1911edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{Rank-2 begin}} | ||
|- | |- | ||
| 13 | | 13 | ||
| Line 33: | Line 26: | ||
| 4/3<br />(176/175) | | 4/3<br />(176/175) | ||
| [[Protactinium]] | | [[Protactinium]] | ||
{{Rank-2 end}} | |||
{{orf}} | {{orf}} | ||
Revision as of 01:24, 16 November 2024
| ← 1910edo | 1911edo | 1912edo → |
Theory
1911edo is consistent in the 11-odd-limit. The equal temperament tempers out the aluminium comma in the 5-limit, and it provides the optimal patent val for the protactinium temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 subgroup tuning.
Odd harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.086 | -0.128 | +0.091 | +0.016 | +0.289 | -0.089 | +0.132 | +0.297 | +0.250 | -0.295 |
| Relative (%) | +0.0 | +13.7 | -20.5 | +14.5 | +2.6 | +46.0 | -14.1 | +21.1 | +47.3 | +39.8 | -46.9 | |
| Steps (reduced) |
1911 (0) |
3029 (1118) |
4437 (615) |
5365 (1543) |
6611 (878) |
7072 (1339) |
7811 (167) |
8118 (474) |
8645 (1001) |
9284 (1640) |
9467 (1823) | |
Subsets and supersets
Since 1911 factors into 3 × 72 × 13, 1911edo has subset edos 3, 7, 13, 21, 39, 49, 91, 147, 273, 637.
Regular temperament properties
Rank-2 temperaments
Template:Rank-2 begin
|-
| 13
| 793\1911
(58\1911)
| 497.959
(36.421)
| 4/3
(?)
| Aluminium
|-
| 91
| 793\1911
(16\1911)
| 497.959
(10.047)
| 4/3
(176/175)
| Protactinium
Template:Rank-2 end
Template:Orf