66edo: Difference between revisions

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== Theory ==

~~{{Harmonics in equal|66}}~~

The [[patent val]] of 66edo is [[contorted]] in the 5-limit, [[tempering out]] the same [[comma]]s ([[250/243]], [[2048/2025]], [[3125/3072]], etc.) as [[22edo]]. In the 7-limit it tempers out [[686/675]] and [[1029/1024]], in the 11-limit [[55/54]], [[100/99]] and [[121/120]], in the 13-limit [[91/90]], [[169/168]], 196/195 and in the 17-limit 136/135 and [[256/255]]. It provides the [[optimal patent val]] for the 11- and 13-limit [[ammonite]] temperament.

The [[patent val]] is [[contorted]] in the 5-limit, tempering out the same ~~commas~~ [[250/243]], [[2048/2025]] ~~and~~ [[3125/3072]] as [[~~22edo|~~22edo]]. In the 7-limit it tempers out [[686/675]] and [[1029/1024]], in the 11-limit [[55/54]], [[100/99]] and [[121/120]], in the 13-limit [[91/90]], [[169/168]], 196/195 and in the 17-limit 136/135 and [[256/255]]. It provides the [[~~Optimal_patent_val|~~optimal patent val]] for 11- and 13-limit [[~~Porcupine_family#Ammonite|~~ammonite temperament]].

The 66b val tempers out [[16875/16384]] in the 5-limit, [[126/125]], [[1728/1715]] and [[2401/2400]] in the 7-limit, [[99/98]] and [[385/384]] in the 11-limit, and [[105/104]], [[144/143]] and [[847/845]] in the 13-limit.

~~The 66b val tempers out 16875/16384 in~~ the ~~5-limit, 126/125, 1728/1715 and 2401/2400 in the 7-limit, 99/98 and 385/384 in the 11-limit, and 105/104, 144/143 and 847/845 in the 13-limit~~.

109 steps of 66edo is extremely close to the [[acoustic pi]] with only +0.023 cents of error.

~~109 steps of 66edo is extremely close to [[Pitave~~|~~Pi]] with only +0.023 cents of error.~~

=== Odd harmonics ===

== Interval table ==

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 == Theory ==
-{{Harmonics in equal|66}}
+The [[patent val]] of 66edo is [[contorted]] in the 5-limit, [[tempering out]] the same [[comma]]s ([[250/243]], [[2048/2025]], [[3125/3072]], etc.) as [[22edo]]. In the 7-limit it tempers out [[686/675]] and [[1029/1024]], in the 11-limit [[55/54]], [[100/99]] and [[121/120]], in the 13-limit [[91/90]], [[169/168]], 196/195 and in the 17-limit 136/135 and [[256/255]]. It provides the [[optimal patent val]] for the 11- and 13-limit [[ammonite]] temperament.
-The [[patent val]] is [[contorted]] in the 5-limit, tempering out the same commas [[250/243]], [[2048/2025]] and [[3125/3072]] as [[22edo|22edo]]. In the 7-limit it tempers out [[686/675]] and [[1029/1024]], in the 11-limit [[55/54]], [[100/99]] and [[121/120]], in the 13-limit [[91/90]], [[169/168]], 196/195 and in the 17-limit 136/135 and [[256/255]]. It provides the [[Optimal_patent_val|optimal patent val]] for 11- and 13-limit [[Porcupine_family#Ammonite|ammonite temperament]].
+The 66b val tempers out [[16875/16384]] in the 5-limit, [[126/125]], [[1728/1715]] and [[2401/2400]] in the 7-limit, [[99/98]] and [[385/384]] in the 11-limit, and [[105/104]], [[144/143]] and [[847/845]] in the 13-limit.
-The 66b val tempers out 16875/16384 in the 5-limit, 126/125, 1728/1715 and 2401/2400 in the 7-limit, 99/98 and 385/384 in the 11-limit, and 105/104, 144/143 and 847/845 in the 13-limit.
+steps of 66edo is extremely close to the [[acoustic pi]] with only +0.023 cents of error.
-steps of 66edo is extremely close to [[Pitave|Pi]] with only +0.023 cents of error.
+=== Odd harmonics ===
+{{Harmonics in equal|66}}
 == Interval table ==