2814edo: Difference between revisions
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→Theory: even 20% relative error doesn't guarantee consistency in the 17-odd-limit. 1/3 does |
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== Theory == | == Theory == | ||
2814edo has all | 2814edo has all the harmonics from 3 to 17 approximated below 1/3 relative error and it is as a corollary [[consistent]] in the [[17-odd-limit]]. | ||
In the 7-limit, it is contorted, with the same commas tempered out as [[1407edo]]. | In the 7-limit, it is contorted, with the same commas tempered out as [[1407edo]]. | ||
In the 11-limit, it supports rank | In the 11-limit, it supports rank-3 [[odin]] temperament. | ||
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. | ||
Revision as of 08:35, 16 December 2022
| ← 2813edo | 2814edo | 2815edo → |
Theory
2814edo has all the harmonics from 3 to 17 approximated below 1/3 relative error and it is as a corollary consistent in the 17-odd-limit.
In the 7-limit, it is contorted, with the same commas tempered out as 1407edo.
In the 11-limit, it supports rank-3 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) | |