Amity: Difference between revisions

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~~{{See~~ also|~~Amity family #Amity}}~~

'''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]].

~~{{See also~~|~~Ragismic microtemperaments #Amity}}~~

~~'''Amity'''~~ is ~~a temperament for the 5~~, 7, 11, and 13 ~~[[Harmonic~~ limit~~|prime limits]]~~. ~~Equal temperaments that support amity include [[46edo|~~46~~]], [[53edo|~~53]], ~~[[99edo|99]], [[152edo|152]]~~, and ~~[[205edo|205]]~~.

Extending amity from the 7-limit to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: 11-limit amity (53&205) and hitchcock (46&53). Tempering out 540/539 leads 11-limit amity, supported by 53et, 152et, and 205et. Tempering out 121/120 leads 11-limit hitchcock, supported by 46et, 53et, and 99et. They can be extended to the 13-limit by the 352/351 comma, and results in 625/624 and 729/728 being tempered out in 13-limit amity; 169/168 and 325/324 being tempered out in 13-limit hitchcock. In the 17-limit, 46&53 tempers out 154/153, 256/255, and 273/272.

~~In the 7-limit, amity tempers out 4375/4374 and 5120/5103, as well as 5-limit~~ [[~~amity comma~~]], 1600000/1594323. But extending it from the 7-limit to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: 11-limit amity (53&205) and hitchcock (46&53).

See [[Amity family #Amity]] or [[Ragismic microtemperaments #Amity]] for more technical data.

Tempering out 540/539 leads 11-limit amity, supported by 53et, 152et, and 205et. Tempering out 121/120 leads 11-limit hitchcock, supported by 46et, 53et, and 99et. They can be extended to the 13-limit by the 352/351 comma, and results in 625/624 and 729/728 being tempered out in 13-limit amity; 169/168 and 325/324 being tempered out in 13-limit hitchcock. In the 17-limit, 46&53 tempers out 154/153, 256/255, and 273/272.

== Interval chain ==

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== Tuning spectra ==

=== Spectrum of amity tunings ===

13-limit commas: 352/351, 540/539, 625/624, 729/728

~~13-limit commas: 352/351, 540/539, 625/624, 729/728~~

{| class="wikitable center-all left-3"

|-

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| 11/8

| 339.495

| 13- and, 15-odd-limit minimax

| 13- and 15-odd-limit minimax

|-

| 14/13

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=== Spectrum of hitchcock tunings ===

13-limit commas: 121/120, 169/168, 176/175, 325/324

~~13-limit commas: 121/120, 169/168, 176/175, 325/324~~

{| class="wikitable center-all left-3"

|-

! Eigenmonzo

! Generator

! ~~Comment~~

! Comments

|-

| 12/11

@@ Line 1: / Line 1: @@
-{{See also|Amity family #Amity}}
+'''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]].
-{{See also|Ragismic microtemperaments #Amity}}
-'''Amity''' is a temperament for the 5, 7, 11, and 13 [[Harmonic limit|prime limits]]. Equal temperaments that support amity include [[46edo|46]], [[53edo|53]], [[99edo|99]], [[152edo|152]], and [[205edo|205]].
+Extending amity from the 7-limit to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: 11-limit amity (53&amp;205) and hitchcock (46&amp;53). Tempering out 540/539 leads 11-limit amity, supported by 53et, 152et, and 205et. Tempering out 121/120 leads 11-limit hitchcock, supported by 46et, 53et, and 99et. They can be extended to the 13-limit by the 352/351 comma, and results in 625/624 and 729/728 being tempered out in 13-limit amity; 169/168 and 325/324 being tempered out in 13-limit hitchcock. In the 17-limit, 46&amp;53 tempers out 154/153, 256/255, and 273/272.
-In the 7-limit, amity tempers out 4375/4374 and 5120/5103, as well as 5-limit [[amity comma]], 1600000/1594323. But extending it from the 7-limit to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: 11-limit amity (53&amp;205) and hitchcock (46&amp;53).
+See [[Amity family #Amity]] or [[Ragismic microtemperaments #Amity]] for more technical data.
-Tempering out 540/539 leads 11-limit amity, supported by 53et, 152et, and 205et. Tempering out 121/120 leads 11-limit hitchcock, supported by 46et, 53et, and 99et. They can be extended to the 13-limit by the 352/351 comma, and results in 625/624 and 729/728 being tempered out in 13-limit amity; 169/168 and 325/324 being tempered out in 13-limit hitchcock. In the 17-limit, 46&amp;53 tempers out 154/153, 256/255, and 273/272.
 == Interval chain ==
@@ Line 263: / Line 260: @@
 == Tuning spectra ==
 === Spectrum of amity tunings ===
+-limit commas: 352/351, 540/539, 625/624, 729/728
--limit commas: 352/351, 540/539, 625/624, 729/728
 {| class="wikitable center-all left-3"
 |-
@@ Line 325: / Line 322: @@
 | 11/8
 | 339.495
-| 13- and, 15-odd-limit minimax
+| 13- and 15-odd-limit minimax
 |-
 | 14/13
@@ Line 365: / Line 362: @@
 === Spectrum of hitchcock tunings ===
+-limit commas: 121/120, 169/168, 176/175, 325/324
--limit commas: 121/120, 169/168, 176/175, 325/324
 {| class="wikitable center-all left-3"
 |-
 ! Eigenmonzo
 ! Generator
-! Comment
+! Comments
 |-
 | 12/11