571edo: Difference between revisions
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{{EDO intro|571}} | |||
571edo [[tempering out|tempers out]] the [[parakleisma]], 1224440064/1220703125 and the [[counterschisma]], {{monzo| -69 45 -1 }} in the [[5-limit]], as well as the lafa comma, {{monzo| 77 -31 -12 }}; [[2401/2400]], 14348907/14336000, and 29360128/29296875 in the [[7-limit]]; [[3025/3024]], 5632/5625, [[41503/41472]], and 17537553/17500000 in the [[11-limit]]; [[1001/1000]], [[1716/1715]], [[4096/4095]], 17303/17280, and 107811/107653 in the [[13-limit]], supporting the 13-limit [[quasiorwell]] temperament; [[1089/1088]], [[1701/1700]], 2431/2430, [[2601/2600]], [[5832/5831]] and 7744/7735 in the [[17-limit]]. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log<sub>2</sub>7, after [[109edo|109]] and before [[2393edo|2393]]. | |||
571edo is the 105th [[prime EDO]]. | 571edo is the 105th [[prime EDO]]. | ||
{{Harmonics in equal|571|columns=11}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
[[Category:Quasiorwell]] | |||
Revision as of 18:18, 17 August 2022
571edo tempers out the parakleisma, 1224440064/1220703125 and the counterschisma, [-69 45 -1⟩ in the 5-limit, as well as the lafa comma, [77 -31 -12⟩; 2401/2400, 14348907/14336000, and 29360128/29296875 in the 7-limit; 3025/3024, 5632/5625, 41503/41472, and 17537553/17500000 in the 11-limit; 1001/1000, 1716/1715, 4096/4095, 17303/17280, and 107811/107653 in the 13-limit, supporting the 13-limit quasiorwell temperament; 1089/1088, 1701/1700, 2431/2430, 2601/2600, 5832/5831 and 7744/7735 in the 17-limit. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log27, after 109 and before 2393.
571edo is the 105th prime EDO.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.029 | +0.376 | +0.001 | -0.705 | +0.103 | +0.123 | +0.911 | +0.097 | +0.195 | +0.323 |
| Relative (%) | +0.0 | -1.4 | +17.9 | +0.0 | -33.5 | +4.9 | +5.9 | +43.3 | +4.6 | +9.3 | +15.4 | |
| Steps (reduced) |
571 (0) |
905 (334) |
1326 (184) |
1603 (461) |
1975 (262) |
2113 (400) |
2334 (50) |
2426 (142) |
2583 (299) |
2774 (490) |
2829 (545) | |