Amity: Difference between revisions

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'''Amity''' is the [[microtemperament]] ~~tempering~~ out the [[amity comma]], 1600000/1594323~~, in the 5-limit~~. This ~~article~~ also assumes the canonical ~~mapping for~~ 7, which means tempering out [[4375/4374]] and [[5120/5103]] ~~in the 7-limit~~. Equal temperaments that support amity include ~~[[46edo~~|46]], ~~[[53edo|~~53]], ~~[[99edo|~~99]], ~~[[152edo|~~152]], and ~~[[205edo|~~205]].

'''Amity''' is the [[rank]]-2 [[microtemperament]] on the [[5-limit]] that tempers out the [[amity comma]], 1600000/1594323. This page also assumes the canonical [[extension]] to the [[7-limit]], which means tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that support amity include {{EDOs|46, 53, 99, 152, and 205}}.

Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity (53 & 152), catamite (46 & 145), and hitchcock (46 & 53). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to -62 generator steps. Catamite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to -9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in catamite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. In the 17-limit, hitchcock tempers out 154/153, 256/255, and 273/272.

~~See [[~~Amity ~~family #Amity]] for more technical data~~.

== Etymology ==

Origin: Paul Erlich (2002)

Meaning: A restructuring of the words "acute minor third." The ideal generator for Amity is between a minor third and neutral third.

== Interval chain ==

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-'''Amity''' is the [[microtemperament]] tempering out the [[amity comma]], 1600000/1594323, in the 5-limit. This article also assumes the canonical mapping for 7, which means tempering out [[4375/4374]] and [[5120/5103]] in the 7-limit. Equal temperaments that support amity include [[46edo|46]], [[53edo|53]], [[99edo|99]], [[152edo|152]], and [[205edo|205]].
+{{tdhat|Amity family #Amity}}
+'''Amity''' is the [[rank]]-2 [[microtemperament]] on the [[5-limit]] that tempers out the [[amity comma]], 1600000/1594323. This page also assumes the canonical [[extension]] to the [[7-limit]], which means tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that support amity include {{EDOs|46, 53, 99, 152, and 205}}.
 Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity (53 & 152), catamite (46 & 145), and hitchcock (46 & 53). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to -62 generator steps. Catamite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to -9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in catamite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. In the 17-limit, hitchcock tempers out 154/153, 256/255, and 273/272.
-See [[Amity family #Amity]] for more technical data.
+== Etymology ==
+Origin: Paul Erlich (2002)
+Meaning: A restructuring of the words "acute minor third." The ideal generator for Amity is between a minor third and neutral third.
 == Interval chain ==