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Semicomma family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (2/2)
Line 240: Line 240:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~75/64 = 271.622{{c}}
* [[WE]]: ~2 = 1200.3056{{c}}, ~75/64 = 271.6760{{c}}
: [[error map]]: {{val| +0.306 -0.223 -0.425 +0.049 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~75/64 = 271.6110{{c}}
: error map: {{val| 0.000 -0.678 -1.147 -0.558 }}
<!-- * [[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{{c}}, ~75/64 = 271.607{{c}}
* [[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 }} -->


{{Optimal ET sequence|legend=1| 53, 137d, 190, 243, 1511bccd }}
{{Optimal ET sequence|legend=1| 53, 137d, 190, 243, 1511bccd }}


[[Badness]] (Smith): 0.088355
[[Badness]] (Sintel): 2.24


== Triwell ==
== Triwell ==
Line 256: Line 260:
[[Comma list]]: 1029/1024, 235298/234375
[[Comma list]]: 1029/1024, 235298/234375


{{Mapping|legend=1| 1 7 0 1 | 0 -21 9 7 }}
{{Mapping|legend=1| 1 -14 9 8 | 0 21 -9 -7 }}
: mapping generators: ~2, ~448/375
: mapping generators: ~2, ~375/224


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~448/375 = 309.456{{c}}
* [[WE]]: ~2 = 1200.4763{{c}}, ~375/224 = 890.8812{{c}}
: [[error map]]: {{val| +0.476 -0.118 +0.042 -1.184 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/224 = 890.5312{{c}}
: error map: {{val| 0.000 -0.799 -1.095 -2.545 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~375/224 = 890.544{{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{{c}}, ~448/375 = 309.472{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~375/224 = 890.528{{c}}
: error map: {{val| 0.000 -0.872 -1.063 -2.520 }}
: error map: {{val| 0.000 -0.872 -1.063 -2.520 }} -->


{{Optimal ET sequence|legend=1| 31, 97, 128, 159, 190 }}
{{Optimal ET sequence|legend=1| 31, 97, 128, 159, 190 }}


[[Badness]] (Smith): 0.080575
[[Badness]] (Sintel): 2.04


=== 11-limit ===
=== 11-limit ===
Line 274: Line 282:
Comma list: 385/384, 441/440, 456533/455625
Comma list: 385/384, 441/440, 456533/455625


Mapping: {{mapping| 1 7 0 1 13 | 0 -21 9 7 -37 }}
Mapping: {{mapping| 1 -14 9 8 -24 | 0 21 -9 -7 37 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~448/375 = 309.444{{c}}
* WE: ~2 = 1200.4804{{c}}, ~375/224 = 890.8854{{c}}
* POTE: ~2 = 1200.000{{c}}, ~448/375 = 309.471{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~375/224 = 890.5344{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~375/224 = 890.556{{c}}
* POTE: ~2 = 1200.000{{c}}, ~375/224 = 890.529{{c}} -->


{{Optimal ET sequence|legend=0| 31, 97, 128, 159, 190 }}
{{Optimal ET sequence|legend=0| 31, 97, 128, 159, 190 }}


Badness (Smith): 0.029807
Badness (Sintel): 0.985


== Quadrawell ==
== Quadrawell ==
Line 291: Line 301:
[[Comma list]]: 2401/2400, 2109375/2097152
[[Comma list]]: 2401/2400, 2109375/2097152


{{Mapping|legend=1| 1 7 0 3 | 0 -28 12 -1 }}
{{Mapping|legend=1| 1 -21 12 2 | 0 28 -12 1 }}
: mapping generators: ~2, ~8/7
: mapping generators: ~2, ~7/4


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 232.082{{c}}
* [[WE]]: ~2 = 1200.3006{{c}}, ~7/4 = 968.1489{{c}}
: [[error map]]: {{val| +0.301 -0.098 -0.493 -0.076 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 967.9090{{c}}
: error map: {{val| 0.000 -0.503 -1.222 -0.917 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~7/4 = 967.918{{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{{c}}, ~8/7 = 232.094{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/4 = 967.906{{c}}
: error map: {{val| 0.000 -0.574 -1.191 -0.919 }}
: error map: {{val| 0.000 -0.574 -1.191 -0.919 }} -->


{{Optimal ET sequence|legend=1| 31, 119, 150, 181, 212, 243, 698cd, 941cd }}
{{Optimal ET sequence|legend=1| 31, 119, 150, 181, 212, 243, 698cd, 941cd }}


[[Badness]] (Smith): 0.075754
[[Badness]] (Sintel): 1.92


=== 11-limit ===
=== 11-limit ===
Line 309: Line 323:
Comma list: 385/384, 1375/1372, 14641/14580
Comma list: 385/384, 1375/1372, 14641/14580


