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Countercomp family: Difference between revisions

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Line 9: Line 9:
[[Mapping]]: [{{val| 41 65 0 }}, {{val| 0 0 1 }}]
[[Mapping]]: [{{val| 41 65 0 }}, {{val| 0 0 1 }}]


Mapping generators: ~531441/524288, ~5/1
: mapping generators: ~531441/524288, ~5/1


[[Optimal tuning]] ([[POTE]]): ~531441/524288 = 1\41, ~5/4 = 386.668
[[Optimal tuning]]s:
* [[CTE]]: ~531441/524288 = 29.2683¢ (1 ⧵ 41), ~5/4 = 386.3137¢
* [[CWE]]: ~531441/524288 = 29.2683¢ (1 ⧵ 41), ~5/4 = 386.5501¢


{{Optimal ET sequence|legend=1| 41, 123, 164, 205, 369, 574, 779, 2132bc }}
{{Optimal ET sequence|legend=1| 41, 123, 164, 205, 369, 574, 779, 2132bc }}


[[Badness]]: 0.934310
[[Badness]] (Sintel): 21.917


== Gamelacomp ==
== Gamelacomp ==
Line 24: Line 26:
[[Mapping]]: [{{val| 41 65 0 115 }}, {{val| 0 0 1 0 }}]
[[Mapping]]: [{{val| 41 65 0 115 }}, {{val| 0 0 1 0 }}]


[[Optimal tuning]] ([[POTE]]): ~64/63 = 1\41, ~5/4 = 385.731
[[Optimal tuning]]s:
* [[CTE]]: ~64/63 = 29.2683¢ (1 ⧵ 41), ~5/4 = 386.3137¢
* [[CWE]]: ~64/63 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.8764¢


{{Optimal ET sequence|legend=1| 41, 123, 164, 205d, 246d, 451dd }}
{{Optimal ET sequence|legend=1| 41, 123, 164, 205d, 246d, 451dd }}


[[Badness]]: 0.161056
[[Badness]] (Sintel): 4.076


=== 11-limit ===
=== 11-limit ===
Line 37: Line 41:
Mapping: [{{val| 41 65 0 115 237 }}, {{val| 0 0 1 0 -1 }}]
Mapping: [{{val| 41 65 0 115 237 }}, {{val| 0 0 1 0 -1 }}]


Optimal tuning (POTE): ~56/55 = 1\41, ~5/4 = 385.871
Optimal tunings:
* CTE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.9888¢
* CWE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.8909¢


{{Optimal ET sequence|legend=1| 41, 123e, 164, 205d, 451dd }}
{{Optimal ET sequence|legend=0| 41, 123e, 164, 205d, 451dd }}


Badness: 0.076537
Badness (Sintel): 2.530


=== 13-limit ===
=== 13-limit ===
Line 50: Line 56:
Mapping: [{{val| 41 65 0 115 237 247 }}, {{val| 0 0 1 0 -1 -1 }}]
Mapping: [{{val| 41 65 0 115 237 247 }}, {{val| 0 0 1 0 -1 -1 }}]


Optimal tuning (POTE): ~56/55 = 1\41, ~5/4 = 386.604
Optimal tunings:
* CTE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~5/4 = 386.5763¢
* CWE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~5/4 = 386.5997¢


{{Optimal ET sequence|legend=1| 41, 123e, 164, 205d }}
{{Optimal ET sequence|legend=1| 41, 123e, 164, 205d }}


Badness: 0.054921
Badness (Sintel): 2.269


== Mermacomp ==
== Mermacomp ==
Line 63: Line 71:
[[Mapping]]: [{{val| 41 65 0 20 }}, {{val| 0 0 1 1 }}]
[[Mapping]]: [{{val| 41 65 0 20 }}, {{val| 0 0 1 1 }}]


[[Optimal tuning]] ([[POTE]]): ~50/49 = 1\41, ~5/4 = 385.667
[[Optimal tuning]]s:
* [[CTE]]: ~50/49 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.1546¢
* [[CWE]]: ~50/49 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.4966¢


{{Optimal ET sequence|legend=1| 41, 123d, 164d, 205, 246, 451d, 697dd }}
{{Optimal ET sequence|legend=1| 41, 123d, 164d, 205, 246, 451d, 697dd }}


[[Badness]]: 0.142344
[[Badness]] (Sintel): 3.602


=== 11-limit ===
=== 11-limit ===
Line 76: Line 86:
Mapping: [{{val| 41 65 0 20 237 }}, {{val| 0 0 1 1 -1 }}]
Mapping: [{{val| 41 65 0 20 237 }}, {{val| 0 0 1 1 -1 }}]


Optimal tuning (POTE): ~55/54 = 1\41, ~5/4 = 385.309
Optimal tunings:
* CTE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.1784¢
* CWE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.2847¢


{{Optimal ET sequence|legend=1| 41, 164d, 205, 246 }}
{{Optimal ET sequence|legend=0| 41, 164d, 205, 246 }}


