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. | 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 === | === Odd harmonics === | ||
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=== Subsets and supersets === | === 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 == | == Intervals == | ||
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== Instruments == | == Instruments == | ||
=== Lumatone === | |||
[[Lumatone mapping for 100edo]] | |||
=== Skip fretting === | === Skip fretting === | ||
One way to play 100edo on a [[20edo]] guitar is to tune the strings 13\100 apart, or 156 [[cents]]. All examples on this page are for 7-string guitar. | One way to play 100edo on a [[20edo]] guitar is to tune the strings 13\100 apart, or 156 [[cents]]. All examples on this page are for 7-string guitar. | ||
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* [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (2022) | * [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (2022) | ||
; [[Iceface H. Wakabayashi]] (微分音チャンネル) | |||
* [https://www.youtube.com/watch?v=shcrw2vtmJU ''Microtonal Piano in 100 tone equal temperament (100EDO) (Microtonal Music)''] (2016) (this is the same as the video linked above, to use in case the embedded video refuses to play) | |||