Tone Clock · Set classes · 8 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 6 | 5 | 5 | 6 | 2 |
Every set in the class holds four semitones, six whole tones, five minor thirds, five major thirds, six fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 4 | 6 | 5 | 5 | 6 | 4 | 6 | 5 | 5 | 6 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 6 | 5 | 6 | 6 | 4 | 7 | 4 | 7 | 4 | 5 | 6 |
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.
0123568t
- 0123568tC C# D D# F F# G# Bb
- 1234679eC# D D# E F# G A B
- 0234578tD D# E F G G# Bb C
- 1345689eD# E F F# G# A B C#
- 0245679tE F F# G A Bb C D
- 135678teF F# G G# Bb B C# D#
- 0246789eF# G G# A B C D E
- 0135789tG G# A Bb C C# D# F
- 124689teG# A Bb B C# D E F#
- 023579teA Bb B C D D# F G
- 013468teBb B C C# D# E F# G#
- 0124579eB C C# D E F G A
0134568t
- 0134568tC C# D# E F F# G# Bb
- 1245679eC# D E F F# G A B
- 0235678tD D# F F# G G# Bb C
- 1346789eD# E F# G G# A B C#
- 0245789tE F G G# A Bb C D
- 135689teF F# G# A Bb B C# D#
- 024679teF# G A Bb B C D E
- 013578teG G# Bb B C C# D# F
- 0124689eG# A B C C# D E F#
- 0123579tA Bb C C# D D# F G
- 123468teBb B C# D D# E F# G#
- 0234579eB C D D# E F G A
Relations
- Complement
- 4-22 0247
- Z-partner
- none: no other class has this interval vector
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×4 · 2-2 ×6 · 2-3 ×5 · 2-4 ×5 · 2-5 ×6 · 2-6 ×2
3 notes: 3-1 ×2 · 3-2 ×6 · 3-3 ×4 · 3-4 ×6 · 3-5 ×4 · 3-6 ×4 · 3-7 ×9 · 3-8 ×6 · 3-9 ×5 · 3-10 ×2 · 3-11 ×7 · 3-12
4 notes: 4-1 · 4-2 ×2 · 4-3 · 4-4 ×3 · 4-5 ×2 · 4-6 · 4-7 · 4-8 · 4-10 ×3 · 4-11 ×5 · 4-12 ×2 · 4-13 ×3 · 4-14 ×5 · 4-Z15 ×3 · 4-16 ×4 · 4-17 · 4-18 · 4-19 ×3 · 4-20 ×2 · 4-21 ×2 · 4-22 ×7 · 4-23 ×4 · 4-24 ×2 · 4-25 · 4-26 ×3 · 4-27 ×4 · 4-Z29 ×3
5 notes: 5-2 ×2 · 5-3 · 5-4 · 5-5 · 5-6 · 5-9 · 5-10 ×2 · 5-11 ×2 · 5-Z12 · 5-13 · 5-14 ×2 · 5-15 · 5-Z17 · 5-Z18 · 5-20 ×2 · 5-21 · 5-23 ×5 · 5-24 ×3 · 5-25 ×3 · 5-26 ×2 · 5-27 ×4 · 5-28 ×2 · 5-29 ×3 · 5-30 ×3 · 5-32 · 5-33 · 5-34 ×2 · 5-35 ×3 · 5-Z36 · 5-Z37 · 5-Z38
6 notes: 6-Z3 · 6-8 · 6-9 · 6-Z11 · 6-14 · 6-16 · 6-22 · 6-Z23 · 6-Z24 ×2 · 6-Z25 ×2 · 6-Z26 · 6-31 · 6-32 ×2 · 6-33 ×3 · 6-34 ×2 · 6-Z39 · 6-Z40 · 6-Z41 · 6-Z43 · 6-Z46 · 6-Z47 · 6-Z48
7 notes: 7-11 · 7-23 · 7-24 · 7-27 · 7-30 · 7-34 · 7-35 · 7-Z36
- Around it
- 9-6 · 9-7 · 9-9 · 9-11 · and 6 larger classes