Magic family: Difference between revisions
Restore some info from the previous edit. Some of these are specific to 5-limit magic so they belong to that section. |
-diamond monotone and tradeoff range (trivial and lack of significance) |
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* 5-odd-limit [[diamond monotone]]: ~5/4 = [360.000, 400.000] (3\10 to 1\3) | * 5-odd-limit [[diamond monotone]]: ~5/4 = [360.000, 400.000] (3\10 to 1\3) | ||
* 5-odd-limit [[diamond tradeoff]]: ~5/4 = [378.910, 386.314] (1/4-comma to untempered) | * 5-odd-limit [[diamond tradeoff]]: ~5/4 = [378.910, 386.314] (1/4-comma to untempered) | ||
[[Algebraic generator]]: Terzbirat, the positive root of 9''x''<sup>2</sup> - 8''x'' - 4 = (4 + 2√13)/9; approximately 380.3175 [[cent]]s. | [[Algebraic generator]]: Terzbirat, the positive root of 9''x''<sup>2</sup> - 8''x'' - 4 = (4 + 2√13)/9; approximately 380.3175 [[cent]]s. | ||
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* 7- and 9-odd-limit [[diamond monotone]]: ~5/4 = [378.947, 381.818] (6\19 to 7\22) | * 7- and 9-odd-limit [[diamond monotone]]: ~5/4 = [378.947, 381.818] (6\19 to 7\22) | ||
* 7- and 9-odd-limit [[diamond tradeoff]]: ~5/4 = [378.910, 386.314] (1/4-comma to untempered) | * 7- and 9-odd-limit [[diamond tradeoff]]: ~5/4 = [378.910, 386.314] (1/4-comma to untempered) | ||
[[Algebraic generator]]: Tirzbirat or Septimage, the real root of 5''x''<sup>5</sup> + 4''x'' - 20, 380.7604 cents. | [[Algebraic generator]]: Tirzbirat or Septimage, the real root of 5''x''<sup>5</sup> + 4''x'' - 20, 380.7604 cents. | ||
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* 11-odd-limit diamond monotone: ~5/4 = [378.947, 381.818] (6\19 to 7\22) | * 11-odd-limit diamond monotone: ~5/4 = [378.947, 381.818] (6\19 to 7\22) | ||
* 11-odd-limit diamond tradeoff: ~5/4 = [378.910, 386.314] (1/4-comma to untempered) | * 11-odd-limit diamond tradeoff: ~5/4 = [378.910, 386.314] (1/4-comma to untempered) | ||
Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41, 104, 145c, 249cce }} | Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41, 104, 145c, 249cce }} | ||
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* 13- and 15-odd-limit diamond monotone: ~5/4 = [378.947, 381.818] (6\19 to 7\22) | * 13- and 15-odd-limit diamond monotone: ~5/4 = [378.947, 381.818] (6\19 to 7\22) | ||
* 13- and 15-odd-limit diamond tradeoff: ~5/4 = [378.617, 386.314] | * 13- and 15-odd-limit diamond tradeoff: ~5/4 = [378.617, 386.314] | ||
Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }} | Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }} | ||
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===== Evening ===== | ===== Evening ===== | ||
Evening is a remarkable subgroup temperament of 19 & 41 with prime harmonics of 29 and 31. | |||
Subgroup: 2.3.5.7.11.13.29.31 | Subgroup: 2.3.5.7.11.13.29.31 | ||
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* [[9-odd-limit]] diamond monotone: ~5/4 = 378.947 (6\19) | * [[9-odd-limit]] diamond monotone: ~5/4 = 378.947 (6\19) | ||
* 7- and 9-odd-limit [[diamond tradeoff]]: ~5/4 = [375.882, 386.314] | * 7- and 9-odd-limit [[diamond tradeoff]]: ~5/4 = [375.882, 386.314] | ||
{{Optimal ET sequence|legend=1| 16, 19, 73bcd, 92bcdd, 111bcddd }} | {{Optimal ET sequence|legend=1| 16, 19, 73bcd, 92bcdd, 111bcddd }} | ||
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* 11-odd-limit diamond monotone: ~5/4 = 378.947 (6\19) | * 11-odd-limit diamond monotone: ~5/4 = 378.947 (6\19) | ||
* 11-odd-limit diamond tradeoff: ~5/4 = [347.408, 386.314] | * 11-odd-limit diamond tradeoff: ~5/4 = [347.408, 386.314] | ||
Optimal ET sequence: {{Optimal ET sequence| 16, 19, 54bd }} | Optimal ET sequence: {{Optimal ET sequence| 16, 19, 54bd }} | ||
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== Darkstone == | == Darkstone == | ||
Darkstone (16 & 19d) is a low-accuacy temperament which tempers out 36/35 and 1875/1792. It makes the major third and the fifth even flatter than those of muggles. In [http://www.tonalsoft.com/enc/m/magic.aspx ''Encyclopedia of Microtonal Music Theory'', Tonalsoft], this temperament is given a name ''witch''. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||