Undim family: Difference between revisions
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→Septimal undim: +intro to note its utility |
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== Septimal undim == | == Septimal undim == | ||
Septimal undim tempers out the [[dimcomp comma]], mapping ~25/21 to the 1/4-octave period. It can be described as 12 & 140, and is the unique temperament that equates a syntonic~septimal comma with a stack of three [[marvel comma]]s. A [[Pythagorean comma]] is then found as a stack of four marvel commas. In some 7-limit adaptive-tuning practice, the marvel comma corresponds to a melodic unit called a [[kleisma]], with three kleismas making a comma, so this temperament may be useful for modeling that. [[292edo]] makes for an excellent tuning. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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{{Multival|legend=1| 4 -20 -44 -41 -81 -46 }} | {{Multival|legend=1| 4 -20 -44 -41 -81 -46 }} | ||
[[Optimal tuning]] ([[POTE]]): ~25/21 = | [[Optimal tuning]] ([[POTE]]): ~25/21 = 300.000, ~3/2 = 702.7362 | ||
{{Optimal ET sequence|legend=1| 140, 152, 292 }} | {{Optimal ET sequence|legend=1| 140, 152, 292 }} | ||
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Mapping: {{mapping| 4 0 41 81 128 | 0 1 -5 -11 -18 }} | Mapping: {{mapping| 4 0 41 81 128 | 0 1 -5 -11 -18 }} | ||
Optimal tuning (POTE): ~25/21 = | Optimal tuning (POTE): ~25/21 = 300.000, ~3/2 = 702.6886 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 140, 152, 292, 444d, 596d }} | ||
Badness: 0.034837 | Badness: 0.034837 | ||
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Mapping: {{mapping| 4 0 41 81 128 148 | 0 1 -5 -11 -18 -21 }} | Mapping: {{mapping| 4 0 41 81 128 148 | 0 1 -5 -11 -18 -21 }} | ||
Optimal tuning (POTE): ~25/21 = | Optimal tuning (POTE): ~25/21 = 300.000, ~3/2 = 702.7363 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 140, 152f, 292 }} | ||
Badness: 0.028172 | Badness: 0.028172 | ||