106edo: Difference between revisions

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The '''106 equal division''' divides the octave into 106 equal parts of 11.321 cents each. Since 106 = 2*53 it 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]], 3125/3097, [[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 '''106 equal division of the octave''' ('''106edo''') divides the [[octave]] into 106 [[equal]] parts of 11.321 [[cent]]s each.  
 
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.
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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== See also ==
== See also ==
Artists using 106 et:
Artists using 106 et:
* [[Dolores Catherino]] -- [http://dolorescatherino.com her website], [https://www.youtube.com/user/dolomuse YouTube profile: dolomuse]
* [[Dolores Catherino]] [http://dolorescatherino.com her website], [https://www.youtube.com/user/dolomuse YouTube profile: dolomuse]
* [http://chrisvaisvil.com/still-life-in-106-notes-per-octave/ Still Life in 106 Notes Per Octave « Music &amp; Techniques by Chris Vaisvil]
* [http://chrisvaisvil.com/still-life-in-106-notes-per-octave/ Still Life in 106 Notes Per Octave « Music &amp; Techniques by Chris Vaisvil]