1171edo: Difference between revisions

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== Theory ==

1171edo is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It has a 5-limit [[comma basis]] consisting of the [[monzisma]], {{monzo| 54 -37 2 }} and whoosh, {{monzo| 37 25 -33 }}. While not a strong higher-limit system, it is ~~uniquely~~ consistent through the [[27-odd-limit]], and is very strong on the 2.3.5.11 subgroup.

1171edo is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It has a 5-limit [[comma basis]] consisting of the [[monzisma]], {{monzo| 54 -37 2 }} and whoosh, {{monzo| 37 25 -33 }}. While not a strong higher-limit system, it is [[consistency|distinctly consistent]] through the [[27-odd-limit]], and is very strong on the 2.3.5.11 [[subgroup]].

=== Prime harmonics ===

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=== Subsets and supersets ===

1171edo is the 193rd [[prime edo]].

1171edo is the 193rd [[prime edo]]. [[2342edo]] which doubles it, corrects its [[harmonic]] [[7/1|7]] to a near-just quality.

== Regular temperament properties ==

=== Rank-2 temperaments ===

{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

|-

! Periods<br>per 8ve

! Generator*

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 == Theory ==
-edo is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It has a 5-limit [[comma basis]] consisting of the [[monzisma]], {{monzo| 54 -37 2 }} and whoosh, {{monzo| 37 25 -33 }}. While not a strong higher-limit system, it is uniquely consistent through the [[27-odd-limit]], and is very strong on the 2.3.5.11 subgroup.
+edo is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It has a 5-limit [[comma basis]] consisting of the [[monzisma]], {{monzo| 54 -37 2 }} and whoosh, {{monzo| 37 25 -33 }}. While not a strong higher-limit system, it is [[consistency|distinctly consistent]] through the [[27-odd-limit]], and is very strong on the 2.3.5.11 [[subgroup]].
 === Prime harmonics ===
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 === Subsets and supersets ===
-edo is the 193rd [[prime edo]].
+edo is the 193rd [[prime edo]]. [[2342edo]] which doubles it, corrects its [[harmonic]] [[7/1|7]] to a near-just quality.
 == Regular temperament properties ==
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
+|+Table of rank-2 temperaments by generator
+|-
 ! Periods<br>per 8ve
 ! Generator*