Tone Clock · Set classes · 8 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 5 | 5 | 5 | 5 | 5 | 3 |
Every set in the class holds five semitones, five whole tones, five 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 | 5 | 5 | 5 | 5 | 5 | 6 | 5 | 5 | 5 | 5 | 5 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 4 | 5 | 6 | 6 | 6 | 6 | 4 | 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.
01234689
- 01234689C C# D D# E F# G# A
- 1234579tC# D D# E F G A Bb
- 234568teD D# E F F# G# Bb B
- 0345679eD# E F F# G A B C
- 0145678tE F F# G G# Bb C C#
- 1256789eF F# G G# A B C# D
- 0236789tF# G G# A Bb C D D#
- 134789teG G# A Bb B C# D# E
- 024589teG# A Bb B C D E F
- 013569teA Bb B C C# D# F F#
- 012467teBb B C C# D E F# G
- 0123578eB C C# D D# F G G#
01356789
- 01356789C C# D# F F# G G# A
- 1246789tC# D E F# G G# A Bb
- 235789teD D# F G G# A Bb B
- 034689teD# E F# G# A Bb B C
- 014579teE F G A Bb B C C#
- 012568teF F# G# Bb B C C# D
- 0123679eF# G A B C C# D D#
- 0123478tG G# Bb C C# D D# E
- 1234589eG# A B C# D D# E F
- 0234569tA Bb C D D# E F F#
- 134567teBb B C# D# E F F# G
- 0245678eB C D E F F# G G#
Relations
- Complement
- 4-Z15 0146 · all-interval tetrachord
- Z-partner
- 8-Z29, the same interval vector in another class
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×5 · 2-2 ×5 · 2-3 ×5 · 2-4 ×5 · 2-5 ×5 · 2-6 ×3
3 notes: 3-1 ×3 · 3-2 ×6 · 3-3 ×5 · 3-4 ×6 · 3-5 ×7 · 3-6 ×3 · 3-7 ×5 · 3-8 ×7 · 3-9 ×3 · 3-10 ×4 · 3-11 ×6 · 3-12
4 notes: 4-1 ×2 · 4-2 ×3 · 4-3 · 4-4 ×2 · 4-5 ×4 · 4-6 ×2 · 4-7 · 4-8 ×2 · 4-9 · 4-10 · 4-11 ×3 · 4-12 ×4 · 4-13 ×4 · 4-14 ×4 · 4-Z15 ×3 · 4-16 ×4 · 4-17 · 4-18 ×4 · 4-19 ×3 · 4-20 ×2 · 4-21 ×2 · 4-22 ×3 · 4-23 · 4-24 ×2 · 4-25 · 4-26 · 4-27 ×4 · 4-28 · 4-Z29 ×4
5 notes: 5-1 · 5-2 · 5-4 ×2 · 5-5 ×3 · 5-6 · 5-7 ×2 · 5-8 · 5-9 ×2 · 5-10 · 5-11 · 5-Z12 · 5-13 ×2 · 5-14 · 5-15 · 5-16 · 5-Z17 · 5-Z18 ×2 · 5-19 ×2 · 5-20 ×3 · 5-21 · 5-22 · 5-23 · 5-24 ×2 · 5-25 · 5-26 ×2 · 5-27 ×2 · 5-28 ×2 · 5-29 ×2 · 5-30 ×2 · 5-31 ×4 · 5-32 · 5-33 · 5-34 · 5-Z36 ×2 · 5-Z38 ×2
6 notes: 6-2 · 6-5 · 6-9 · 6-Z12 · 6-16 · 6-Z17 · 6-18 · 6-Z19 · 6-21 · 6-22 · 6-Z24 · 6-Z25 · 6-Z26 · 6-27 · 6-Z28 · 6-Z29 · 6-30 · 6-31 · 6-34 · 6-Z36 · 6-Z37 · 6-Z38 · 6-Z40 · 6-Z41 · 6-Z42 · 6-Z43 · 6-Z45 · 6-Z46
7 notes: 7-6 · 7-9 · 7-10 · 7-14 · 7-19 · 7-28 · 7-30 · 7-32
- Around it
- 9-3 · 9-5 · 9-7 · 9-8 · and 8 larger classes