157edo: Difference between revisions

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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.~~6433~~ [[cent]]s each.

{{Infobox ET

| Prime factorization = 157 (prime)

| Step size = 7.64331¢

| Fifth = 92\157 (703.18¢)

| Major 2nd = 27\157 (206¢)

| Minor 2nd = 11\157 (84¢)

| Augmented 1sn = 16\157 (122¢)

}}

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.

== Theory ==

157et tempers out 78732/78125 ([[sensipent comma]]) and ~~137438953472/134521003125~~ 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]]). 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]].

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! Associated<br>ratio

! Temperament

|-

| 1

| 13\157

| 99.36

| 18/17

| [[Quinticosiennic]]

|-

| 1

| 23\157

| 175.80

| 72/65

| [[Quadrafifths]]

|-

| 1

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| 428.03

| 2800/2187

| [[~~Osiris~~]]

| [[Geb]] / [[osiris]]

|-

| 1

@@ Line 1: / Line 1: @@
-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 7.6433 [[cent]]s each.
+{{Infobox ET
+| Prime factorization = 157 (prime)
+| Step size = 7.64331¢
+| Fifth = 92\157 (703.18¢)
+| Major 2nd = 27\157 (206¢)
+| Minor 2nd = 11\157 (84¢)
+| Augmented 1sn = 16\157  (122¢)
+}}
+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.
 == Theory ==
-et tempers out 78732/78125 ([[sensipent comma]]) and 137438953472/134521003125 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]]). 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]].
@@ Line 78: / Line 86: @@
 ! Associated<br>ratio
 ! Temperament
+|-
+| 1
+| 13\157
+| 99.36
+| 18/17
+| [[Quinticosiennic]]
+|-
+| 1
+| 23\157
+| 175.80
+| 72/65
+| [[Quadrafifths]]
 |-
 | 1
@@ Line 89: / Line 109: @@
 | 428.03
 | 2800/2187
-| [[Osiris]]
+| [[Geb]] / [[osiris]]
 |-
 | 1