385edo: Difference between revisions
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== Theory == | == Theory == | ||
385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/6655]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit. | 385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/6655]], and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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| 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000 | | 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000 | ||
| {{mapping| 385 610 894 1081 1332 1425 }} | | {{mapping| 385 610 894 1081 1332 1425 }} | ||
| | | −0.0394 | ||
| 0.2207 | | 0.2207 | ||
| 7.08 | | 7.08 | ||
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| 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095 | | 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095 | ||
| {{mapping| 385 610 894 1081 1332 1425 1574 }} | | {{mapping| 385 610 894 1081 1332 1425 1574 }} | ||
| | | −0.0693 | ||
| 0.2171 | | 0.2171 | ||
| 6.97 | | 6.97 | ||
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| [[Pental (temperament)|Pental]] (5-limit) | | [[Pental (temperament)|Pental]] (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:Hemipental]] | [[Category:Hemipental]] | ||