105edo: Difference between revisions

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~~'''105edo''' is the [[equal division of the octave]] into~~ 105 ~~equal parts of 11.429 [[cent]]s each.~~

== Theory ==

105edo is most notable as a tuning of [[meantone]] and in particular higher-limit extensions of meantone. It [[tempers out]] [[81/80]] in the [[5-limit]]; 81/80, [[126/125]] and hence 225/224 in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and if we want to push that far, 144/143 in the [[13-limit]]. This is the sharper fifth mapping of 11-limit meantone (aka huygens rather than meanpop), for which it gives the [[optimal patent val]], and provides a good tuning for the 13-limit extension, though [[74edo]] is in that case the optimal patent val. 105edo's meantone fifth is nearly identical to the [[CTE tuning|CTE generator]] for meantone.

105edo is most notable as a tuning of [[meantone]] and in particular higher-limit extensions of meantone, such as [[grosstone]] and [[Huygens]]. It [[tempers out]] [[81/80]] in the [[5-limit]]; 81/80, [[126/125]] and hence 225/224 in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and if we want to push that far, 144/143 in the [[13-limit]]. This is the sharper fifth mapping of 11-limit meantone (aka huygens rather than meanpop), for which it gives the [[optimal patent val]], and provides a good tuning for the 13-limit extension, though [[74edo]] is in that case the optimal patent val. 105edo's meantone fifth is nearly identical to the [[CTE tuning|CTE generator]] for meantone.

=== Odd harmonics ===

=== Intervals ===

== Intervals ==

[[Table of 105edo intervals]]

=== 15-odd-limit interval mappings ===

=== Miscellany ===

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''105edo''' is the [[equal division of the octave]] into 105 equal parts of 11.429 [[cent]]s each.
+{{EDO intro|105}}
 == Theory ==
-edo is most notable as a tuning of [[meantone]] and in particular higher-limit extensions of meantone. It [[tempers out]] [[81/80]] in the [[5-limit]]; 81/80, [[126/125]] and hence 225/224 in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and if we want to push that far, 144/143 in the [[13-limit]]. This is the sharper fifth mapping of 11-limit meantone (aka huygens rather than meanpop), for which it gives the [[optimal patent val]], and provides a good tuning for the 13-limit extension, though [[74edo]] is in that case the optimal patent val. 105edo's meantone fifth is nearly identical to the [[CTE tuning|CTE generator]] for meantone.
+edo is most notable as a tuning of [[meantone]] and in particular higher-limit extensions of meantone, such as [[grosstone]] and [[Huygens]]. It [[tempers out]] [[81/80]] in the [[5-limit]]; 81/80, [[126/125]] and hence 225/224 in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and if we want to push that far, 144/143 in the [[13-limit]]. This is the sharper fifth mapping of 11-limit meantone (aka huygens rather than meanpop), for which it gives the [[optimal patent val]], and provides a good tuning for the 13-limit extension, though [[74edo]] is in that case the optimal patent val. 105edo's meantone fifth is nearly identical to the [[CTE tuning|CTE generator]] for meantone.
 === Odd harmonics ===
 {{Harmonics in equal|105}}
-=== Intervals ===
+== Intervals ==
-[[Table of 105edo intervals]]
+{{Main|Table of 105edo intervals}}
+=== 15-odd-limit interval mappings ===
+{{15-odd-limit|105}}
 === Miscellany ===