Quince clan: Difference between revisions
m Text replacement - "Category:Temperament clans↵Category:Pages with mostly numerical content" to "Category:Temperament clans" Tags: Manual revert Mobile edit Mobile web edit |
added countermiracle, which is the alternative mapping of 3 for quince on the other side of 31edo |
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* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]] | * ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]] | ||
* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum|Garischismic clan]] | * [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum|Garischismic clan]] | ||
== Mercy == | == Mercy == | ||
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{{Optimal ET sequence|legend=1| 10, 21, 31, 52f }} | {{Optimal ET sequence|legend=1| 10, 21, 31, 52f }} | ||
== Countermiracle == | |||
The ''countermiracle'' temperament (31 & 145) tempers out the trimyna, 50421/50000 and the [[quince comma]], 823543/819200. | |||
{{todo|inline=1|explain relationship to miracle|comment=There's clearly ''some'' relationship, since the extensions are named the same way, but the nature of that relationship isn't obvious from looking at this page.}} | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 6144/6125, 50421/50000 | |||
{{Mapping|legend=1| 1 4 3 3 | 0 -25 -7 -2 }} | |||
: Mapping generators: ~2, ~343/320 | |||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/320 = 115.9169 | |||
{{Optimal ET sequence|legend=1| 31, 114, 145, 176, 559cc, 735cc }} | |||
[[Badness]]: 0.102326 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 441/440, 3388/3375, 6144/6125 | |||
Mapping: {{mapping| 1 4 3 3 8 | 0 -25 -7 -2 -47 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9158 | |||
{{Optimal ET sequence|legend=1| 31, 114e, 145, 176 }} | |||
Badness: 0.039162 | |||
==== Countermiraculous ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 196/195, 352/351, 1001/1000, 6144/6125 | |||
Mapping: {{mapping| 1 4 3 3 8 1 | 0 -25 -7 -2 -47 28 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8803 | |||
{{Optimal ET sequence|legend=1| 31, 83e, 114e, 145, 321ceff }} | |||
Badness: 0.039271 | |||
===== 17-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 196/195, 256/255, 352/351, 1001/1000, 1225/1224 | |||
Mapping: {{mapping| 1 4 3 3 8 1 1 | 0 -25 -7 -2 -47 28 32 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8756 | |||
{{Optimal ET sequence|legend=1| 31, 83e, 114e, 145 }} | |||
Badness: 0.029496 | |||
==== Counterbenediction ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 441/440, 3146/3125, 3584/3575 | |||
Mapping: {{mapping| 1 4 3 3 8 -2 | 0 -25 -7 -2 -47 59 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9335 | |||
{{Optimal ET sequence|legend=1| 31, 114ef, 145f, 176, 207, 383c, 590cc }} | |||
Badness: 0.045569 | |||
===== 17-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 351/350, 441/440, 561/560, 1632/1625, 3146/3125 | |||
Mapping: {{mapping| 1 4 3 3 8 -2 -2 | 0 -25 -7 -2 -47 59 63 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9391 | |||
{{Optimal ET sequence|legend=1| 31, 114efg, 145fg, 176, 207 }} | |||
Badness: 0.036289 | |||
==== Countermanna ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 364/363, 441/440, 3388/3375, 6144/6125 | |||
Mapping: {{mapping| 1 4 3 3 8 15 | 0 -25 -7 -2 -47 -117 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8898 | |||
{{Optimal ET sequence|legend=1| 145, 176, 321ce }} | |||
Badness: 0.053409 | |||
===== 17-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 364/363, 441/440, 595/594, 1632/1625, 3388/3375 | |||
Mapping: {{mapping| 1 4 3 3 8 15 15 | 0 -25 -7 -2 -47 -117 -113 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8832 | |||
{{Optimal ET sequence|legend=1| 145, 321ce }} | |||
Badness: 0.040898 | |||
=== Counterrevelation === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 121/120, 176/175, 50421/50000 | |||
Mapping: {{mapping| 1 4 3 3 5 | 0 -25 -7 -2 -16 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~343/320 = 115.9192 | |||
{{Optimal ET sequence|legend=1| 31, 114, 145e, 176e }} | |||
Badness: 0.064070 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 121/120, 176/175, 196/195, 13750/13689 | |||
Mapping: {{mapping| 1 4 3 3 5 1 | 0 -25 -7 -2 -16 28 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~273/256 = 115.8624 | |||
{{Optimal ET sequence|legend=1| 31, 83, 114, 145e }} | |||
Badness: 0.057497 | |||
==== 17-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 121/120, 154/153, 176/175, 196/195, 10647/10625 | |||
Mapping: {{mapping| 1 4 3 3 5 1 1 | 0 -25 -7 -2 -16 28 32 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~91/85 = 115.8527 | |||
{{Optimal ET sequence|legend=1| 31, 83, 114, 145e }} | |||
Badness: 0.044043 | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||