2814edo: Difference between revisions
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== Theory == | == Theory == | ||
2814edo has all its harmonics below 20% error in the 17-limit and it is as a corollary [[consistent]]. | 2814edo has all its harmonics below 20% error in the 17-limit and it is as a corollary [[consistent]]. | ||
| Line 11: | Line 10: | ||
It is also a tuning for the [[Double Bastille]] temperament in the 2.5.7.11.13 subgroup. | It is also a tuning for the [[Double Bastille]] temperament in the 2.5.7.11.13 subgroup. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|2814}} | |||
[[Category:Equal divisions of the octave|####]]<!-- 4-digit number --> | |||
[[Category:Jacobin]] | |||
Revision as of 18:52, 15 December 2022
| ← 2813edo | 2814edo | 2815edo → |
Theory
2814edo has all its harmonics below 20% error in the 17-limit and it is as a corollary consistent.
In the 7-limit, it is contorted, with the same commas tempered out as 1407edo.
In the 11-limit, it supports rank three Odin temperament.
It is also a tuning for the Double Bastille temperament in the 2.5.7.11.13 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.036 | +0.040 | +0.044 | +0.068 | -0.016 | -0.051 | +0.142 | -0.129 | -0.153 | -0.046 |
| Relative (%) | +0.0 | -8.4 | +9.4 | +10.3 | +15.9 | -3.7 | -12.0 | +33.2 | -30.3 | -35.9 | -10.8 | |
| Steps (reduced) |
2814 (0) |
4460 (1646) |
6534 (906) |
7900 (2272) |
9735 (1293) |
10413 (1971) |
11502 (246) |
11954 (698) |
12729 (1473) |
13670 (2414) |
13941 (2685) | |