 5-3 · 5-4 ×3 · 5-5 ×2 · 5-6 · 5-7 · 5-8 · 5-9 · 5-10 ×3 · 5-11 ×2 · 5-Z12 · 5-14 ×2 · 5-15 · 5-16 ×3 · 5-Z18 ×2 · 5-19 ×3 · 5-20 · 5-23 · 5-24 · 5-25 ×3 · 5-27 · 5-28 ×3 · 5-29 ×3 · 5-31 ×4 · 5-32 ×3 · 5-34 · 5-35 · 5-Z36 ×3 · 5-Z38 ×2
6 notes: 6-2 · 6-Z3 · 6-5 · 6-Z10 · 6-Z11 · 6-Z12 · 6-Z13 · 6-18 · 6-Z23 · 6-Z25 · 6-27 ×2 · 6-Z29 · 6-30 · 6-33 · 6-Z36 ×2 · 6-Z40 · 6-Z41 ×2 · 6-Z42 · 6-Z43 · 6-Z45 · 6-Z46 · 6-Z47 ×2 · 6-Z49 · 6-Z50
7 notes: 7-4 · 7-10 · 7-Z12 · 7-19 · 7-25 · 7-29 · 7-31 · 7-Z36
- Around it
- 9-2 · 9-5 · 9-7 · 9-10 · and 7 larger classes