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¢). | ||
Latest revision as of 22:13, 10 August 2025
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
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.