176edo: Difference between revisions

Line 4:

| Fifth = 103\176 (702.27¢)

| Major 2nd = 30\176 (205¢)

| ~~Minor 2nd~~ = 13~~\176~~ (89¢)

| Semitones = 17:13 (116¢ : 89¢)

| ~~Augmented 1sn~~ = ~~17\176 (116¢)~~

| Consistency = 11

}}

The '''176 equal divisions of the octave''' ('''176edo'''), or the '''176(-tone) equal temperament''' ('''176tet''', '''176et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 176 parts of about 6.82 [[cent]]s each, a size close to [[243/242]], the rastma.

== Theory ==

176edo is [[consistent]] to the [[11-odd-limit]], tempering out 78732/78125 ([[sensipent comma]]) and {{monzo| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and 50421/50000 in the 7-limit; [[441/440]], 3388/3375, 6912/6875, ~~and~~ [[8019/8000]] in the 11-limit, supporting the [[bison]] temperament and the [[commatic]] temperament.

176edo is [[consistent]] to the [[11-odd-limit]], tempering out 78732/78125 ([[sensipent comma]]) and {{monzo| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and 50421/50000 in the 7-limit; [[441/440]], 3388/3375, 6912/6875, [[8019/8000]] and [[9801/9800]] in the 11-limit, supporting the [[bison]] temperament and the [[commatic]] temperament. Using the [[patent val]], [[351/350]], [[364/363]], [[2080/2079]], [[2197/2187]], and [[4096/4095]] in the 13-limit.

=== Prime harmonics ===

Line 105:

| 20.45

| 81/80

| [[Commatic]] ~~(176f)~~

| [[Commatic]]

|-

| 2

Line 117:

| 565.91<br>(34.09)

| 168/121<br>(55/54)

| [[Octowerck]] (176f)

| [[Octowerck]] (176f) / octowerckis (176)

|-

| 11

Line 133:

[[Category:Equal divisions of the octave]]

[[Category:Countermiracle]]

@@ Line 4: / Line 4: @@
 | Fifth = 103\176 (702.27¢)
 | Major 2nd = 30\176 (205¢)
-| Minor 2nd = 13\176 (89¢)
+| Semitones = 17:13 (116¢ : 89¢)
-| Augmented 1sn = 17\176  (116¢)
+| Consistency = 11
 }}
 The '''176 equal divisions of the octave''' ('''176edo'''), or the '''176(-tone) equal temperament''' ('''176tet''', '''176et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 176 parts of about 6.82 [[cent]]s each, a size close to [[243/242]], the rastma.
 == Theory ==
-edo is [[consistent]] to the [[11-odd-limit]], tempering out 78732/78125 ([[sensipent comma]]) and {{monzo| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and 50421/50000 in the 7-limit; [[441/440]], 3388/3375, 6912/6875, and [[8019/8000]] in the 11-limit, supporting the [[bison]] temperament and the [[commatic]] temperament.
+edo is [[consistent]] to the [[11-odd-limit]], tempering out 78732/78125 ([[sensipent comma]]) and {{monzo| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and 50421/50000 in the 7-limit; [[441/440]], 3388/3375, 6912/6875, [[8019/8000]] and [[9801/9800]] in the 11-limit, supporting the [[bison]] temperament and the [[commatic]] temperament. Using the [[patent val]], [[351/350]], [[364/363]], [[2080/2079]], [[2197/2187]], and [[4096/4095]] in the 13-limit.
 === Prime harmonics ===
@@ Line 105: / Line 105: @@
 | 20.45
 | 81/80
-| [[Commatic]] (176f)
+| [[Commatic]]
 |-
 | 2
@@ Line 117: / Line 117: @@
 | 565.91<br>(34.09)
 | 168/121<br>(55/54)
-| [[Octowerck]] (176f)
+| [[Octowerck]] (176f) / octowerckis (176)
 |-
 | 11
@@ Line 133: / Line 133: @@
 [[Category:Equal divisions of the octave]]
+[[Category:Countermiracle]]