460edo: Difference between revisions

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== Theory ==

460edo is a very strong 19-limit system and is [[~~consistency|~~distinctly consistent]] to the [[21-odd-limit]], with [[harmonic]]s of 3 to 19 all tuned flat.

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.

The equal temperament [[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 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 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.

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| [[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 ~~it is~~ distinct

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

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 == Theory ==
-edo is a very strong 19-limit system and is [[consistency|distinctly consistent]] to the [[21-odd-limit]], with [[harmonic]]s of 3 to 19 all tuned flat.
+edo 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.
 The equal temperament [[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 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 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.
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 | [[Soviet ferris wheel]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct