241edo: Difference between revisions

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== Theory ==

241edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]], [[19683/19600]] and [[3136/3125]] in the [[7-limit]], [[540/539]], 43923/43904, [[65536/65219]], and [[151263/151250]] in the [[11-limit]], and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[subpental]].

241edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp.

As an equal temperament, it [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]], [[19683/19600]] and [[3136/3125]] in the [[7-limit]], [[540/539]], [[43923/43904]], [[65536/65219]], and [[151263/151250]] in the [[11-limit]], and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[subpental]].

=== Prime harmonics ===

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=== Subsets and supersets ===

241edo is the 53rd [[prime edo]].

241edo is the 53rd [[prime edo]]. As such, it does not contain any nontrivial subset edos. [[1205edo]], which slices its step in five, is a notable higher-limit system.

== Regular temperament properties ==

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| [[Gary]]

|}

<nowiki />* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if distinct

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

[[Category:Subpental]]

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 {{Infobox ET}}
-{{EDO intro|241}}
+{{ED intro}}
 == Theory ==
-edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]], [[19683/19600]] and [[3136/3125]] in the [[7-limit]], [[540/539]], 43923/43904, [[65536/65219]], and [[151263/151250]] in the [[11-limit]], and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[subpental]].
+edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp.
+As an equal temperament, it [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]], [[19683/19600]] and [[3136/3125]] in the [[7-limit]], [[540/539]], [[43923/43904]], [[65536/65219]], and [[151263/151250]] in the [[11-limit]], and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[subpental]].
 === Prime harmonics ===
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 === Subsets and supersets ===
-edo is the 53rd [[prime edo]].
+edo is the 53rd [[prime edo]]. As such, it does not contain any nontrivial subset edos. [[1205edo]], which slices its step in five, is a notable higher-limit system.
 == Regular temperament properties ==
@@ Line 99: / Line 101: @@
 | [[Gary]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 [[Category:Subpental]]