Semicomma family: Difference between revisions
m →Newspeak: Add intersection at 31edo |
m Units & misc. cleanup |
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| Line 10: | Line 10: | ||
{{Mapping|legend=1| 1 0 3 | 0 7 -3 }} | {{Mapping|legend=1| 1 0 3 | 0 7 -3 }} | ||
: mapping generators: ~2, ~75/64 | : mapping generators: ~2, ~75/64 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~75/64 = 271.670 | * [[CTE]]: ~2 = 1200.000{{c}}, ~75/64 = 271.670{{c}} | ||
: [[error map]]: {{val| 0.000 -0.264 -1.324 }} | : [[error map]]: {{val| 0.000 -0.264 -1.324 }} | ||
* [[POTE]]: ~2 = 1200.000, ~75/64 = 271.627 | * [[POTE]]: ~2 = 1200.000{{c}}, ~75/64 = 271.627{{c}} | ||
: error map: {{val| 0.000 -0.564 -1.195 }} | : error map: {{val| 0.000 -0.564 -1.195 }} | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* 5-odd-limit [[diamond monotone]]: ~75/64 = [257.143, 276.923] (3\14 to 3\13) | * [[5-odd-limit]] [[diamond monotone]]: ~75/64 = [257.143, 276.923] (3\14 to 3\13) | ||
* 5-odd-limit [[diamond tradeoff]]: ~75/64 = [271.229, 271.708] (1/3-comma to 2/7-comma) | * 5-odd-limit [[diamond tradeoff]]: ~75/64 = [271.229, 271.708] (1/3-comma to 2/7-comma) | ||
| Line 49: | Line 48: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~7/6 = 271.513 | * [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 271.513{{c}} | ||
: [[error map]]: {{val| 0.000 -1.364 -0.853 +3.278 }} | : [[error map]]: {{val| 0.000 -1.364 -0.853 +3.278 }} | ||
* [[POTE]]: ~2 = 1200.000, ~7/6 = 271.509 | * [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 271.509{{c}} | ||
: error map: {{val| 0.000 -1.394 -0.840 +3.243 }} | : error map: {{val| 0.000 -1.394 -0.840 +3.243 }} | ||
| Line 57: | Line 56: | ||
* [[7-odd-limit]]: ~7/6 = {{monzo| 2/11 0 -1/11 1/11 }} | * [[7-odd-limit]]: ~7/6 = {{monzo| 2/11 0 -1/11 1/11 }} | ||
: {{monzo list| 1 0 0 0 | 14/11 0 -7/11 7/11 | 27/11 0 3/11 -3/11 | 27/11 0 -8/11 8/11 }} | : {{monzo list| 1 0 0 0 | 14/11 0 -7/11 7/11 | 27/11 0 3/11 -3/11 | 27/11 0 -8/11 8/11 }} | ||
: [[ | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5 | ||
* [[9-odd-limit]]: ~7/6 = {{monzo| 3/17 2/17 -1/17 }} | * [[9-odd-limit]]: ~7/6 = {{monzo| 3/17 2/17 -1/17 }} | ||
: {{monzo list| 1 0 0 0 | 21/17 14/17 -7/17 0 | 42/17 -6/17 3/17 0 | 41/17 16/17 -8/17 0 }} | : {{monzo list| 1 0 0 0 | 21/17 14/17 -7/17 0 | 42/17 -6/17 3/17 0 | 41/17 16/17 -8/17 0 }} | ||
: [[ | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5 | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
| Line 82: | Line 81: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~7/6 = 271.560 | * CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.560{{c}} | ||
* POTE: ~2 = 1200.000, ~7/6 = 271.426 | * POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.426{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 106: | Line 105: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~7/6 = 271.556 | * CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.556{{c}} | ||
* POTE: ~2 = 1200.000, ~7/6 = 271.546 | * POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.546{{c}} | ||
Tuning ranges: | Tuning ranges: | ||
| Line 125: | Line 124: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~7/6 = 271.747 | * CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.747{{c}} | ||
