Amity: Difference between revisions

Line 1:

'''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 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]] EDOs.

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.

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 53, 152, and 205 EDOs. Tempering out 121/120 leads 11-limit hitchcock, supported by 46, 53, and 99 EDOs. 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.

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

Line 260:

== Tuning spectra ==

=== Amity ===

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

Gencom: [2 128/105; 352/351 540/539 625/624 729/728]

Gencom mapping: [{{val| 1 3 6 -2 21 17 }}, {{val| 0 -5 -13 17 -62 -47 }}]

{| class="wikitable center-all"

Line 362:

Line 364:

=== Hitchcock ===

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

Gencom: [2 11/9; 121/120 169/168 176/175 325/324]

Gencom mapping: [{{val| 1 3 6 -2 6 2 }}, {{val| 0 -5 -13 17 -9 6 }}]

{| class="wikitable center-all"

@@ Line 1: / Line 1: @@
-'''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 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]] EDOs.
-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.
+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 53, 152, and 205 EDOs. Tempering out 121/120 leads 11-limit hitchcock, supported by 46, 53, and 99 EDOs. 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.
 See [[Amity family #Amity]] or [[Ragismic microtemperaments #Amity]] for more technical data.
@@ Line 260: / Line 260: @@
 == Tuning spectra ==
 === Amity ===
--limit commas: 352/351, 540/539, 625/624, 729/728
+Gencom: [2 128/105; 352/351 540/539 625/624 729/728]
+Gencom mapping: [{{val| 1 3 6 -2 21 17 }}, {{val| 0 -5 -13 17 -62 -47 }}]
 {| class="wikitable center-all"
@@ Line 362: / Line 364: @@
 === Hitchcock ===
--limit commas: 121/120, 169/168, 176/175, 325/324
+Gencom: [2 11/9; 121/120 169/168 176/175 325/324]
+Gencom mapping: [{{val| 1 3 6 -2 6 2 }}, {{val| 0 -5 -13 17 -9 6 }}]
 {| class="wikitable center-all"