108edo: Difference between revisions

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==Theory==

== Theory ==

~~108edo~~ tempers out the Pythagorean comma~~, 531441/524288,~~ in the 3-limit and 1990656/1953125~~, the valensixthtone~~ comma, in the 5-limit. In the 7-limit it tempers out 126/125 and 1029/1024, ~~supporting~~ [[~~Starling_temperaments#Valentine temperament|~~valentine ~~temperament~~]], and making for a good tuning for it and for starling temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out 540/539 and the 108e val tempers out 121/120 ~~and~~ 176/175, supporting 11-limit valentine for which it is again a good tuning.

108et [[tempering out|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the [[patent val]] tempers out [[540/539]] and 1344/1331, and the 108e val tempers out [[121/120]], [[176/175]], [[385/384]], and [[441/440]], supporting 11-limit valentine for which it is again a good tuning.

108edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.

~~108edo is the smallest 12n-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.~~

=== Prime harmonics ===

=== Subsets and supersets ===

Since 108 factors into {{factorization|108}}, 108edo has subset edos {{EDOs| 2, 3, 4, 6, 9, 12, 18, 27, 36, and 54 }}.

== Intervals ==

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

== Music ==

; [[Billy Stiltner]]

* [https://billystiltner.bandcamp.com/track/108-tone-equal 108 tone equal]

[[Category:Valentine]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|108}}
+{{ED intro}}
-==Theory==
+== Theory ==
-edo tempers out the Pythagorean comma, 531441/524288, in the 3-limit and 1990656/1953125, the valensixthtone comma, in the 5-limit. In the 7-limit it tempers out 126/125 and 1029/1024, supporting [[Starling_temperaments#Valentine temperament|valentine temperament]], and making for a good tuning for it and for starling temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out 540/539 and the 108e val tempers out 121/120 and 176/175, supporting 11-limit valentine for which it is again a good tuning.
+et [[tempering out|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the [[patent val]] tempers out [[540/539]] and 1344/1331, and the 108e val tempers out [[121/120]], [[176/175]], [[385/384]], and [[441/440]], supporting 11-limit valentine for which it is again a good tuning.
+edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.
-edo is the smallest 12n-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.
 === Prime harmonics ===
 {{Harmonics in equal|108}}
+=== Subsets and supersets ===
+Since 108 factors into {{factorization|108}}, 108edo has subset edos {{EDOs| 2, 3, 4, 6, 9, 12, 18, 27, 36, and 54 }}.
 == Intervals ==
 {{Interval table}}
- [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+== Music ==
+; [[Billy Stiltner]]
+* [https://billystiltner.bandcamp.com/track/108-tone-equal 108 tone equal]
 [[Category:Valentine]]