Quinticular comma: Difference between revisions
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Quintic-particular is an idiosyncratic term Tags: Mobile edit Mobile web edit |
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The '''quinticular comma''' is a 2.3.17 [[subgroup]] comma of measuring 3.27 [[cent]]s, with frequency ratio of 1419857/1417176. It forms the difference between five semitones of [[18/17]] and a perfect fourth, [[4/3]]. It is a quintic-particular interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)). | The '''quinticular comma''' is a 2.3.17 [[subgroup]] comma of measuring 3.27 [[cent]]s, with frequency ratio of 1419857/1417176. It forms the difference between five semitones of [[18/17]] and a perfect fourth, [[4/3]]. It is a quintic-particular{{idiosyncratic}} interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)). | ||
== Temperaments == | == Temperaments == | ||
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| 12''n''+11 ||{{Optimal ET sequence|2507, 2519, 2531, 2543, 2555}} | | 12''n''+11 ||{{Optimal ET sequence|2507, 2519, 2531, 2543, 2555}} | ||
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=== Quinticular === | |||
[[Subgroup]]: 2.3.17 | |||
[[Mapping]]: {{mapping|1 2 5|0 -5 -11}} | |||
: Mapping generators: ~2, ~18/17 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~18/17 = 99.5839 | |||
{{Optimal ET sequence|legend=1|12, 133, 145, 157, 169, 181, 193, 205, 217, 229, 241, 735, 976, 1217, 1458g}} | |||
[[Badness]]: 0.002442 | |||
== Etymology == | == Etymology == | ||