Badness: 0.076588
Badness (Sintel): 2.532
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 540/539, 729/728, 75625/75264
 
Mapping: [{{val| 41 65 0 20 237 247 }}, {{val| 0 0 1 1 -1 -1 }}]
 
Optimal tunings:
* CTE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.7331¢
* CWE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.8418¢
 
{{Optimal ET sequence|legend=0| 41, 164d, 205, 246f }}
 
Badness (Sintel): 2.293


== Hemicountercomp ==
== Hemicountercomp ==
Line 89: Line 116:
[[Mapping]]: [{{val| 41 65 1 68 }}, {{val| 0 0 2 1 }}]
[[Mapping]]: [{{val| 41 65 1 68 }}, {{val| 0 0 2 1 }}]


Mapping generators: ~100352/98415, ~567/256
: mapping generators: ~100352/98415, ~567/256


[[Optimal tuning]] ([[CTE]]): ~100352/98415 = 1\41, ~567/512 = 178.5314 (~5120/5103 = 2.9216)
[[Optimal tuning]]s:
* [[CTE]]: ~100352/98415 = 29.2683¢ (1 ⧵ 41), ~567/512 = 178.5314¢
* [[CWE]]: ~100352/98415 = 29.2683¢ (1 ⧵ 41), ~567/512 = 178.6568¢


{{Optimal ET sequence|legend=1| 41, …, 328, 369, 779, 1927bc }}
{{Optimal ET sequence|legend=1| 41, …, 328, 369, 779, 1927bc }}


[[Badness]]: 0.134559
[[Badness]] (Sintel): 3.405


=== Hemicocomp ===
=== Hemicocomp ===
Line 104: Line 133:
Mapping: [{{val| 41 65 1 68 189 }}, {{val| 0 0 2 1 -1 }}]
Mapping: [{{val| 41 65 1 68 189 }}, {{val| 0 0 2 1 -1 }}]


Optimal tuning (CTE): ~56/55 = 1\41, ~567/512 = 178.6944 (~3025/3024 = 3.0846)
Optimal tunings:
* CTE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~567/512 = 178.6944¢
* CWE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~567/512 = 178.8825¢


{{Optimal ET sequence|legend=1| 41, …, 328, 369, 1066cee }}
{{Optimal ET sequence|legend=0| 41, …, 328, 369, 1066cee }}


Badness: 0.064400
Badness (Sintel): 2.129


==== 13-limit ====
==== 13-limit ====
Line 117: Line 148:
Mapping: [{{val| 41 65 1 68 189 246 }}, {{val| 0 0 2 1 -1 -2 }}]
Mapping: [{{val| 41 65 1 68 189 246 }}, {{val| 0 0 2 1 -1 -2 }}]


Optimal tuning (CTE): ~56/55 = 1\41, ~72/65 = 178.9389 (~352/351 = 3.3291)
Optimal tunings:
* CTE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~72/65 = 178.9389¢
* CWE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~72/65 = 179.0133¢


{{Optimal ET sequence|legend=1| 41, …, 328, 369f, 697cef }}
{{Optimal ET sequence|legend=0| 41, …, 328, 369f, 697cef }}


Badness: 0.0416
Badness (Sintel): 1.718


=== Hemermacomp ===
=== Hemermacomp ===
Line 130: Line 163:
Mapping: [{{val| 41 65 1 68 236 }}, {{val| 0 0 2 1 -2 }}]
Mapping: [{{val| 41 65 1 68 236 }}, {{val| 0 0 2 1 -2 }}]


Optimal tuning (CTE): ~55/54 = 1\41, ~256/231 = 178.3836 (~3024/3025 = 2.7738)
Optimal tunings:
* CTE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~256/231 = 178.3836¢
* CWE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~256/231 = 178.3736¢


{{Optimal ET sequence|legend=1| 41, …, 410, 451, 861e }}
{{Optimal ET sequence|legend=0| 41, …, 410, 451, 861e }}


Badness: 0.100152
Badness (Sintel): 3.311


==== 13-limit ====
==== 13-limit ====
Line 143: Line 178:
Mapping: [{{val| 41 65 1 68 236 293 }}, {{val| 0 0 2 1 -2 -3 }}]
Mapping: [{{val| 41 65 1 68 236 293 }}, {{val| 0 0 2 1 -2 -3 }}]


Optimal tuning (CTE): ~55/54 = 1\41, ~72/65 = 178.3755 (~352/351 = 2.7657)
Optimal tunings:
* CTE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~72/65 = 178.3755¢
* CWE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~72/65 = 178.3772¢


{{Optimal ET sequence|legend=1| 41, …, 410, 451, 861e }}
{{Optimal ET sequence|legend=0| 41, …, 410, 451, 861e }}


Badness: 0.0605
Badness (Sintel): 2.500


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Countercomp family| ]] <!-- main article -->
[[Category:Countercomp family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
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