1911edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1911}} | {{EDO intro|1911}} | ||
== Theory == | |||
1911edo is consistent in the 11-limit and tempers out the [[aluminium comma]] in the 5-limit. 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. | 1911edo is consistent in the 11-limit and tempers out the [[aluminium comma]] in the 5-limit. 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 === | === Odd harmonics === | ||
| Line 13: | Line 13: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | !Periods<br>per 8ve | ||
per 8ve | !Generator<br>(Reduced) | ||
!Generator | !Cents<br>(Reduced) | ||
(Reduced) | !Associated<br>Ratio | ||
!Cents | |||
(Reduced) | |||
!Associated | |||
Ratio | |||
!Temperaments | !Temperaments | ||
|- | |- | ||
|13 | |13 | ||
|793\1911 | |793\1911<br>(58\1911) | ||
(58\1911) | |497.959<br>(36.421) | ||
|497.959 | |4/3<br>(?) | ||
(36.421) | |||
|4/3 | |||
(?) | |||
|[[Aluminium]] | |[[Aluminium]] | ||
|- | |- | ||
|91 | |91 | ||
|793\1911 | |793\1911<br>(16\1911) | ||
(16\1911) | |497.959<br>(10.047) | ||
|497.959 | |4/3<br>(176/175) | ||
(10.047) | |||
|4/3 | |||
(176/175) | |||
|[[Protactinium]] | |[[Protactinium]] | ||
|} | |} | ||
Revision as of 21:20, 17 July 2023
| ← 1910edo | 1911edo | 1912edo → |
Theory
1911edo is consistent in the 11-limit and tempers out the aluminium comma in the 5-limit. 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
1911edo has subset edos 1, 3, 7, 13, 21, 39, 49, 91, 147, 273, 637.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 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 |