Syntonic–chromatic equivalence continuum: Difference between revisions
m Linking. Clarify. Fix abuse of parentheses |
Review tunings and optimal ET sequences |
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{{Mapping|legend=1| 1 2 2 | 0 -3 2 }} | {{Mapping|legend=1| 1 2 2 | 0 -3 2 }} | ||
[[Optimal tuning]] | : mapping generators: ~2, ~16/15 | ||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~16/15 = 170.6715 | |||
* [[POTE]]: ~2 = 1/1, ~16/15 = 173.101 | |||
{{Optimal ET sequence|legend=1| 6b, 7 }} | {{Optimal ET sequence|legend=1| 6b, 7 }} | ||
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{{See also| Porwell temperaments #Absurdity }} | {{See also| Porwell temperaments #Absurdity }} | ||
Absurdity corresponds to ''n'' = 7, and can be described as the 77 & 84 temperament, so named because it truly is an absurd temperament. The generator is ~81/80 and the period is ~800/729, which is (10/9) / (81/80). | Absurdity corresponds to ''n'' = 7, and can be described as the 77 & 84 temperament, so named because it truly is an absurd temperament. The generator is ~81/80 and the period is ~800/729, which is (10/9)/(81/80). | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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: mapping generators: ~800/729, ~3 | : mapping generators: ~800/729, ~3 | ||
[[Optimal tuning]] ([[POTE]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~800/729 = 1\7, ~3/2 = 700.5378 (~81/80 = 14.8235) | |||
* [[POTE]]: ~800/729 = 1\7, ~3/2 = 700.1870 (~81/80 = 14.4727) | |||
{{Optimal ET sequence|legend=1| 7, 70, 77, 84, 329 }} | {{Optimal ET sequence|legend=1| 7, …, 70, 77, 84, 329, 413b, 497b }} | ||
[[Badness]]: 0.341202 | [[Badness]]: 0.341202 | ||
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: mapping generators: ~2, ~400/243 | : mapping generators: ~2, ~400/243 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1\1, ~400/243 = 855.2127 | |||
* [[CWE]]: ~2 = 1\1, ~400/243 = 855.1959 | |||
{{Optimal ET sequence|legend=1| 7, … 73, 80, 87 }} | {{Optimal ET sequence|legend=1| 7, … 73, 80, 87 }} | ||
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{{Mapping|legend=1| 7 0 -6 | 0 1 2 }} | {{Mapping|legend=1| 7 0 -6 | 0 1 2 }} | ||
[[Optimal tuning]] ([[POTE]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~10/9 = 1\7, ~3/2 = 705.5264 (~250/243 = 19.8121) | |||
* [[POTE]]: ~10/9 = 1\7, ~3/2 = 706.288 (~250/243 = 20.574) | |||
{{Optimal ET sequence|legend=1| 7, 42, 49, 56, 119 }} | {{Optimal ET sequence|legend=1| 7, 42, 49, 56, 119 }} | ||
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{{Mapping|legend=1| 7 0 5 | 0 1 1 }} | {{Mapping|legend=1| 7 0 5 | 0 1 1 }} | ||
[[Optimal tuning]] ([[POTE]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~125/108 = 1\7, ~3/2 = 710.6056 (~25/24 = 24.8913) | |||
* [[POTE]]: ~125/108 = 1\7, ~3/2 = 706.410 (~25/24 = 20.696) | |||
{{Optimal ET sequence|legend=1| 7, 35b, 42c | {{Optimal ET sequence|legend=1| 7, 35b, 42c }} | ||
[[Badness]]: 0.4377 | [[Badness]]: 0.4377 | ||
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: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2/1 = 1\1, ~3/2 = 689.8791 | |||
* [[CWE]]: ~2/1 = 1\1, ~3/2 = 689.3122 | |||
{{Optimal ET sequence|legend=1| 7, 33, 40, 47, 54b }} | {{Optimal ET sequence|legend=1| 7, 33, 40, 47, 54b }} | ||
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: mapping generators: ~2, ~2560/2187 | : mapping generators: ~2, ~2560/2187 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1\1, ~2560/2187 = 345.9462 | |||
* [[CWE]]: ~2 = 1\1, ~2560/2187 = 345.5992 | |||
{{Optimal ET sequence|legend=1| 7, 38c, 45c, 52, 59b, 66b }} | {{Optimal ET sequence|legend=1| 7, 38c, 45c, 52, 59b, 66b }} | ||
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: mapping generators: ~2, ~729/640 | : mapping generators: ~2, ~729/640 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1\1, ~729/640 = 168.9826 | |||
* [[CWE]]: ~2 = 1\1, ~729/640 = 169.2234 | |||
{{Optimal ET sequence|legend=1| 7, 57c, 64, 71b, 78b, 85b }} | {{Optimal ET sequence|legend=1| 7, 57c, 64, 71b, 78b, 85b }} | ||