1911edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== 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 === | === Subsets and supersets === | ||
1911edo has subset edos {{EDOs| | Since 1911 factors into {{factorization|1911}}, 1911edo has subset edos {{EDOs| 3, 7, 13, 21, 39, 49, 91, 147, 273, 637 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
per 8ve | |- | ||
!Generator | ! Periods<br />per 8ve | ||
! Generator* | |||
!Cents | ! Cents* | ||
! Associated<br />ratio* | |||
!Associated | ! 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) | | [[Aluminium]] | ||
|4/3 | |||
(?) | |||
|[[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) | | [[Protactinium]] | ||
|4/3 | |||
(176/175) | |||
|[[Protactinium]] | |||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||