* POTE: ~2 = 1200.000, ~7/6 = 271.301 | * POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.301{{c}} | ||
{{Optimal ET sequence|legend=0| 9, 22, 31f }} | {{Optimal ET sequence|legend=0| 9, 22, 31f }} | ||
| Line 140: | Line 139: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~7/6 = 271.163 | * CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.163{{c}} | ||
* POTE: ~2 = 1200.000, ~7/6 = 271.088 | * POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.088{{c}} | ||
Tuning ranges: | Tuning ranges: | ||
| Line 161: | Line 160: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~13/12 = 135.811 | * CTE: ~2 = 1200.000{{c}}, ~13/12 = 135.811{{c}} | ||
* POTE: ~2 = 1200.000, ~13/12 = 135.723 | * POTE: ~2 = 1200.000{{c}}, ~13/12 = 135.723{{c}} | ||
Tuning ranges: | Tuning ranges: | ||
| Line 182: | Line 181: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~7/6 = 271.316 | * CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.316{{c}} | ||
* POTE: ~2 = 1200.000, ~7/6 = 271.288 | * POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.288{{c}} | ||
Tuning ranges: | Tuning ranges: | ||
| Line 199: | Line 198: | ||
Mapping: {{mapping| 1 7 0 9 17 | 0 -14 6 -16 -35 }} | Mapping: {{mapping| 1 7 0 9 17 | 0 -14 6 -16 -35 }} | ||
: mapping generators: ~2, ~72/55 | : mapping generators: ~2, ~72/55 | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~55/36 = 735.754 | * CTE: ~2 = 1200.000{{c}}, ~55/36 = 735.754{{c}} | ||
* POTE: ~2 = 1200.000, ~55/36 = 735.752 | * POTE: ~2 = 1200.000{{c}}, ~55/36 = 735.752{{c}} | ||
{{Optimal ET sequence|legend=0| 31, 75e, 106, 137 }} | {{Optimal ET sequence|legend=0| 31, 75e, 106, 137 }} | ||
| Line 220: | Line 218: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~75/64 = 271.622 | * [[CTE]]: ~2 = 1200.000{{c}}, ~75/64 = 271.622{{c}} | ||
: [[error map]]: {{val| 0.000 -0.599 -1.180 +0.131 }} | : [[error map]]: {{val| 0.000 -0.599 -1.180 +0.131 }} | ||
* [[POTE]]: ~2 = 1200.000, ~75/64 = 271.607 | * [[POTE]]: ~2 = 1200.000{{c}}, ~75/64 = 271.607{{c}} | ||
: error map: {{val| 0.000 -0.707 -1.134 -0.808 }} | : error map: {{val| 0.000 -0.707 -1.134 -0.808 }} | ||
| Line 237: | Line 235: | ||
{{Mapping|legend=1| 1 7 0 1 | 0 -21 9 7 }} | {{Mapping|legend=1| 1 7 0 1 | 0 -21 9 7 }} | ||
: mapping generators: ~2, ~448/375 | : mapping generators: ~2, ~448/375 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~448/375 = 309.456 | * [[CTE]]: ~2 = 1200.000{{c}}, ~448/375 = 309.456{{c}} | ||
: [[error map]]: {{val| 0.000 -0.522 -1.213 -2.637 }} | : [[error map]]: {{val| 0.000 -0.522 -1.213 -2.637 }} | ||
* [[POTE]]: ~2 = 1200.000, ~448/375 = 309.472 | * [[POTE]]: ~2 = 1200.000{{c}}, ~448/375 = 309.472{{c}} | ||
: error map: {{val| 0.000 -0.872 -1.063 -2.520 }} | : error map: {{val| 0.000 -0.872 -1.063 -2.520 }} | ||
| Line 258: | Line 255: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~448/375 = 309.444 | * CTE: ~2 = 1200.000{{c}}, ~448/375 = 309.444{{c}} | ||
* POTE: ~2 = 1200.000, ~448/375 = 309.471 | * POTE: ~2 = 1200.000{{c}}, ~448/375 = 309.471{{c}} | ||
{{Optimal ET sequence|legend=0| 31, 97, 128, 159, 190 }} | {{Optimal ET sequence|legend=0| 31, 97, 128, 159, 190 }} | ||
