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|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 [[Marvel_family#Spectacle|spectacle temperament]] and [[Semicomma_family#Borwell|borwell temperament]].

The division is notable for the fact that it is related to the [[turkish_cent|turkish cent]], ot türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[Relative_cent|relative cent]] division for 106edo. Conversely, it makes the [[Relative_cent|relative cent]] which most closely approximates 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|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|relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[Relative_cent|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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 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|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 [[Marvel_family#Spectacle|spectacle temperament]] and [[Semicomma_family#Borwell|borwell temperament]].
-The division is notable for the fact that it is related to the [[turkish_cent|turkish cent]], ot türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[Relative_cent|relative cent]] division for 106edo. Conversely, it makes the [[Relative_cent|relative cent]] which most closely approximates 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|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|relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[Relative_cent|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: