Amity: Difference between revisions
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'''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}}. | '''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. | 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. | ||
{{Tdhat|Amity family #Amity}} | |||
== Etymology == | == Etymology == | ||
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[[Category:Amity| ]] <!-- main article --> | [[Category:Amity| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Amity family]] | [[Category:Amity family]] | ||
[[Category:Ragismic microtemperaments]] | [[Category:Ragismic microtemperaments]] | ||
[[Category:Hemifamity temperaments]] | [[Category:Hemifamity temperaments]] | ||