Mapping: {{mapping| 1 7 0 3 11 | 0 -28 12 -1 -39 }}
Mapping: {{mapping| 1 -21 12 2 -28 | 0 28 -12 1 39 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 232.065{{c}}
* WE: ~2 = 1200.3622{{c}}, ~7/4 = 968.2089{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 232.083{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 967.9206{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~7/4 = 967.935{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 967.917{{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 }}


Badness (Smith): 0.036493
Badness (Sintel): 1.21


== Rainwell ==
== Rainwell ==
Line 326: Line 342:
[[Comma list]]: 16875/16807, 2100875/2097152
[[Comma list]]: 16875/16807, 2100875/2097152


{{Mapping|legend=1| 1 14 -3 6 | 0 -35 15 -9 }}
{{Mapping|legend=1| 1 -21 12 -3 | 0 35 -15 9 }}


: mapping generators: ~2, ~2625/2048
: mapping generators: ~2, ~2625/2048


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~2625/2048 = 425.666{{c}}
* [[WE]]: ~2 = 1200.2032{{c}}, ~2401/1536 = 774.4577{{c}}
: [[error map]]: {{val| +0.203 -0.204 -0.740 +0.683 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~2401/1536 = 774.3282{{c}}
: error map: {{val| 0.000 -0.469 -1.236 +0.128 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~2401/1536 = 774.334{{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{{c}}, ~2625/2048 = 425.673{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~2401/1536 = 774.327{{c}}
: error map: {{val| 0.000 -0.526 -1.212 0.113 }}
: error map: {{val| 0.000 -0.526 -1.212 0.113 }} -->


{{Optimal ET sequence|legend=1| 31, 172, 203, 234, 265, 296 }}
{{Optimal ET sequence|legend=1| 31, 172, 203, 234, 265, 296 }}


[[Badness]] (Smith): 0.143488
[[Badness]] (Sintel): 3.63


=== 11-limit ===
=== 11-limit ===
Line 345: Line 365:
Comma list: 540/539, 1375/1372, 2100875/2097152
Comma list: 540/539, 1375/1372, 2100875/2097152


Mapping: {{mapping| 1 14 -3 6 29 | 0 -35 15 -9 -72 }}
Mapping: {{mapping| 1 -21 12 -3 -43 | 0 35 -15 9 72 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~2625/2048 = 425.671{{c}}
* WE: ~2 = 1200.1915{{c}}, ~2205/1408 = 774.4451{{c}}
* POTE: ~2 = 1200.000{{c}}, ~2625/2048 = 425.679{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~2205/1408 = 774.3233{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~2205/1408 = 774.329{{c}}
* POTE: ~2 = 1200.000{{c}}, ~2205/1408 = 774.321{{c}} -->


{{Optimal ET sequence|legend=0| 31, 234, 265, 296, 919bc }}
{{Optimal ET sequence|legend=0| 31, 234, 265, 296, 919bc }}


Badness (Smith): 0.052774
Badness (Sintel): 1.74


== Quinwell ==
== Quinwell ==
Line 363: Line 385:


{{Mapping|legend=1| 1 0 3 0 | 0 35 -15 62 }}
{{Mapping|legend=1| 1 0 3 0 | 0 35 -15 62 }}
: mapping generators: ~2, ~405/392
: mapping generators: ~2, ~405/392


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~405/392 = 54.335{{c}}
* [[WE]]: ~2 = 1200.2860{{c}}, ~405/392 = 54.3373{{c}}
: [[error map]]: {{val| +0.286 -0.151 -0.515 +0.084 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~405/392 = 54.3273{{c}}
: error map: {{val| 0.000 -0.501 -1.223 -0.536 }}
<!-- * [[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{{c}}, ~405/392 = 54.324{{c}}
* [[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 }} -->


{{Optimal ET sequence|legend=1| 22, …, 199d, 221, 243, 751c, 994cd, 1237bccd, 1480bccd }}
{{Optimal ET sequence|legend=1| 22, …, 199d, 221, 243, 751c, 994cd, 1237bccd, 1480bccd }}


[[Badness]] (Smith): 0.168897
[[Badness]] (Sintel): 4.27


=== 11-limit ===
=== 11-limit ===
Line 384: Line 409:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~33/32 = 54.338{{c}}
* WE: ~2 = 1200.0642{{c}}, ~33/32 = 54.3395{{c}}
* POTE: ~2 = 1200.000{{c}}, ~33/32 = 54.334{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 54.3369{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~33/32 = 54.338{{c}}
* 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 }}


Badness (Smith): 0.097202
Badness (Sintel): 3.21


=== Quinbetter ===
=== Quinbetter ===
Line 399: Line 426:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~405/392 = 54.332{{c}}
* WE: ~2 = 1200.0642{{c}}, ~405/392 = 54.3373{{c}}
* POTE: ~2 = 1200.000{{c}}, ~405/392 = 54.316{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~405/392 = 54.3192{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~405/392 = 54.332{{c}}
* 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 }}


Badness (Smith): 0.078657
Badness (Sintel): 2.60


[[Category:Temperament families]]
[[Category:Temperament families]]
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