4/9-comma meantone: Difference between revisions
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{{Mathematical interest}} | {{Mathematical interest}} | ||
'''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 [[ | '''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 [[2187/1250]] (968.430¢), which is only a ragisma ([[4375/4374]], 0.396¢) flat of [[7/4]] (968.826¢). | ||
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. | ||
Latest revision as of 23:53, 15 July 2026
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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 2187/1250 (968.430¢), which is only a ragisma (4375/4374, 0.396¢) flat of 7/4 (968.826¢).
The most accurate choice for extending 4/9-comma meantone into the 7-limit, 11-limit or 13-limit is flattone temperament.