Porwell temperaments: Difference between revisions
→Nessafof: decanonicalize 11-limit; name it *fof* |
Move grendel here cuz mirkwai clan is a no-2 clan, which doesn't explain its structure very well |
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* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth|Escapade family]] | * ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth|Escapade family]] | ||
* ''[[Hemimabila]]'' (+117649/116640) → [[Mabila family #Hemimabila|Mabila family]] | * ''[[Hemimabila]]'' (+117649/116640) → [[Mabila family #Hemimabila|Mabila family]] | ||
* ''[[Countermiracle]]'' (+823543/819200) → [[Quince clan #Countermiracle|Quince clan]] | * ''[[Countermiracle]]'' (+823543/819200) → [[Quince clan #Countermiracle|Quince clan]] | ||
* ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]] | * ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]] | ||
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Badness (Sintel): 2.26 | Badness (Sintel): 2.26 | ||
== Grendel == | |||
: ''For the 5-limit version, see [[Syntonic–31 equivalence continuum #Counterwürschmidt]].'' | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 6144/6125, 16875/16807 | |||
{{Mapping|legend=1| 1 -14 3 -6 | 0 23 -1 13 }} | |||
: mapping generators: ~2, ~8/5 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.7348{{c}}, ~8/5 = 812.9574{{c}} | |||
: [[error map]]: {{val| -0.265 -0.220 -0.067 +1.212 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/5 = 813.1311{{c}} | |||
: error map: {{val| 0.000 +0.059 +0.555 +1.878 }} | |||
{{Optimal ET sequence|legend=1| 31, 90, 121, 152, 335d, 822dd }} | |||
[[Badness]] (Sintel): 1.31 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 540/539, 1375/1372, 5632/5625 | |||
Mapping: {{mapping| 1 -14 3 -6 -25 | 0 23 -1 13 42 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.7355{{c}}, ~8/5 = 812.9622{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 813.1353{{c}} | |||
{{Optimal ET sequence|legend=0| 31, 90e, 121, 152, 335d, 487d }} | |||
Badness (Sintel): 0.656 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 352/351, 540/539, 625/624, 1375/1372 | |||
Mapping: {{mapping| 1 -14 3 -6 -25 22 | 0 23 -1 13 42 -27 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.4412{{c}}, ~8/5 = 812.7956{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 813.1209{{c}} | |||
{{Optimal ET sequence|legend=0| 31, 90e, 121, 152f, 273def, 425deff }} | |||
Badness (Sintel): 1.03 | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274 | |||
Mapping: {{mapping| 1 -14 3 -6 -25 22 19 | 0 23 -1 13 42 -27 -22 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.3029{{c}}, ~8/5 = 812.7156{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 813.1843{{c}} | |||
{{Optimal ET sequence|legend=0| 31, 90e, 121, 152fg, 273defgg }} | |||
Badness (Sintel): 1.09 | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714 | |||
Mapping: {{mapping| 1 -14 3 -6 -25 22 19 30 | 0 23 -1 13 42 -27 -22 -38 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.3587{{c}}, ~8/5 = 812.7462{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 813.1796{{c}} | |||
{{Optimal ET sequence|legend=0| 31, 90e, 121, 152fg, 273defgg }} | |||
Badness (Sintel): 1.12 | |||
== Twothirdtonic == | == Twothirdtonic == | ||