Tone Clock · Set classes · 8 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 5 | 6 | 5 | 5 | 3 |
Every set in the class holds four semitones, five whole tones, six minor thirds, five major thirds, five fourths and three tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 4 | 5 | 6 | 5 | 5 | 6 | 5 | 5 | 6 | 5 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 4 | 6 | 6 | 4 | 6 | 6 | 4 | 6 | 6 | 5 | 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.
0124578t
- 0124578tC C# D E F G G# Bb
- 1235689eC# D D# F F# G# A B
- 0234679tD D# E F# G A Bb C
- 134578teD# E F G G# Bb B C#
- 0245689eE F F# G# A B C D
- 0135679tF F# G A Bb C C# D#
- 124678teF# G G# Bb B C# D E
- 0235789eG G# A B C D D# F
- 0134689tG# A Bb C C# D# E F#
- 124579teA Bb B C# D E F G
- 023568teBb B C D D# F F# G#
- 0134679eB C C# D# E F# G A
0134678t
- 0134678tC C# D# E F# G G# Bb
- 1245789eC# D E F G G# A B
- 0235689tD D# F F# G# A Bb C
- 134679teD# E F# G A Bb B C#
- 024578teE F G G# Bb B C D
- 0135689eF F# G# A B C C# D#
- 0124679tF# G A Bb C C# D E
- 123578teG G# Bb B C# D D# F
- 0234689eG# A B C D D# E F#
- 0134579tA Bb C C# D# E F G
- 124568teBb B C# D E F F# G#
- 0235679eB C D D# F F# G A
Relations
- Complement
- 4-27 0258 · dominant or half-diminished seventh
- 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 ×5 · 2-3 ×6 · 2-4 ×5 · 2-5 ×5 · 2-6 ×3
3 notes: 3-1 · 3-2 ×6 · 3-3 ×6 · 3-4 ×4 · 3-5 ×6 · 3-6 ×3 · 3-7 ×7 · 3-8 ×7 · 3-9 ×3 · 3-10 ×5 · 3-11 ×7 · 3-12
4 notes: 4-2 ×2 · 4-3 ×2 · 4-4 · 4-5 · 4-6 · 4-7 · 4-8 · 4-9 · 4-10 ×2 · 4-11 ×3 · 4-12 ×5 · 4-13 ×5 · 4-14 ×3 · 4-Z15 ×4 · 4-16 ×3 · 4-17 ×2 · 4-18 ×5 · 4-19 ×3 · 4-20 · 4-21 ×2 · 4-22 ×4 · 4-23 ×2 · 4-24 ×2 · 4-25 · 4-26 ×2 · 4-27 ×6 · 4-28 · 4-Z29 ×4
5 notes: 5-3 · 5-7 · 5-8 · 5-9 · 5-10 ×3 · 5-11 · 5-Z12 · 5-13 · 5-14 · 5-16 ×3 · 5-Z17 · 5-Z18 ×2 · 5-19 ×3 · 5-20 · 5-21 · 5-22 · 5-23 ×2 · 5-24 ×2 · 5-25 ×3 · 5-26 ×3 · 5-27 · 5-28 ×3 · 5-29 ×3 · 5-30 ×2 · 5-31 ×4 · 5-32 ×3 · 5-33 · 5-34 ×2 · 5-35 · 5-Z36 ×2 · 5-Z38
6 notes: 6-Z10 · 6-Z11 · 6-Z12 · 6-Z13 · 6-15 · 6-Z17 · 6-18 · 6-Z19 · 6-21 · 6-Z23 · 6-Z24 ×2 · 6-Z25 · 6-27 ×2 · 6-Z28 · 6-Z29 · 6-30 · 6-31 · 6-33 ×2 · 6-34 ×2 · 6-Z45 · 6-Z46 · 6-Z47 · 6-Z49 · 6-Z50
7 notes: 7-25 · 7-26 · 7-28 · 7-29 · 7-31 · 7-32 · 7-34 · 7-Z38
- Around it
- 9-7 · 9-8 · 9-10 · 9-11 · and 7 larger classes