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 | 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. | ||
== Etymology == | == Etymology == | ||
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{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
|- | |- | ||
! rowspan="2"| # | ! rowspan="2" | # | ||
! rowspan="2"| Cents* | ! rowspan="2" | Cents* | ||
! colspan="3" | Approximate | ! colspan="3" | Approximate ratios | ||
|- | |- | ||
! 7-limit | ! 7-limit | ||
! 13-limit Extensions<br>Amity Mapping (53 & 152) | ! 13-limit Extensions<br />Amity Mapping (53 & 152) | ||
! 13-limit Extensions<br>Hitchcock Mapping (46 & 53) | ! 13-limit Extensions<br />Hitchcock Mapping (46 & 53) | ||
|- | |- | ||
| 0 | | 0 | ||
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| | | | ||
|} | |} | ||
<nowiki>* | <nowiki />* In 7-limit POTE tuning, octave reduced | ||
== Tuning spectra == | == Tuning spectra == | ||
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{| class="wikitable center-all left-3" | {| class="wikitable center-all left-3" | ||
|- | |- | ||
! [[ | ! [[Eigenmonzo|Eigenmonzo<br />(unchanged-interval)]] | ||
! | ! Generator<br />(¢) | ||
! | ! Comments | ||
|- | |- | ||
| 10/9 | | 10/9 | ||
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{| class="wikitable center-all left-3" | {| class="wikitable center-all left-3" | ||
|- | |- | ||
! | ! Eigenmonzo<br />(unchanged-interval) | ||
! | ! Generator<br>(¢) | ||
! | ! Comments | ||
|- | |- | ||
| 12/11 | | 12/11 | ||
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== Music == | == Music == | ||
; [[User:Francium|Francium]] | ; [[User:Francium|Francium]] | ||
* [https://youtu.be/AsDaJXCBd_w?si=6BfHt5gYpCPD1oxq ''For Amity''] (2023) | * [https://youtu.be/AsDaJXCBd_w?si=6BfHt5gYpCPD1oxq ''For Amity''] (2023) – amity in 463edo tuning | ||
[[Category:Amity| ]] <!-- main article --> | [[Category:Amity| ]] <!-- main article --> | ||