106edo: Difference between revisions

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== 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. ~~(''See [[regular temperament]] for more about what all this means and how to use it.'')~~

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]].

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 == 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. (''See [[regular temperament]] for more about what all this means and how to use it.'')
+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]].