509edo: Difference between revisions
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509edo has a sharp tendency in lower [[harmonic]]s. The 13-limit [[TE tuning|optimal tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave compression]] tight. | 509edo has a sharp tendency in lower [[harmonic]]s. The 13-limit [[TE tuning|optimal tuning]] of this temperament is consistent to the 15-integer-limit, so one might want to keep the [[octave compression]] tight. | ||
It [[tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit; [[2401/2400]] and 29360128/29296875 in the 7-limit; and [[3025/3024]], [[5632/5625]], [[41503/41472]], 42592/42525, 151263/151250, 172032/171875, 180224/180075, 322102/321489, 422576/421875, 456533/455625, and [[1953125/1948617]] in the 11-limit. It provides the [[optimal patent val]] for [[petrtri]], the 2.11/5.13/5 subgroup temperament tempering out [[2200/2197]]. | |||
=== Odd harmonics === | === Odd harmonics === | ||
| Line 28: | Line 28: | ||
| {{monzo| 807 -509 }} | | {{monzo| 807 -509 }} | ||
| {{mapping| 509 807 }} | | {{mapping| 509 807 }} | ||
| | | −0.1890 | ||
| 0.1889 | | 0.1889 | ||
| 8.01 | | 8.01 | ||
| Line 35: | Line 35: | ||
| {{monzo| 9 -13 5 }}, {{monzo| 93 -3 -38 }} | | {{monzo| 9 -13 5 }}, {{monzo| 93 -3 -38 }} | ||
| {{mapping| 509 807 1182 }} | | {{mapping| 509 807 1182 }} | ||
| | | −0.1729 | ||
| 0.1559 | | 0.1559 | ||
| 6.61 | | 6.61 | ||
| Line 42: | Line 42: | ||
| 2401/2400, 1600000/1594323, 29360128/29296875 | | 2401/2400, 1600000/1594323, 29360128/29296875 | ||
| {{mapping| 509 807 1182 1429 }} | | {{mapping| 509 807 1182 1429 }} | ||
| | | −0.1415 | ||
| 0.1456 | | 0.1456 | ||
| 6.18 | | 6.18 | ||
| Line 49: | Line 49: | ||
| 2401/2400, 3025/3024, 5632/5625, 1600000/1594323 | | 2401/2400, 3025/3024, 5632/5625, 1600000/1594323 | ||
| {{mapping| 509 807 1182 1429 1761 }} | | {{mapping| 509 807 1182 1429 1761 }} | ||
| | | −0.1335 | ||
| 0.1312 | | 0.1312 | ||
| 5.57 | | 5.57 | ||
| Line 56: | Line 56: | ||
| 2080/2079, 2200/2197, 2401/2400, 3025/3024, 5632/5625 | | 2080/2079, 2200/2197, 2401/2400, 3025/3024, 5632/5625 | ||
| {{mapping| 509 807 1182 1429 1761 1884 }} | | {{mapping| 509 807 1182 1429 1761 1884 }} | ||
| | | −0.1618 | ||
| 0.1354 | | 0.1354 | ||
| 5.74 | | 5.74 | ||
| Line 63: | Line 63: | ||
| 1225/1224, 2080/2079, 2200/2197, 2401/2400, 2431/2430, 4914/4913 | | 1225/1224, 2080/2079, 2200/2197, 2401/2400, 2431/2430, 4914/4913 | ||
| {{mapping| 509 807 1182 1429 1761 1884 2081 }} | | {{mapping| 509 807 1182 1429 1761 1884 2081 }} | ||
| | | −0.1784 | ||
| 0.1318 | | 0.1318 | ||
| 5.59 | | 5.59 | ||
| Line 102: | Line 102: | ||
| [[Amity]] | | [[Amity]] | ||
|} | |} | ||
<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 | ||
== Music == | == Music == | ||