581edo: Difference between revisions
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== Theory == | == Theory == | ||
581edo is a very strong 19- and 23-limit system, [[consistency|distinctly consistent]] to the [[25-odd-limit]]. | 581edo is a very strong 19- and 23-limit system, [[consistency|distinctly consistent]] to the [[25-odd-limit]]. It [[tempers out]] [[2401/2400]] in the 7-limit, [[3025/3024]], [[19712/19683]], 151263/151250 in the 11-limit, and [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]] in the 13-limit. It [[support]]s and gives a good tuning for [[newt]], the {{nowrap|270 & 311}} microtemperament, which features a neutral-third generator. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 26: | Line 26: | ||
| {{monzo| 921 -581 }} | | {{monzo| 921 -581 }} | ||
| {{mapping| 581 921 }} | | {{mapping| 581 921 }} | ||
| | | −0.0891 | ||
| 0.0891 | | 0.0891 | ||
| 4.32 | | 4.32 | ||
| Line 33: | Line 33: | ||
| {{monzo| -29 -11 20 }}, {{monzo| 33 -34 9 }} | | {{monzo| -29 -11 20 }}, {{monzo| 33 -34 9 }} | ||
| {{mapping| 581 921 1349 }} | | {{mapping| 581 921 1349 }} | ||
| | | −0.0475 | ||
| 0.0936 | | 0.0936 | ||
| 4.53 | | 4.53 | ||
| Line 40: | Line 40: | ||
| 2401/2400, 33554432/33480783, 48828125/48771072 | | 2401/2400, 33554432/33480783, 48828125/48771072 | ||
| {{mapping| 581 921 1349 1631 }} | | {{mapping| 581 921 1349 1631 }} | ||
| | | −0.0222 | ||
| 0.0922 | | 0.0922 | ||
| 4.46 | | 4.46 | ||
| Line 47: | Line 47: | ||
| 2401/2400, 3025/3024, 19712/19683, 234375/234256 | | 2401/2400, 3025/3024, 19712/19683, 234375/234256 | ||
| {{mapping| 581 921 1349 1631 2010 }} | | {{mapping| 581 921 1349 1631 2010 }} | ||
| | | −0.0261 | ||
| 0.0828 | | 0.0828 | ||
| 4.01 | | 4.01 | ||
| Line 54: | Line 54: | ||
| 2080/2079, 2401/2400, 3025/3024, 4096/4095, 78125/78078 | | 2080/2079, 2401/2400, 3025/3024, 4096/4095, 78125/78078 | ||
| {{mapping| 581 921 1349 1631 2010 2150 }} | | {{mapping| 581 921 1349 1631 2010 2150 }} | ||
| | | −0.0259 | ||
| 0.0756 | | 0.0756 | ||
| 3.66 | | 3.66 | ||
| Line 61: | Line 61: | ||
| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4096/4095, 4914/4913 | | 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4096/4095, 4914/4913 | ||
| {{mapping| 581 921 1349 1631 2010 2150 2375 }} | | {{mapping| 581 921 1349 1631 2010 2150 2375 }} | ||
| | | −0.0355 | ||
| 0.0738 | | 0.0738 | ||
| 3.58 | | 3.58 | ||
| Line 68: | Line 68: | ||
| 1216/1215, 1225/1224, 1540/1539, 1729/1728, 2058/2057, 2080/2079, 4914/4913 | | 1216/1215, 1225/1224, 1540/1539, 1729/1728, 2058/2057, 2080/2079, 4914/4913 | ||
| {{mapping| 581 921 1349 1631 2010 2150 2375 2468 }} | | {{mapping| 581 921 1349 1631 2010 2150 2375 2468 }} | ||
| | | −0.0283 | ||
| 0.0717 | | 0.0717 | ||
| 3.47 | | 3.47 | ||
| Line 75: | Line 75: | ||
| 1216/1215, 1225/1224, 1288/1287, 1540/1539, 1729/1728, 2024/2023, 2058/2057, 2080/2079 | | 1216/1215, 1225/1224, 1288/1287, 1540/1539, 1729/1728, 2024/2023, 2058/2057, 2080/2079 | ||
| {{mapping| 581 921 1349 1631 2010 2150 2375 2468 2628 }} | | {{mapping| 581 921 1349 1631 2010 2150 2375 2468 2628 }} | ||
| | | −0.0155 | ||
| 0.0800 | | 0.0800 | ||
| 3.87 | | 3.87 | ||
| Line 128: | Line 128: | ||
| [[Countritonic]] (5-limit) | | [[Countritonic]] (5-limit) | ||
|} | |} | ||
<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 | ||
[[Category:Newt]] | [[Category:Newt]] | ||