552edo: Difference between revisions
Notable as a 2.3.5.7.11.13.19 subgroup temp |
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== Theory == | == Theory == | ||
552edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. The equal temperament [[tempering out|tempers out]] {{monzo| 8 14 -3 }} ([[parakleisma]]) in the 5-limit; 250047/250000 ([[landscape comma]]), 589824/588245 ([[hewuermera comma]]), 26873856/26796875, and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[5632/5625]], [[9801/9800]], 46656/46585, 151263/151250, and 161280/161051 in the 11-limit; and [[1716/1715]], [[2080/2079]], [[10648/10647]], and 20480/20449 in the 13-limit. It [[support]]s [[sextile]] and gives a good tuning for it. | 552edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. The equal temperament [[tempering out|tempers out]] {{monzo| 8 14 -3 }} ([[parakleisma]]) in the 5-limit; 250047/250000 ([[landscape comma]]), 589824/588245 ([[hewuermera comma]]), 26873856/26796875, and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[5632/5625]], [[9801/9800]], 46656/46585, 151263/151250, and 161280/161051 in the 11-limit; and [[1716/1715]], [[2080/2079]], [[10648/10647]], and 20480/20449 in the 13-limit. It [[support]]s [[sextile]] and gives a good tuning for it. | ||
It is also consistent in the no-17 [[23-odd-limit]] and the no-17 no-25 [[33-odd-limit]]. In the 2.3.5.7.11.13.19 subgroup, it tempers out [[1216/1215]], [[2376/2375]], [[2926/2925]], [[3136/3135]], 3328/3325, [[3971/3969]] among other commas. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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| 0.0961 | | 0.0961 | ||
| 4.42 | | 4.42 | ||
|- | |||
| 2.3.5.7.11.13.19 | |||
| 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625, 15390/15379 | |||
| {{mapping| 552 875 1282 1550 1910 2043 2345 }} | |||
| -0.1727 | |||
| 0.0977 | |||
| 4.50 | |||
|} | |} | ||
* 552et is notable for being the first equal temperament to beat [[270edo|270]] in the 2.3.5.7.11.13.19 subgroup in terms of absolute error. The next equal temperament that does better in this subgroup is [[581edo|581]]. | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
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| 497.83<br>(97.83) | | 497.83<br>(97.83) | ||
| 4/3<br>(?) | | 4/3<br>(?) | ||
| [[Palladium]] | | [[Palladium]] (5-limit) | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||