460edo: Difference between revisions

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The '''460 equal divisions of the octave''' divides the octave into 460 equal parts of 2.~~609 cents~~ each.

{{Infobox ET

| Prime factorization = 2<sup>2</sup> × 5 × 23

| Step size = 2.60870¢

| Fifth = 269\460 (701.74¢)

| Semitones = 43:35 (112.17¢ : 91.30¢)

| Consistency = 21

}}

The '''460 equal divisions of the octave''' ('''460edo'''), or the '''460(-tone) equal temperament''' ('''460tet''', '''460et''') when viewed from a [[regular temperament]] perspective, divides the octave into 460 equal parts of about 2.61 [[cent]]s each.

== Theory ==

460edo is a very strong 19-limit system and is uniquely [[consistent]] to the [[21-odd-limit]], with harmonics of 3 to 19 all tuned flat. It 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]]. In the 11-limit it tempers of 43923/43904, [[3025/3024]] and [[9801/9800]]; in the 13-limit [[1001/1000]], [[4225/4224]] and [[10648/10647]]; 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 five temperament tempering out 833/832 and 1001/1000.

460 factors into 2<sup>2</sup> × 5 × 23, and has subset edos 2, 4, 5, 10, 20, 23, 46, 92, 115, and 230.

=== Prime harmonics ===

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-The '''460 equal divisions of the octave''' divides the octave into 460 equal parts of 2.609 cents each.
+{{Infobox ET
+| Prime factorization = 2<sup>2</sup> × 5 × 23
+| Step size = 2.60870¢
+| Fifth = 269\460 (701.74¢)
+| Semitones = 43:35 (112.17¢ : 91.30¢)
+| Consistency = 21
+}}
+The '''460 equal divisions of the octave''' ('''460edo'''), or the '''460(-tone) equal temperament''' ('''460tet''', '''460et''') when viewed from a [[regular temperament]] perspective, divides the octave into 460 equal parts of about 2.61 [[cent]]s each.
+== Theory ==
 edo is a very strong 19-limit system and is uniquely [[consistent]] to the [[21-odd-limit]], with harmonics of 3 to 19 all tuned flat. It 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]]. In the 11-limit it tempers of 43923/43904, [[3025/3024]] and [[9801/9800]]; in the 13-limit [[1001/1000]], [[4225/4224]] and [[10648/10647]]; 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 five temperament tempering out 833/832 and 1001/1000.
+factors into 2<sup>2</sup> × 5 × 23, and has subset edos 2, 4, 5, 10, 20, 23, 46, 92, 115, and 230.
 === Prime harmonics ===