Tone Clock · Set classes · 8 notes
One shape, its own mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 4 | 4 | 8 | 4 | 4 | 4 |
Every set in the class holds four semitones, four whole tones, eight minor thirds, four major thirds, four fourths and four tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 4 | 4 | 8 | 4 | 4 | 8 | 4 | 4 | 8 | 4 | 4 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 8 | 4 | 4 | 8 | 4 | 4 | 8 | 4 | 4 | 8 | 4 |
Notes a set keeps when inverted about n.
Its 3 sets
Set theory treats D# and Eb as one pitch class; the names under each set use one fixed spelling, sharps except Bb.
0134679t · octatonic scale
Relations
- Complement
- 4-28 0369 · diminished seventh chord
- Z-partner
- none: no other class has this interval vector
- Symmetry
- 4 transpositions and 4 inversions map it onto itself
- Inside it
2 notes: 2-1 ×4 · 2-2 ×4 · 2-3 ×8 · 2-4 ×4 · 2-5 ×4 · 2-6 ×4
3 notes: 3-2 ×8 · 3-3 ×8 · 3-5 ×8 · 3-7 ×8 · 3-8 ×8 · 3-10 ×8 · 3-11 ×8
4 notes: 4-3 ×4 · 4-9 ×2 · 4-10 ×4 · 4-12 ×8 · 4-13 ×8 · 4-Z15 ×8 · 4-17 ×4 · 4-18 ×8 · 4-25 ×2 · 4-26 ×4 · 4-27 ×8 · 4-28 ×2 · 4-Z29 ×8
5 notes: 5-10 ×8 · 5-16 ×8 · 5-19 ×8 · 5-25 ×8 · 5-28 ×8 · 5-31 ×8 · 5-32 ×8
6 notes: 6-Z13 ×4 · 6-Z23 ×4 · 6-27 ×8 · 6-30 ×4 · 6-Z49 ×4 · 6-Z50 ×4
7 notes: 7-31 ×8
- Around it
- 9-10 ×4 · and 4 larger classes