Horwell temperaments: Difference between revisions

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Bezique splits the octave into 32 equal parts and reaches 3/2, 8/5 and 11/8 in just one generator with the 64-tone mos. The card game of bezique is played with two packs of 32 cards, hence the name.

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Comma list: 65625/65536, 847288609443/843308032000

[[Comma list]]: 65625/65536, 847288609443/843308032000

Mapping: 32 ~~32 93 15 92~~, 0 1 -1 4 1

[[Mapping]]: [{{val| 32 0 125 -113 }}, {{val| 0 1 -1 4 }}]

Mapping generators: ~100352/98415 ~~= 1\32~~, ~3~~/2 = 701.610~~

Mapping generators: ~100352/98415, ~3

Optimal tuning (CTE): ~3/2 = 701.~~953~~

[[Optimal tuning]] ([[CTE]]): ~100352/98415 = 1\32, ~3/2 = 701.610

=== 11-limit ===

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Comma list: 9801/9800, 46656/46585, 65625/65536

Mapping: 32 ~~32 93 15 92~~, 0 1 -1 4 1

Mapping: [{{val| 32 0 125 -113 60 }}, {{val| 0 1 -1 4 1 }}]

~~Mapping generators~~: ~45/44 = 1\32, ~3/2 = 701.601

Optimal tuning (CTE): ~45/44 = 1\32, ~3/2 = 701.601

~~Optimal tuning (CTE): ~3/2 = 701.953~~

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 729/728, 1575/1573, ~~67392~~/~~67375~~, ~~78975~~/~~78848~~

Comma list: 729/728, 1575/1573, 4225/4224, 6656/6655

Mapping: 32 ~~32 93 15 92 81~~, 0 1 -1 4 1 2

Mapping: [{{val| 32 0 125 -113 60 17 }}, {{val| 0 1 -1 4 1 2 }}]

~~Mapping generators~~: ~45/44 = 1\32, ~3/2 = 701.593

Optimal tuning (CTE): ~45/44 = 1\32, ~3/2 = 701.593

~~Optimal tuning (CTE)~~: ~~~3/2 = 701~~.~~953~~

Vals: 224, 320, 544, 768, 992, 1216, 1312, ...

~~Vals: 224, 320, 544, 768, 992, 1216, 1312, ...~~

[[Category:Temperament collections]]

[[Category:Horwell temperaments| ]]

[[Category:Horwell]]

[[Category:Rank 2]]

@@ Line 208: / Line 208: @@
 Bezique splits the octave into 32 equal parts and reaches 3/2, 8/5 and 11/8 in just one generator with the 64-tone mos. The card game of bezique is played with two packs of 32 cards, hence the name.
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma list: 65625/65536, 847288609443/843308032000
+[[Comma list]]: 65625/65536, 847288609443/843308032000
-Mapping: 32 32 93 15 92, 0 1 -1 4 1
+[[Mapping]]: [{{val| 32 0 125 -113 }}, {{val| 0 1 -1 4 }}]
-Mapping generators: ~100352/98415 = 1\32, ~3/2 = 701.610
+Mapping generators: ~100352/98415, ~3
-Optimal tuning (CTE): ~3/2 = 701.953
+[[Optimal tuning]] ([[CTE]]): ~100352/98415 = 1\32, ~3/2 = 701.610
 === 11-limit ===
@@ Line 223: / Line 223: @@
 Comma list: 9801/9800, 46656/46585, 65625/65536
-Mapping: 32 32 93 15 92, 0 1 -1 4 1
+Mapping: [{{val| 32 0 125 -113 60 }}, {{val| 0 1 -1 4 1 }}]
-Mapping generators: ~45/44 = 1\32, ~3/2 = 701.601
+Optimal tuning (CTE): ~45/44 = 1\32, ~3/2 = 701.601
-Optimal tuning (CTE): ~3/2 = 701.953
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 729/728, 1575/1573, 67392/67375, 78975/78848
+Comma list: 729/728, 1575/1573, 4225/4224, 6656/6655
-Mapping: 32 32 93 15 92 81, 0 1 -1 4 1 2
+Mapping: [{{val| 32 0 125 -113 60 17 }}, {{val| 0 1 -1 4 1 2 }}]
-Mapping generators: ~45/44 = 1\32, ~3/2 = 701.593
+Optimal tuning (CTE): ~45/44 = 1\32, ~3/2 = 701.593
-Optimal tuning (CTE): ~3/2 = 701.953
+Vals: 224, 320, 544, 768, 992, 1216, 1312, ...
-Vals: 224, 320, 544, 768, 992, 1216, 1312, ...
 [[Category:Temperament collections]]
 [[Category:Horwell temperaments| ]] <!-- main article -->
 [[Category:Horwell]]
 [[Category:Rank 2]]