460edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
460edo is a very strong 19-limit system and is [[ | 460edo is a very strong 19-limit system and is [[distinctly consistent]] to the [[21-odd-limit]], with [[harmonic]]s of 3 to 19 all tuned flat. | ||
It [[tempering out|tempers out]] the [[schisma]], 32805/32768, in the 5-limit and [[4375/4374]] and [[65536/65625]] in the 7-limit, so that it [[support]]s [[pontiac]], the {{nowrap|171 & 289}} temperament. In the 11-limit it tempers of [[3025/3024]] and [[9801/9800]], and 43923/43904; in the 13-limit [[1001/1000]], [[4225/4224]] and [[10648/10647]], so that it supports [[deca]], the {{nowrap|190 & 270}} temperament; in the 17-limit [[833/832]], [[1089/1088]], [[1225/1224]], [[1701/1700]], [[2058/2057]], [[2431/2430]], [[2601/2600]] and [[4914/4913]]; and in the 19-limit 1331/1330, [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 2376/2375, 2926/2925, 3136/3135, 3250/3249 and 4200/4199. It serves as the [[optimal patent val]] for various temperaments such as the rank-5 temperament tempering out 833/832 and 1001/1000. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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| [[Soviet ferris wheel]] | | [[Soviet ferris wheel]] | ||
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<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 | ||