571edo: Difference between revisions

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~~'''571edo''' is the [[~~EDO|~~equal division of the octave]] into~~ 571 ~~parts of 2.101576~~ [[~~cent]]s each. It [[tempering_out~~|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 [[~~Breedsmic temperaments|~~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 [[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]].

[[Category:Equal divisions of the octave|###]]

[[Category:Prime EDO]]

[[Category:Quasiorwell]]

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-'''571edo''' is the [[EDO|equal division of the octave]] into 571 parts of 2.101576 [[cent]]s each. It [[tempering_out|tempers out]] the [[parakleisma]], 1224440064/1220703125 and the counterschisma, |-69 45 -1&gt; in the [[5-limit]], as well as the lafa comma, |77 -31 -12&gt;; 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 [[Breedsmic temperaments|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]].
+{{EDO intro|571}}
+edo [[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]].
 edo is the 105th [[prime EDO]].
+{{Harmonics in equal|571|columns=11}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Prime EDO]]
+[[Category:Quasiorwell]]