Gamelismic clan: Difference between revisions

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 * ''[[Blacksmith]]'', {28/27, 49/48} → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
 * [[Lemba]], {50/49, 525/512} → [[Jubilismic clan #Lemba|Jubilismic clan]]
-* ''[[Mothra]]'', {81/80, 1029/1024} → [[Meantone family #Mothra|Meantone family]]
 * [[Valentine]], {126/125, 1029/1024} → [[Starling temperaments #Valentine|Starling temperaments]]
 * ''[[Echidnic]]'', {686/675, 1029/1024} → [[Diaschismic family #Echidnic|Diaschismic family]]
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 Badness: 0.028444
+== Mothra ==
+Mothra tempers out [[81/80]] and finds the prime 5 at a stack of four fifths as does any temperament in the [[meantone family]]. It also tempers out [[1728/1715]], the orwellisma. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a mos should be used as a scale to get the most out of mothra.
+Note that mothra is also called '''cynder''' in the 7-limit, which can be a little confusing sometimes.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 81/80, 1029/1024
+{{Mapping|legend=1| 1 1 0 3 | 0 3 12 -1 }}
+: mapping generators: ~2, ~8/7
+{{Multival|legend=1| 3 12 -1 12 -10 -36 }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 232.193
+[[Algebraic generator]]: Rabrindanath, largest real root of ''x''<sup>8</sup> - 3''x''<sup>2</sup> + 1, or 232.0774 cents.
+[[Minimax tuning]]:
+* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 0 0 1/12 }}
+: [{{Monzo| 1 0 0 0 }}, {{monzo| 1 0 1/4 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 3 0 -1/12 0 }}]
+: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5
+{{Optimal ET sequence|legend=1| 5, 26, 31 }}
+[[Badness]]: 0.037146
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 81/80, 99/98, 385/384
+Mapping: {{mapping| 1 1 0 3 5 | 0 3 12 -1 -8 }}
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.031
+{{Optimal ET sequence|legend=1| 5, 26, 31, 88, 150be, 181bee }}
+Badness: 0.025642
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 81/80, 99/98, 105/104, 144/143
+Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 12 -1 -8 14 }}
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 231.811
+{{Optimal ET sequence|legend=1| 5, 26, 31, 57, 88 }}
+Badness: 0.023954
+; Music:
+* [http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 Prelude for solo piano in mothra16, brat 4 tuning] by [http://chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ Chris Vaisvil]
+=== Cynder ===
+Subgroup: 2.3.5.7.11
+Comma list: 45/44, 81/80, 1029/1024
+Mapping: {{mapping| 1 1 0 3 0 | 0 3 12 -1 18 }}
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 231.317
+{{Optimal ET sequence|legend=1| 5e, 26, 57e, 83bce }}
+Badness: 0.055706
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 45/44, 78/77, 81/80, 640/637
+Mapping: {{mapping| 1 1 0 3 0 1 | 0 3 12 -1 18 14 }}
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 231.293
+{{Optimal ET sequence|legend=1| 5e, 26, 57e, 83bce }}
+Badness: 0.034124
+=== Mosura ===
+Subgroup: 2.3.5.7.11
+Comma list: 81/80, 176/175, 540/539
+Mapping: {{mapping| 1 1 0 3 -1 | 0 3 12 -1 23 }}
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.419
+{{Optimal ET sequence|legend=1| 31, 129, 160be, 191bce, 222bce, 253bcee }}
+Badness: 0.031334
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 81/80, 144/143, 176/175, 196/195
+Mapping: {{mapping| 1 1 0 3 -1 7 | 0 3 12 -1 23 -17 }}
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.640
+{{Optimal ET sequence|legend=1| 31, 36, 67, 98 }}
+Badness: 0.036857
 == Gorgo ==