100edo: Difference between revisions

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100edo is closely related to [[50edo]], but the [[patent val]]s differ on the mapping for [[7/1|7]]. It tempers out [[6144/6125]] in the 7-limit, [[99/98]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit, and like 50edo [[81/80]] in the 5-limit. It provides the [[optimal patent val]] for the 11- and 13- limit {{nowrap|43 & 57}} temperament tempering out 81/80, 99/98, 1350/1331, and in the 13-limit, 144/143.

Like [[6edo|6-]], [[35edo|35-]], [[47edo|47-]] and [[88edo]], 100edo possesses two approximations of the perfect fifth (at 58\100 and 59\100 respectively), each almost exactly six cents from just. One interesting consequence of this property is that one may have a closed circle of twelve good fifths (four wide, eight narrow) that bears little resemblance to [[12edo]].

Like [[6edo|6-]], [[35edo|35-]], [[47edo|47-]] and [[88edo]], 100edo possesses two approximations of the perfect fifth (at 58\100 and 59\100 respectively), each almost exactly six cents from just. It is therefore a strong 2.9.5.7.11.13.17.19 system for its size. One interesting consequence of this property is that one may have a closed circle of twelve good fifths (four wide, eight narrow) that bears little resemblance to [[12edo]].

=== Odd harmonics ===

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=== Subsets and supersets ===

Since 100 factors into {{factorization|100}}, 100edo has subset edos {{EDOs| 2, 4, 5, 10, 20, 25, and 50 }}.

Since 100 factors into {{factorization|100}}, 100edo has subset edos {{EDOs| 2, 4, 5, 10, 20, 25, and 50 }}. [[200edo]], which doubles it, corrects the perfect fifth to near-just quality. [[400edo]] further corrects many harmonics, making for a strong 19-limit system. [[1600edo]] and [[2000edo]] do very well in high prime limits.

== Intervals ==

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 edo is closely related to [[50edo]], but the [[patent val]]s differ on the mapping for [[7/1|7]]. It tempers out [[6144/6125]] in the 7-limit, [[99/98]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit, and like 50edo [[81/80]] in the 5-limit. It provides the [[optimal patent val]] for the 11- and 13- limit {{nowrap|43 &amp; 57}} temperament tempering out 81/80, 99/98, 1350/1331, and in the 13-limit, 144/143.
-Like [[6edo|6-]], [[35edo|35-]], [[47edo|47-]] and [[88edo]], 100edo possesses two approximations of the perfect fifth (at 58\100 and 59\100 respectively), each almost exactly six cents from just. One interesting consequence of this property is that one may have a closed circle of twelve good fifths (four wide, eight narrow) that bears little resemblance to [[12edo]].
+Like [[6edo|6-]], [[35edo|35-]], [[47edo|47-]] and [[88edo]], 100edo possesses two approximations of the perfect fifth (at 58\100 and 59\100 respectively), each almost exactly six cents from just. It is therefore a strong 2.9.5.7.11.13.17.19 system for its size. One interesting consequence of this property is that one may have a closed circle of twelve good fifths (four wide, eight narrow) that bears little resemblance to [[12edo]].
 === Odd harmonics ===
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-Since 100 factors into {{factorization|100}}, 100edo has subset edos {{EDOs| 2, 4, 5, 10, 20, 25, and 50 }}.
+Since 100 factors into {{factorization|100}}, 100edo has subset edos {{EDOs| 2, 4, 5, 10, 20, 25, and 50 }}. [[200edo]], which doubles it, corrects the perfect fifth to near-just quality. [[400edo]] further corrects many harmonics, making for a strong 19-limit system. [[1600edo]] and [[2000edo]] do very well in high prime limits.
 == Intervals ==