4/9-comma meantone: Difference between revisions
Add note about how close 15\26 is to the 4/9-comma meantone fifth; add ToDo tag (intended for 11-limit, 13-limit extensions) |
Add ragisma = 4375/4374 |
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{{Novelty}} | {{Novelty}} | ||
'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2|fifth]] is flattened by 4/9 of the [[81/80|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only 0. | '''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2|fifth]] is flattened by 4/9 of the [[81/80|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only a ragisma ([[4375/4374]], 0.395756¢) sharp of [[8/7]] (231.174094¢). | ||
The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament. | The most accurate choice for extending 4/9-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament. | ||