157edo: Difference between revisions

Line 4:

| Fifth = 92\157 (703.18¢)

| Major 2nd = 27\157 (206¢)

| ~~Minor 2nd~~ = 11~~\157~~ (84¢)

| Semitones = 16:11 (122¢ : 84¢)

| ~~Augmented 1sn~~ = ~~16\157 (122¢)~~

| Consistency = 9

}}

The '''157 equal divisions of the octave''' ('''157edo'''), or the '''157(-tone) equal temperament''' ('''157tet''', '''157et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 157 parts of 7.64 [[cent]]s each.

The '''157 equal divisions of the octave''' ('''157edo'''), or the '''157(-tone) equal temperament''' ('''157tet''', '''157et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 157 parts of about 7.64 [[cent]]s each.

== Theory ==

157et tempers out 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} (quinticosiennic comma) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit (supporting the [[hemififths]] and the [[catafourth]]). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and 8019/8000 in the 11-limit; [[351/350]], [[352/351]], [[847/845]], 1573/1568, and 2197/2187 in the 13-limit.

157et tempers out 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} (quinticosiennic comma) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit (supporting the [[hemififths]] and the [[catafourth]] temperaments). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and [[8019/8000]] in the 11-limit; [[351/350]], [[352/351]], [[847/845]], [[1573/1568]], and [[2197/2187]] in the 13-limit.

157edo is the 37th [[prime EDO]].

@@ Line 4: / Line 4: @@
 | Fifth = 92\157 (703.18¢)
 | Major 2nd = 27\157 (206¢)
-| Minor 2nd = 11\157 (84¢)
+| Semitones = 16:11 (122¢ : 84¢)
-| Augmented 1sn = 16\157  (122¢)
+| Consistency = 9
 }}
-The '''157 equal divisions of the octave''' ('''157edo'''), or the '''157(-tone) equal temperament''' ('''157tet''', '''157et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 157 parts of 7.64 [[cent]]s each.
+The '''157 equal divisions of the octave''' ('''157edo'''), or the '''157(-tone) equal temperament''' ('''157tet''', '''157et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 157 parts of about 7.64 [[cent]]s each.
 == Theory ==
-et tempers out 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} (quinticosiennic comma) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit (supporting the [[hemififths]] and the [[catafourth]]). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and 8019/8000 in the 11-limit; [[351/350]], [[352/351]], [[847/845]], 1573/1568, and 2197/2187 in the 13-limit.
+et tempers out 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} (quinticosiennic comma) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit (supporting the [[hemififths]] and the [[catafourth]] temperaments). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and [[8019/8000]] in the 11-limit; [[351/350]], [[352/351]], [[847/845]], [[1573/1568]], and [[2197/2187]] in the 13-limit.
 edo is the 37th [[prime EDO]].