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 [[~~Saturation~~|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 supports [[spectacle]] temperament and [[borwell]] temperament.

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 [[Contorsion|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 supports [[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¢, πr¢), 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¢, πr¢), which most closely approximates equally dividing an exact [[3/2]], if you care about such a thing.

Artists using 106 et:

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* [http://chrisvaisvil.com/still-life-in-106-notes-per-octave/ Still Life in 106 Notes Per Octave « Music & Techniques by Chris Vaisvil]

[[Category:Edo]]

[[Category:53edo]]

[[Category:Polychromatic]]

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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 [[Saturation|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 supports [[spectacle]] temperament and [[borwell]] temperament.
+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 [[Contorsion|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 supports [[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.
 Artists using 106 et:
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 * [http://chrisvaisvil.com/still-life-in-106-notes-per-octave/ Still Life in 106 Notes Per Octave « Music &amp; Techniques by Chris Vaisvil]
+[[Category:Edo]]
 [[Category:53edo]]
 [[Category:Polychromatic]]