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| Line 53: |
Line 53: |
| * ''[[Plutus]]'' → [[Very low accuracy temperaments #Plutus|Very low accuracy temperaments]] | | * ''[[Plutus]]'' → [[Very low accuracy temperaments #Plutus|Very low accuracy temperaments]] |
| * [[Godzilla]] → [[Slendro clan #Godzilla|Slendro clan]] | | * [[Godzilla]] → [[Slendro clan #Godzilla|Slendro clan]] |
| | * [[Mothra]] → [[Gamelismic clan #Mothra|Gamelismic clan]] |
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| The rest are considered below. | | The rest are considered below. |
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| Scales: [[mohaha7]], [[mohaha10]] | | Scales: [[mohaha7]], [[mohaha10]] |
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| == Mothra ==
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| {{See also| Gamelismic clan }}
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| Mothra splits the fifth into three ~8/7 generators. It uses [[1029/1024]], the gamelisma, to accomplish this deed and also tempers out [[1728/1715]], the orwell comma. 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. In the 2.3.7 subgroup, mothra is identical to [[slendric]].
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| Note that mothra is also called '''cynder''' in the 7-limit, which can be a little confusing sometimes.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 81/80, 1029/1024
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| [[Mapping]]: [{{val| 1 1 0 3 }}, {{val| 0 3 12 -1 }}]
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| : mapping generators: ~2, ~8/7
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| {{Multival|legend=1| 3 12 -1 12 -10 -36 }}
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 232.193
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| [[Algebraic generator]]: Rabrindanath, largest real root of ''x''<sup>8</sup> - 3''x''<sup>2</sup> + 1, or 232.0774 cents.
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| [[Minimax tuning]]:
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| * [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 0 0 1/12 }}
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| : [{{Monzo| 1 0 0 0 }}, {{monzo| 1 0 1/4 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 3 0 -1/12 0 }}]
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| : [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5
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| {{Optimal ET sequence|legend=1| 5, 26, 31 }}
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| [[Badness]]: 0.037146
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 81/80, 99/98, 385/384
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| Mapping: [{{val| 1 1 0 3 5 }}, {{val| 0 3 12 -1 -8 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.031
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| {{Optimal ET sequence|legend=1| 5, 26, 31, 88, 150be, 181bee }}
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| Badness: 0.025642
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 81/80, 99/98, 105/104, 144/143
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| Mapping: [{{val| 1 1 0 3 5 1 }}, {{val| 0 3 12 -1 -8 14 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 231.811
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| {{Optimal ET sequence|legend=1| 5, 26, 31, 57, 88 }}
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| Badness: 0.023954
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| ; Music:
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| * [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]
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| === Cynder ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 45/44, 81/80, 1029/1024
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| Mapping: [{{val| 1 1 0 3 0 }}, {{val| 0 3 12 -1 18 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 231.317
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| {{Optimal ET sequence|legend=1| 5e, 26, 57e, 83bce }}
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| Badness: 0.055706
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 45/44, 78/77, 81/80, 640/637
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| Mapping: [{{val| 1 1 0 3 0 1 }}, {{val| 0 3 12 -1 18 14 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 231.293
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| {{Optimal ET sequence|legend=1| 5e, 26, 57e, 83bce }}
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| Badness: 0.034124
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| === Mosura ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 81/80, 176/175, 540/539
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| Mapping: [{{val| 1 1 0 3 -1 }}, {{val| 0 3 12 -1 23 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.419
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| {{Optimal ET sequence|legend=1| 31, 129, 160be, 191bce, 222bce, 253bcee }}
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| Badness: 0.031334
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 81/80, 144/143, 176/175, 196/195
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| Mapping: [{{val| 1 1 0 3 -1 7 }}, {{val| 0 3 12 -1 23 -17 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.640
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| {{Optimal ET sequence|legend=1| 31, 36, 67, 98 }}
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| Badness: 0.036857
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| == Liese == | | == Liese == |