106edo: Difference between revisions

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~~The '''~~106 ~~equal division of the octave'''~~ (~~'''106edo'''~~) ~~divides the~~ [[~~octave~~]] ~~into 106 [[equal]] parts of 11~~.~~321 [[cent]]s each~~.

{{Infobox ET

| Prime factorization = 2 × 53

| Step size = 12.12121¢

| Fifth = 62\106 (701.89¢) (→[[53edo|31\53]])

| Semitones = 10:8 (113.21¢ : 90.57¢)

| Consistency = 5

}}

Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], 2109375/2097152 in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament.

== Theory ==

Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], [[2109375/2097152]] in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament.

The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact [[3/2]], if you care about such a thing.

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-The '''106 equal division of the octave''' ('''106edo''') divides the [[octave]] into 106 [[equal]] parts of 11.321 [[cent]]s each.
+{{Infobox ET
+| Prime factorization = 2 × 53
+| Step size = 12.12121¢
+| Fifth = 62\106 (701.89¢) (→[[53edo|31\53]])
+| Semitones = 10:8 (113.21¢ : 90.57¢)
+| Consistency = 5
+}}
+{{EDO intro|106}}
-Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], 2109375/2097152 in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament.
+== Theory ==
+Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], [[2109375/2097152]] in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament.
 The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact [[3/2]], if you care about such a thing.