123edo: Difference between revisions

Line 2:

The equal temperament [[tempering out|tempers out]] the [[valentine comma]], 1990656/1953125 and the [[misty comma]], 67108864/66430125 in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]~~, providing the [[optimal patent val]] for the [[gravid]] temperament~~; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]].

123 = 3 × 41, and 123edo shares its [[perfect fifth|fifth]] with [[41edo]]. The equal temperament [[tempering out|tempers out]] the [[valentine comma]], 1990656/1953125 and the [[misty comma]], 67108864/66430125 in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.

Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.

Line 12:

=== Prime harmonics ===

=== Subsets and supersets ===

Since 123 factors into {{factorization|123}}, 123edo contains [[3edo]] and [[41edo]] as its subsets.

[[Category:Gravid]]

@@ Line 2: / Line 2: @@
 {{EDO intro|123}}
-The equal temperament [[tempering out|tempers out]] the [[valentine comma]], 1990656/1953125 and the [[misty comma]], 67108864/66430125 in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]], providing the [[optimal patent val]] for the [[gravid]] temperament; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]].
+= 3 × 41, and 123edo shares its [[perfect fifth|fifth]] with [[41edo]]. The equal temperament [[tempering out|tempers out]] the [[valentine comma]], 1990656/1953125 and the [[misty comma]], 67108864/66430125 in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.
 Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.
@@ Line 12: / Line 12: @@
 === Prime harmonics ===
 {{Harmonics in equal|123}}
+=== Subsets and supersets ===
+Since 123 factors into {{factorization|123}}, 123edo contains [[3edo]] and [[41edo]] as its subsets.
 [[Category:Gravid]]