16808edo: Difference between revisions

Line 9:

Its [[3/2|perfect fifth]] ultimately comes from [[2101edo]], so it not only has two [[chain of fifths|circles of fifths]] ([[hemipyth]]), but ''eight'', giving itself another edge over similar systems.

Among the enormous list of 31-limit [[comma]]s it [[tempering out|tempers out]], the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out [[123201/123200]] ~~and~~ 1990656/1990625; in the 17-limit [[194481/194480]] and [[336141/336140]]; in the 19-limit 43681/43680, 89376/89375 and 104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.

Among the enormous list of 31-limit [[comma]]s it [[tempering out|tempers out]], the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out [[123201/123200]], [[5767168/5767125]], [[1990656/1990625]] supporting [[insanismic]]; in the 17-limit [[194481/194480]] and [[336141/336140]]; in the 19-limit 43681/43680, 89376/89375 and 104976/104975, supporting [[insatinismic]]. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.

=== Prime harmonics ===

@@ Line 9: / Line 9: @@
 Its [[3/2|perfect fifth]] ultimately comes from [[2101edo]], so it not only has two [[chain of fifths|circles of fifths]] ([[hemipyth]]), but ''eight'', giving itself another edge over similar systems.
-Among the enormous list of 31-limit [[comma]]s it [[tempering out|tempers out]], the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out [[123201/123200]] and 1990656/1990625; in the 17-limit [[194481/194480]] and [[336141/336140]]; in the 19-limit 43681/43680, 89376/89375 and 104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.
+Among the enormous list of 31-limit [[comma]]s it [[tempering out|tempers out]], the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out [[123201/123200]], [[5767168/5767125]], [[1990656/1990625]] supporting [[insanismic]]; in the 17-limit [[194481/194480]] and [[336141/336140]]; in the 19-limit 43681/43680, 89376/89375 and 104976/104975, supporting [[insatinismic]]. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.
 === Prime harmonics ===