100edo: Difference between revisions
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'''100 EDO''' is the [[equal division of the octave]] into 100 parts of exact 12 cents each. It is closely related to [[50 EDO]], but the [[patent val]]s 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 EDO [[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. | '''100 EDO''' is the [[equal division of the octave]] into 100 parts of exact 12 cents each. It is closely related to [[50 EDO]], but the [[patent val]]s 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 EDO [[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. | ||
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Other, "gentle" alternatives to 22 EDO for pajara include [[78edo|78ddd]] and [[56edo|56d]]. The resulting 22-note scales have large and small steps in ratios of 4:3 or 3:2, respectively, and the rest of the spectrum of 22&[[34edo|34d]] temperaments is also usable. On the other hand, the “rough” alternatives to 22 EDO for pajara include [[58edo|58d]] and [[46edo|46d]]. The resulting 22-note scales have large and small steps in ratios of 4:1 or 3:1, respectively, and the rest of the spectrum of 12&[[34edo|34d]] temperaments up to 58d is also usable. | Other, "gentle" alternatives to 22 EDO for pajara include [[78edo|78ddd]] and [[56edo|56d]]. The resulting 22-note scales have large and small steps in ratios of 4:3 or 3:2, respectively, and the rest of the spectrum of 22&[[34edo|34d]] temperaments is also usable. On the other hand, the “rough” alternatives to 22 EDO for pajara include [[58edo|58d]] and [[46edo|46d]]. The resulting 22-note scales have large and small steps in ratios of 4:1 or 3:1, respectively, and the rest of the spectrum of 12&[[34edo|34d]] temperaments up to 58d is also usable. | ||
== Video == | |||
<youtube>shcrw2vtmJU</youtube> | |||
[[Category:100edo]] | [[Category:100edo]] | ||
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