460edo: Difference between revisions

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== 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.

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. 460edo supports the 460 & [[1789edo|1789]] temperament in the 2.9.5.7.11 subgroup called [[commatose]].

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

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! Associated<br>ratio

! Temperaments

|-

|1

|9\460

|23.48

|531441/524288

|[[Commatose]]

|-

| 1

@@ Line 9: / Line 9: @@
 == 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.
+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. 460edo supports the 460 & [[1789edo|1789]] temperament in the 2.9.5.7.11 subgroup called [[commatose]].
 factors into 2<sup>2</sup> × 5 × 23, and has subset edos 2, 4, 5, 10, 20, 23, 46, 92, 115, and 230.
@@ Line 85: / Line 85: @@
 ! Associated<br>ratio
 ! Temperaments
+|-
+|1
+|9\460
+|23.48
+|531441/524288
+|[[Commatose]]
 |-
 | 1