100edo: Difference between revisions

Line 1:

<youtube>shcrw2vtmJU</youtube>

~~The 100~~ equal ~~temperament divides~~ the octave into 100 ~~equal~~ parts of ~~precisely~~ 12 cents each. It is closely related to ~~50edo~~, but the patent vals differ on the mapping for 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 50 81/80 in the 5-limit. It provides the optimal patent val for the 11- and 13- limit 43&57 temperament tempering out 81/80, 99/98, 1350/1331, and in the 13-limit, 144/143.

'''100EDO''' is the [[EDO|equal division of the octave]] into 100 parts of exact 12 cents each. It is closely related to 50EDO, but the patent vals differ on the mapping for 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 43&57 temperament tempering out 81/80, 99/98, 1350/1331, and in the 13-limit, 144/143.

Like [[6edo|~~6edo~~]], [[35edo|~~35edo~~]], [[47edo|~~47edo~~]] and [[88edo|~~88edo~~]], ~~[[100edo|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|~~12edo~~]].

Like [[6edo|6EDO]], [[35edo|35EDO]], [[47edo|47EDO]] and [[88edo|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|12EDO]].

=Scales=

@@ Line 1: / Line 1: @@
 <youtube>shcrw2vtmJU</youtube>
-The 100 equal temperament divides the octave into 100 equal parts of precisely 12 cents each. It is closely related to 50edo, but the patent vals differ on the mapping for 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 50 81/80 in the 5-limit. It provides the optimal patent val for the 11- and 13- limit 43&amp;57 temperament tempering out 81/80, 99/98, 1350/1331, and in the 13-limit, 144/143.
+'''100EDO''' is the [[EDO|equal division of the octave]] into 100 parts of exact 12 cents each. It is closely related to 50EDO, but the patent vals differ on the mapping for 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 43&amp;57 temperament tempering out 81/80, 99/98, 1350/1331, and in the 13-limit, 144/143.
-Like [[6edo|6edo]], [[35edo|35edo]], [[47edo|47edo]] and [[88edo|88edo]], [[100edo|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|12edo]].
+Like [[6edo|6EDO]], [[35edo|35EDO]], [[47edo|47EDO]] and [[88edo|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|12EDO]].
 =Scales=