1911edo: Difference between revisions

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== Theory ==

1911edo is [[consistent]] in the 11-limit ~~and~~ [[Tempering out|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-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 ===

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=== Subsets and supersets ===

Since 1911 factors into ~~3 × 72 × 13~~, 1911edo has subset edos {{EDOs| 3, 7, 13, 21, 39, 49, 91, 147, 273, 637 }}.

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"

|+Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated Ratio

! Associated Ratio*

! Temperaments

|-

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 == Theory ==
-edo is [[consistent]] in the 11-limit and [[Tempering out|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.
+edo 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 ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-Since 1911 factors into 3 × 7<sup>2</sup> × 13, 1911edo has subset edos {{EDOs| 3, 7, 13, 21, 39, 49, 91, 147, 273, 637 }}.
+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"
+|+Table of rank-2 temperaments by generator
+|-
 ! Periods<br>per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-