357edo: Difference between revisions
ArrowHead294 (talk | contribs) m Partial undo |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
While not highly accurate for its size, 357et is the point where a few important temperaments meet. | While not highly accurate for its size, 357et is the point where a few important temperaments meet. It [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]), and {{monzo| 61 4 -29 }} (squarschimidt comma) in the [[5-limit]]; 10976/10935 ([[hemimage comma]]), 235298/234375 ([[triwellisma]]), 250047/250000 ([[landscape comma]]), 2100875/2097152 ([[rainy comma]]) in the [[7-limit]]; [[3025/3024]], [[5632/5625]], [[12005/11979]] in the [[11-limit]]; [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]] in the [[13-limit]]. | ||
It [[support]]s 5-limit [[amity]] and 7-limit weak extensions [[calamity]] and [[chromat]]. It provides the [[optimal patent val]] for 11- and 13-limit [[hemichromat]], the 159 & 198 temperament. It also supports [[ | It [[support]]s 5-limit [[amity]] and 7-limit weak extensions [[calamity]] and [[chromat]]. It provides the [[optimal patent val]] for 11- and 13-limit [[hemichromat]], the 159 & 198 temperament. It also supports [[avicenna (temperament)|avicenna]], but [[270edo]] is better suited for this purpose. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 11: | Line 11: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 357 factors into | Since 357 factors into 3 × 7 × 17, 357edo has subset edos {{EDOs| 3, 7, 17, 21, 51, and 119 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 28: | Line 28: | ||
| {{monzo| 566 -357 }} | | {{monzo| 566 -357 }} | ||
| {{mapping| 357 566 }} | | {{mapping| 357 566 }} | ||
| | | −0.1786 | ||
| 0.1785 | | 0.1785 | ||
| 5.31 | | 5.31 | ||
| Line 35: | Line 35: | ||
| 1600000/1594323, {{monzo| 61 4 -29 }} | | 1600000/1594323, {{monzo| 61 4 -29 }} | ||
| {{mapping| 357 566 829 }} | | {{mapping| 357 566 829 }} | ||
| | | −0.1536 | ||
| 0.1500 | | 0.1500 | ||
| 4.46 | | 4.46 | ||
| Line 42: | Line 42: | ||
| 10976/10935, 235298/234375, 2100875/2097152 | | 10976/10935, 235298/234375, 2100875/2097152 | ||
| {{mapping| 357 566 829 1002 }} | | {{mapping| 357 566 829 1002 }} | ||
| | | −0.0477 | ||
| 0.2248 | | 0.2248 | ||
| 6.69 | | 6.69 | ||
| Line 49: | Line 49: | ||
| 3025/3024, 5632/5625, 10976/10935, 102487/102400 | | 3025/3024, 5632/5625, 10976/10935, 102487/102400 | ||
| {{mapping| 357 566 829 1002 1235 }} | | {{mapping| 357 566 829 1002 1235 }} | ||
| | | −0.0348 | ||
| 0.2027 | | 0.2027 | ||
| 6.03 | | 6.03 | ||
| Line 56: | Line 56: | ||
| 676/675, 1001/1000, 3025/3024, 4096/4095, 10976/10935 | | 676/675, 1001/1000, 3025/3024, 4096/4095, 10976/10935 | ||
| {{mapping| 357 566 829 1002 1235 1321 }} | | {{mapping| 357 566 829 1002 1235 1321 }} | ||
| | | −0.0204 | ||
| 0.1879 | | 0.1879 | ||
| 5.59 | | 5.59 | ||
| Line 113: | Line 113: | ||
| [[Pnict]] | | [[Pnict]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||