21edo: Difference between revisions
From Xenharmonic Reference
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== Basic theory == | == Basic theory == | ||
=== Intervals and notation === | === Intervals and notation === | ||
Since 21edo's best fifth is from 7edo, 21edo is notated with CDEFGAB representing 7edo and up/down representing 1\21. | |||
=== Prime harmonic approximations === | === Prime harmonic approximations === | ||
Revision as of 23:08, 22 January 2026
21edo is an equal division of the octave into 21 steps of 1200c/21 ~= 57.1c each.
Basic theory
Intervals and notation
Since 21edo's best fifth is from 7edo, 21edo is notated with CDEFGAB representing 7edo and up/down representing 1\21.
Prime harmonic approximations
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | -16.2 | +13.7 | +2.6 | +20.1 | +16.6 | +9.3 | -11.8 | +0.3 | -1.0 | -2.2 |
| Relative (%) | 0.0 | -28.4 | +24.0 | +4.6 | +35.2 | +29.1 | +16.3 | -20.6 | +0.5 | -1.8 | -3.8 | |
| Steps
(reduced) |
21
(0) |
33
(12) |
49
(7) |
59
(17) |
73
(10) |
78
(15) |
86
(2) |
89
(5) |
95
(11) |
102
(18) |
104
(20) | |
Edostep interpretations
21edo's edostep has the following interpretations in the 2.3.5.7.23.29.31 subgroup:
- 32/31
- 31/30
- 30/29
- 29/28
- 49/48
- 46/45
- 64/63
