Kleismic family: Difference between revisions
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Obvious 13-limti extensions to catalan and quartkeenlig by 325/324 and 625/624 -> 3 gensteps ~ 26/15 |
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* 7- and 9-odd-limit diamond monotone and tradeoff: ~6/5 = [317.647, 319.265] | * 7- and 9-odd-limit diamond monotone and tradeoff: ~6/5 = [317.647, 319.265] | ||
{{Optimal ET sequence|legend=1| 15, 34d, 49, | {{Optimal ET sequence|legend=1| 15, 34d, 49, 132bcdd, 181bbcddd }} | ||
[[Badness]]: 0.094872 | [[Badness]]: 0.094872 | ||
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* 11-odd-limit diamond monotone and tradeoff: ~6/5 = [317.647, 320.000] | * 11-odd-limit diamond monotone and tradeoff: ~6/5 = [317.647, 320.000] | ||
{{Optimal ET sequence|legend=1| 15, 34d, 49 }} | {{Optimal ET sequence|legend=1| 15, 34d, 49, 181bbcdddeee }} | ||
Badness: 0.036894 | Badness: 0.036894 | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 64/63, 100/99, 144/143, 275/273 | |||
Mapping: {{mapping| 1 0 1 6 4 0 | 0 6 5 -12 -2 14 }} | |||
Optimal tuning (CTE): ~2 = 1\1, ~6/5 = 317.9159 | |||
{{Optimal ET sequence|legend=1| 15, 34d, 49f, 83def, 132bcddeefff }} | |||
Badness: 0.0263 | |||
== Catakleismic == | == Catakleismic == | ||
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[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/56 = 505.705 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/56 = 505.705 | ||
{{Optimal ET sequence|legend=1| 19, 121, 140, 579, 719, 859bcd, 999bcd, 1858bbccdd }} | {{Optimal ET sequence|legend=1| 19, …, 121, 140, 579, 719, 859bcd, 999bcd, 1858bbccdd }} | ||
[[Badness]]: 0.063448 | [[Badness]]: 0.063448 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 505.684 | Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 505.684 | ||
{{Optimal ET sequence|legend=1| 19, 140, 159, 299 }} | {{Optimal ET sequence|legend=1| 19, 121e, 140, 159, 299 }} | ||
Badness: 0.058902 | Badness: 0.058902 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 505.686 | Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 505.686 | ||
{{Optimal ET sequence|legend=1| 19, 140, 159, 299 }} | {{Optimal ET sequence|legend=1| 19, 121e, 140, 159, 299 }} | ||
Badness: 0.030082 | Badness: 0.030082 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 505.740 | Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 505.740 | ||
{{Optimal ET sequence|legend=1| 19e, 121, 140, 261, 401 | {{Optimal ET sequence|legend=1| 19e, …, 121, 140, 261, 401 }} | ||
Badness: 0.061172 | Badness: 0.061172 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 505.740 | Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 505.740 | ||
{{Optimal ET sequence|legend=1| 19e, 121, 140, 261, 401 | {{Optimal ET sequence|legend=1| 19e, …, 121, 140, 261, 401 }} | ||
Badness: 0.028671 | Badness: 0.028671 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 505.771 | Optimal tuning (POTE): ~2 = 1\1, ~75/56 = 505.771 | ||
{{Optimal ET sequence|legend=1| 19, 121 }} | {{Optimal ET sequence|legend=1| 19, 102df, 121 }} | ||
Badness: 0.038317 | Badness: 0.038317 | ||
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[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~56/45 = 379.252 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~56/45 = 379.252 | ||
{{Optimal ET sequence|legend=1| 19, 193, 212, 617c, 829c }} | {{Optimal ET sequence|legend=1| 19, …, 193, 212, 617c, 829c }} | ||
[[Badness]]: 0.104253 | [[Badness]]: 0.104253 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 379.257 | Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 379.257 | ||
{{Optimal ET sequence|legend=1| 19e, 193, 212, 405, 617c, 1022cce }} | {{Optimal ET sequence|legend=1| 19e, …, 193, 212, 405, 617c, 1022cce }} | ||
Badness: 0.075624 | Badness: 0.075624 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 379.256 | Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 379.256 | ||
{{Optimal ET sequence|legend=1| 19e, 193, 212, 405f, 617cff }} | {{Optimal ET sequence|legend=1| 19e, …, 193, 212, 405f, 617cff }} | ||
Badness: 0.043728 | Badness: 0.043728 | ||
== Quartkeenlig == | == Quartkeenlig == | ||
Quartkeenlig uses a generator in the 11-limit that is 33/32~36/35 tempered together, and is called so because it tempers out the [[quartisma]] by virtue of five 33/32's being with 7/6, keenanisma, 385/384, tempering 33/32 and 36/35 together, and liganellus comma (6250/6237). It can also be viewed as a regular temperament interpretation of [[23edo and octave stretching|stretched 23edo]]. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Badness: 0.0865 | Badness: 0.0865 | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 325/324, 385/384, 625/624, 16807/16731 | |||
Mapping: {{mapping| 1 0 1 1 5 0 | 0 36 30 41 -35 84 }} | |||
Optimal tuning (CTE): ~2 = 1\1, ~33/32 = 52.8562 | |||
{{Optimal ET sequence|legend=1| 68, 159, 386d, 545ddf }} | |||
Badness: 0.0477 | |||
== Novemkleismic == | == Novemkleismic == | ||
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Optimal tuning (POTE): ~250/231 = 1\9, ~6/5 = 317.086 | Optimal tuning (POTE): ~250/231 = 1\9, ~6/5 = 317.086 | ||
{{Optimal ET sequence|legend=1| 72, 261, 333, 738cf | {{Optimal ET sequence|legend=1| 72, 189f, 261, 333, 738cf }} | ||
Badness: 0.039072 | Badness: 0.039072 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.585 | Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.585 | ||
{{Optimal ET sequence|legend=1| 72, 121, 193 }} | {{Optimal ET sequence|legend=1| 49f, 72, 121, 193 }} | ||
Badness: 0.020040 | Badness: 0.020040 | ||
| Line 1,065: | Line 1,091: | ||
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.585 | Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.585 | ||
{{Optimal ET sequence|legend=1| 72, 121, 193 }} | {{Optimal ET sequence|legend=1| 49fg, 72, 121, 193 }} | ||
Badness: 0.013028 | Badness: 0.013028 | ||
| Line 1,078: | Line 1,104: | ||
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.580 | Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.580 | ||
{{Optimal ET sequence|legend=1| 72, 121, 193 }} | {{Optimal ET sequence|legend=1| 49fg, 72, 121, 193 }} | ||
Badness: 0.014748 | Badness: 0.014748 | ||