571edo: Difference between revisions

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-'''571edo''' is the [[EDO|equal division of the octave]] into 571 parts of 2.10158 [[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 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]].
+{{Infobox ET}}
+{{ED intro}}
-edo is the 105th [[prime EDO]].
+== Theory ==
+et [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}, 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]].
-[[Category:Edo]]
+=== Prime harmonics ===
-[[Category:Prime EDO]]
+{{Harmonics in equal|571}}
-[[Category:Theory]]
+=== Subsets and supersets ===
+edo is the 105th [[prime edo]].
+== Regular temperament properties ==
+{| class="wikitable center-4 center-5 center-6"
+|-
+! rowspan="2" | [[Subgroup]]
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
+|-
+| 2.3
+| {{monzo| -905 571 }}
+| {{mapping| 571 905 }}
+| +0.0090
+| 0.0090
+| 0.43
+|-
+| 2.3.5
+| {{monzo| 8 14 -13 }}, {{monzo| -69 45 -1 }}
+| {{mapping| 571 905 1326 }}
+| −0.0480
+| 0.0810
+| 3.85
+|-
+| 2.3.5.7
+| 2401/2400, 14348907/14336000, 29360128/29296875
+| {{mapping| 571 905 1326 1603 }}
+| −0.0361
+| 0.0731
+| 3.48
+|-
+| 2.3.5.7.11
+| 2401/2400, 3025/3024, 5632/5625, 14348907/14336000
+| {{mapping| 571 905 1326 1603 1975 }}
+| +0.0119
+| 0.1161
+| 5.53
+|-
+| 2.3.5.7.11.13
+| 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653
+| {{mapping| 571 905 1326 1603 1975 2113 }}
+| +0.0053
+| 0.1070
+| 5.09
+|-
+| 2.3.5.7.11.13.17
+| 1001/1000, 1089/1088, 1716/1715, 2601/2600, 3025/3024, 4096/4095
+| {{mapping| 571 905 1326 1603 1975 2113 2334 }}
+| +0.0002
+| 0.0999
+| 4.75
+|}
+=== Rank-2 temperaments ===
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! Temperaments
+|-
+| 1
+| 123\571
+| 258.49
+| {{monzo| -32 13 5 }}
+| [[Lafa]]
+|-
+| 1
+| 129\571
+| 271.10
+| 90/77
+| [[Quasiorwell]]
+|-
+| 1
+| 147\571
+| 315.24
+| 6/5
+| [[Parakleismic]] (5-limit)
+|-
+| 1
+| 237\571
+| 498.07
+| 4/3
+| [[Counterschismic]]
+|-
+| 1
+| 248\571
+| 521.19
+| 875/648
+| [[Maviloid]]
+|}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+== Music ==
+; [[Francium]]
+* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] | [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] | [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]
+* "LEARN TO CAR" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/2icA5S4LIFCdKA7aZPkLgr Spotify] | [https://francium223.bandcamp.com/track/learn-to-car Bandcamp] | [https://www.youtube.com/watch?v=ceVF2FMNKbE YouTube]
+* "George Crispell" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/3mZBLdkeEvHYMDgmHNJu4H Spotify] | [https://francium223.bandcamp.com/track/george-crispell Bandcamp] | [https://www.youtube.com/watch?v=I7SdSaP1UJs YouTube] − in Gentic, 571edo tuning
+[[Category:Listen]]
+[[Category:Quasiorwell]]