| Line 273: | Line 270: | ||
{{Mapping|legend=1| 1 7 0 3 | 0 -28 12 -1 }} | {{Mapping|legend=1| 1 7 0 3 | 0 -28 12 -1 }} | ||
: mapping generators: ~2, ~8/7 | : mapping generators: ~2, ~8/7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~8/7 = 232.082 | * [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 232.082{{c}} | ||
: [[error map]]: {{val| 0.000 -0.255 -1.328 -0.908 }} | : [[error map]]: {{val| 0.000 -0.255 -1.328 -0.908 }} | ||
* [[POTE]]: ~2 = 1200.000, ~8/7 = 232.094 | * [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 232.094{{c}} | ||
: error map: {{val| 0.000 -0.574 -1.191 -0.919 }} | : error map: {{val| 0.000 -0.574 -1.191 -0.919 }} | ||
| Line 294: | Line 290: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~8/7 = 232.065 | * CTE: ~2 = 1200.000{{c}}, ~8/7 = 232.065{{c}} | ||
* POTE: ~2 = 1200.000, ~8/7 = 232.083 | * POTE: ~2 = 1200.000{{c}}, ~8/7 = 232.083{{c}} | ||
{{Optimal ET sequence|legend=0| 31, 119, 150, 181, 212, 455ee, 667cdee }} | {{Optimal ET sequence|legend=0| 31, 119, 150, 181, 212, 455ee, 667cdee }} | ||
| Line 313: | Line 309: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~2625/2048 = 425.666 | * [[CTE]]: ~2 = 1200.000{{c}}, ~2625/2048 = 425.666{{c}} | ||
: [[error map]]: {{val| 0.000 -0.278 -1.318 0.177 }} | : [[error map]]: {{val| 0.000 -0.278 -1.318 0.177 }} | ||
* [[POTE]]: ~2 = 1200.000, ~2625/2048 = 425.673 | * [[POTE]]: ~2 = 1200.000{{c}}, ~2625/2048 = 425.673{{c}} | ||
: error map: {{val| 0.000 -0.526 -1.212 0.113 }} | : error map: {{val| 0.000 -0.526 -1.212 0.113 }} | ||
| Line 330: | Line 326: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~2625/2048 = 425.671 | * CTE: ~2 = 1200.000{{c}}, ~2625/2048 = 425.671{{c}} | ||
* POTE: ~2 = 1200.000, ~2625/2048 = 425.679 | * POTE: ~2 = 1200.000{{c}}, ~2625/2048 = 425.679{{c}} | ||
{{Optimal ET sequence|legend=0| 31, 234, 265, 296, 919bc }} | {{Optimal ET sequence|legend=0| 31, 234, 265, 296, 919bc }} | ||
| Line 349: | Line 345: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~405/392 = 54.335 | * [[CTE]]: ~2 = 1200.000{{c}}, ~405/392 = 54.335{{c}} | ||
: [[error map]]: {{val| 0.000 -0.233 -1.338 -0.061 }} | : [[error map]]: {{val| 0.000 -0.233 -1.338 -0.061 }} | ||
* [[POTE]]: ~2 = 1200.000, ~405/392 = 54.324 | * [[POTE]]: ~2 = 1200.000{{c}}, ~405/392 = 54.324{{c}} | ||
: error map: {{val| 0.000 -0.604 -1.178 -0.718 }} | : error map: {{val| 0.000 -0.604 -1.178 -0.718 }} | ||
| Line 366: | Line 362: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~33/32 = 54.338 | * CTE: ~2 = 1200.000{{c}}, ~33/32 = 54.338{{c}} | ||
* POTE: ~2 = 1200.000, ~33/32 = 54.334 | * POTE: ~2 = 1200.000{{c}}, ~33/32 = 54.334{{c}} | ||
{{Optimal ET sequence|legend=0| 22, 221, 243, 265 }} | {{Optimal ET sequence|legend=0| 22, 221, 243, 265 }} | ||
| Line 381: | Line 377: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~405/392 = 54.332 | * CTE: ~2 = 1200.000{{c}}, ~405/392 = 54.332{{c}} | ||
* POTE: ~2 = 1200.000, ~405/392 = 54.316 | * POTE: ~2 = 1200.000{{c}}, ~405/392 = 54.316{{c}} | ||
{{Optimal ET sequence|legend=0| 22, …, 199d, 221e, 243e, 707bcdeee }} | {{Optimal ET sequence|legend=0| 22, …, 199d, 221e, 243e, 707bcdeee }} | ||