1911edo: Difference between revisions
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== Theory == | |||
1911edo is [[consistent]] in the [[11-odd-limit]]. The equal temperament [[Tempering out|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 === | === Odd harmonics === | ||
{{Harmonics in equal|1911}} | {{Harmonics in equal|1911}} | ||
=== Subsets and supersets === | |||
Since 1911 factors into {{factorization|1911}}, 1911edo has subset edos {{EDOs| 3, 7, 13, 21, 39, 49, 91, 147, 273, 637 }}. | |||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |||
| 13 | |||
| 793\1911<br />(58\1911) | |||
| 497.959<br />(36.421) | |||
| 4/3<br />(?) | |||
| [[Aluminium]] | |||
|- | |||
| 91 | |||
| 793\1911<br />(16\1911) | |||
| 497.959<br />(10.047) | |||
| 4/3<br />(176/175) | |||
| [[Protactinium]] | |||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||