509edo: Difference between revisions

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== Theory ==

509edo has a sharp tendency in lower [[harmonic]]s. ~~The~~ [[13-limit]] [[TE ~~tuning|optimal~~ tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave compression]] tight.

509edo has a sharp tendency in lower [[harmonic]]s. It is only consistent to the [[7-odd-limit]] due to harmonic [[3/1|3]] being too sharp, causing harmonic [[9/1|9]] to become inconsistent, but the [[13-limit]] [[TE tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave stretch|octave compression]] tight.

As an equal temperament, it [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit; [[2401/2400]] and 29360128/29296875 in the 7-limit; and [[3025/3024]], [[5632/5625]], [[41503/41472]], 42592/42525, 151263/151250, 172032/171875, 180224/180075, 322102/321489, 422576/421875, 456533/455625, and [[1953125/1948617]] in the 11-limit. It provides the [[optimal patent val]] for [[petrtri]], the 2.11/5.13/5 subgroup temperament tempering out [[2200/2197]].

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| [[Amity]]

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<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

== Music ==

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 {{Infobox ET}}
-{{EDO intro|509}}
+{{ED intro}}
 == Theory ==
-edo has a sharp tendency in lower [[harmonic]]s. The [[13-limit]] [[TE tuning|optimal tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave compression]] tight.
+edo has a sharp tendency in lower [[harmonic]]s. It is only consistent to the [[7-odd-limit]] due to harmonic [[3/1|3]] being too sharp, causing harmonic [[9/1|9]] to become inconsistent, but the [[13-limit]] [[TE tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave stretch|octave compression]] tight.
 As an equal temperament, it [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit; [[2401/2400]] and 29360128/29296875 in the 7-limit; and [[3025/3024]], [[5632/5625]], [[41503/41472]], 42592/42525, 151263/151250, 172032/171875, 180224/180075, 322102/321489, 422576/421875, 456533/455625, and [[1953125/1948617]] in the 11-limit. It provides the [[optimal patent val]] for [[petrtri]], the 2.11/5.13/5 subgroup temperament tempering out [[2200/2197]].
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 | [[Amity]]
 |}
-<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
 == Music ==