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~~.

== 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. Unfortunately, it is now only consistent to the [[5-odd-limit]] due to 7/5 being closer to 51 steps rather than its patent val mapping of 52 steps. A superset of 53edo with much a higher consistency limit is [[159edo]].

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.

=== Prime harmonics ===

53edo for comparison:

== Intervals ==

== Instruments ==

* [[Lumatone mapping for 106edo]]

== See also ==

Artists using 106 et:

* [[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 & Techniques by Chris Vaisvil]

<ul><li>[[Dolores_Catherino|Dolores Catherino]] -- [http://dolorescatherino.com her website], [https://www.youtube.com/user/dolomuse YouTube profile: dolomuse]</li><li>[http://chrisvaisvil.com/still-life-in-106-notes-per-octave/ Still Life in 106 Notes Per Octave « Music & Techniques by Chris Vaisvil]</li></ul>

[[Category:53edo]]

[[Category:~~polychromatic~~]]

[[Category:Equal divisions of the octave|###]]

[[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|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]].
+{{Infobox ET}}
+{{ED intro}}
-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.
+== 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. Unfortunately, it is now only consistent to the [[5-odd-limit]] due to 7/5 being closer to 51 steps rather than its patent val mapping of 52 steps. A superset of 53edo with much a higher consistency limit is [[159edo]].
+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.
+=== Prime harmonics ===
+{{Harmonics in equal|106|columns=16}}
+edo for comparison:
+{{Harmonics in equal|53|collapsed=1|columns=16}}
+== Intervals ==
+{{Interval table}}
+== Instruments ==
+* [[Lumatone mapping for 106edo]]
+== See also ==
 Artists using 106 et:
+* [[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]
-<ul><li>[[Dolores_Catherino|Dolores Catherino]] -- [http://dolorescatherino.com her website], [https://www.youtube.com/user/dolomuse YouTube profile: dolomuse]</li><li>[http://chrisvaisvil.com/still-life-in-106-notes-per-octave/ Still Life in 106 Notes Per Octave « Music &amp; Techniques by Chris Vaisvil]</li></ul>
 [[Category:53edo]]
-[[Category:polychromatic]]
+[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Polychromatic]]