4/9-comma meantone: Difference between revisions
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'''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¢). | '''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¢). | ||
Revision as of 11:42, 18 March 2025
4/9-comma meantone is a tuning of meantone where the fifth is flattened by 4/9 of the 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.