Smate family: Difference between revisions
Created page with "The '''smate family''' of temperaments tempers out 2048/1875, the smate comma, resulting in equation of four just major thirds (5/4) with the 8/3|just perfect el..." |
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The '''smate family''' of temperaments tempers out [[2048/1875]], the smate comma, resulting in equation of four [[5/4|just major thirds (5/4)]] with the [[8/3|just perfect eleventh (8/3)]]. It therefore requires an extremely sharp tuning of the just major third. [[17edo]] and [[20edo]] provide it and make for good tunings. | The '''smate family''' of temperaments tempers out [[2048/1875]], the smate comma, resulting in equation of four [[5/4|just major thirds (5/4)]] with the [[8/3|just perfect eleventh (8/3)]]. It therefore requires an extremely sharp tuning of the just major third. [[17edo]] and [[20edo]] provide it and make for good tunings. | ||
= Smate = | == Smate == | ||
[[Comma list]]: 2048/1875 | [[Comma list]]: 2048/1875 | ||
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[[Badness]]: 0.179 | [[Badness]]: 0.179 | ||
= 7-limit = | == 7-limit == | ||
{{see also| Mint temperaments #Smate }} | {{see also| Mint temperaments #Smate }} | ||
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[[Badness]]: 0.0779 | [[Badness]]: 0.0779 | ||
== 11-limit == | === 11-limit === | ||
Comma list: 36/35, 56/55, 243/242 | Comma list: 36/35, 56/55, 243/242 | ||
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Badness: 0.0425 | Badness: 0.0425 | ||
== 13-limit == | === 13-limit === | ||
Comma list: 26/25, 36/35, 56/55, 243/242 | Comma list: 26/25, 36/35, 56/55, 243/242 | ||
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Badness: 0.0368 | Badness: 0.0368 | ||
= Hemismate = | == Hemismate == | ||
[[Comma list]]: 256/245, 392/375 | [[Comma list]]: 256/245, 392/375 | ||
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[[Badness]]: 0.1543 | [[Badness]]: 0.1543 | ||
== 11-limit == | === 11-limit === | ||
Comma list: 56/55, 77/75, 256/245 | Comma list: 56/55, 77/75, 256/245 | ||
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Badness: 0.0655 | Badness: 0.0655 | ||
== 13-limit == | === 13-limit === | ||
Comma list: 26/25, 56/55, 77/75, 256/245 | Comma list: 26/25, 56/55, 77/75, 256/245 | ||