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| * Squares adds {{monzo| -3 9 0 -4 }} with a ~9/7 generator, four of which give the [[8/3|eleventh]]. | | * Squares adds {{monzo| -3 9 0 -4 }} with a ~9/7 generator, four of which give the [[8/3|eleventh]]. |
| * Jerome adds {{monzo| 3 7 0 -5 }} and slices the fifth in five. | | * Jerome adds {{monzo| 3 7 0 -5 }} and slices the fifth in five. |
| Temperaments discussed elsewhere include [[Very low accuracy temperaments #Plutus|plutus]]. | | |
| | Temperaments discussed elsewhere include |
| | * ''[[Plutus]]'' → [[Very low accuracy temperaments #Plutus|Very low accuracy temperaments]] |
| | * [[Godzilla]] → [[Slendro clan #Godzilla|Slendro clan]] |
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| | The rest are considered below. |
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| === Mohaha === | | === Mohaha === |
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| == Dominant == | | == Dominant == |
| | {{See also| Archytas clan }} |
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| The interval class for 7 is obtained from two fourths in succession, so that 7/4 is a minor seventh. The 7/6 interval is, like 6/5, now a minor third, and 7/5 is a diminished fifth. An excellent tuning for dominant is [[12edo]], but it also works well with the Pythagorean tuning of pure [[3/2]] fifths, and with [[29edo]], [[41edo]], or [[53edo]]. | | The interval class for 7 is obtained from two fourths in succession, so that 7/4 is a minor seventh. The 7/6 interval is, like 6/5, now a minor third, and 7/5 is a diminished fifth. An excellent tuning for dominant is [[12edo]], but it also works well with the Pythagorean tuning of pure [[3/2]] fifths, and with [[29edo]], [[41edo]], or [[53edo]]. |
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| Badness: 0.040324 | | Badness: 0.040324 |
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| == Godzilla ==
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| <span style="display: block; text-align: right;">[[:de:Semiphor, Semaphor, Godzilla|Deutsch]]</span>
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| {{Main| Semaphore and godzilla }}
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| {{See also| Slendro clan }}
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| Godzilla tempers out [[49/48]], equating 8/7 with 7/6. Two of the step-and-a-quarter intervals these represent give a fourth, and so step-and-a-quarter generators generate godzilla. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. [[MOS scale]]s are of 5, 9, or 14 notes.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 49/48, 81/80
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| [[Mapping]]: [{{val| 1 0 -4 2 }}, {{val| 0 2 8 1 }}]
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| : mapping generators: ~2, ~7/4
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| {{Multival|legend=1| 2 8 1 8 -4 -20 }}
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 252.635
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| [[Tuning ranges]]:
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| * 7- and 9-odd-limit [[diamond monotone]]: ~7/6 = [240.000, 257.143] (1\5 to 3\14)
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| * 7- and 9-odd-limit [[diamond tradeoff]]: ~7/6 = [231.174, 266.871]
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| * 7- and 9-odd-limit diamond monotone and tradeoff: ~7/6 = [240.000, 257.143]
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| {{Optimal ET sequence|legend=1| 5, 14c, 19 }}
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| [[Badness]]: 0.026747
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 45/44, 49/48, 81/80
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| Mapping: [{{val| 1 0 -4 2 -6 }}, {{val| 0 2 8 1 12 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 254.027
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| Tuning ranges:
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| * 11-odd-limit diamond monotone: ~7/6 = [252.632, 257.143] (4\19 to 3\14)
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| * 11-odd-limit diamond tradeoff: ~7/6 = [231.174, 266.871]
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| * 11-odd-limit diamond monotone and tradeoff: ~7/6 = [252.632, 257.143]
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| {{Optimal ET sequence|legend=1| 14c, 19, 33cd, 52cd }}
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| Badness: 0.028947
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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, 49/48, 78/77, 81/80
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| Mapping: [{{val| 1 0 -4 2 -6 -5 }}, {{val| 0 2 8 1 12 11 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 253.603
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| Tuning ranges:
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| * 13- and 15-odd-limit diamond monotone: ~7/6 = 252.632 (4\19)
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| * 13- and 15-odd-limit diamond tradeoff: ~7/6 = [231.174, 289.210]
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| * 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = 252.632
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| {{Optimal ET sequence|legend=1| 14cf, 19, 33cdff, 52cdff }}
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| Badness: 0.022503
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| === Semafour ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 33/32, 49/48, 55/54
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| Mapping: [{{val| 1 0 -4 2 5 }}, {{val| 0 2 8 1 -2 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 254.042
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| {{Optimal ET sequence|legend=1| 14c, 19e, 33cdee }}
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| Badness: 0.028510
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| === Varan ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 49/48, 77/75, 81/80
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| Mapping: [{{val| 1 0 -4 2 -10 }}, {{val| 0 2 8 1 17 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 251.079
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| {{Optimal ET sequence|legend=1| 19e, 24, 43de }}
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| Badness: 0.039647
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 49/48, 66/65, 77/75, 81/80
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| Mapping: [{{val| 1 0 -4 2 -10 -5 }}, {{val| 0 2 8 1 17 11 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 251.165
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| {{Optimal ET sequence|legend=1| 19e, 24, 43de }}
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| Badness: 0.025676
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| === Baragon ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 49/48, 56/55, 81/80
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| Mapping: [{{val| 1 0 -4 2 9 }}, {{val| 0 2 8 1 -7 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 251.173
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| {{Optimal ET sequence|legend=1| 5, 14ce, 19, 24, 43d }}
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| Badness: 0.035673
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 49/48, 56/55, 81/80, 91/90
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| Mapping: [{{val| 1 0 -4 2 9 -5 }}, {{val| 0 2 8 1 -7 11 }}]
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| Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 251.198
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| {{Optimal ET sequence|legend=1| 5, 14cef, 19, 24, 43d }}
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| Badness: 0.026703
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| == Mohajira == | | == Mohajira == |