2/5-comma meantone: Difference between revisions
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'''2/5-comma meantone''' is a tuning of meantone where the [[3/2|fifth]] is flattened by 2/5 of the [[81/80|syntonic comma]], producing a fifth of 693.352 cents. This is approximated well by [[45edo]]. | '''2/5-comma meantone''' is a tuning of meantone where the [[3/2|fifth]] is flattened by 2/5 of the [[81/80|syntonic comma]], producing a fifth of 693.352 cents; its [[eigenmonzo]] is [[27/25]]. This is approximated well by [[45edo]]. | ||
The most accurate choice for extending | The most accurate choice for extending 2/5-comma meantone into the [[7-limit]], [[11-limit]] or [[13-limit]] is [[flattone]] temperament. In fact, 2/5-comma meantone’s fifth is almost exactly the optimal [[CTE]] generator for 11-limit flattone — less than 0.2 cents different. | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||
Latest revision as of 22:31, 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. |
2/5-comma meantone is a tuning of meantone where the fifth is flattened by 2/5 of the syntonic comma, producing a fifth of 693.352 cents; its eigenmonzo is 27/25. This is approximated well by 45edo.
The most accurate choice for extending 2/5-comma meantone into the 7-limit, 11-limit or 13-limit is flattone temperament. In fact, 2/5-comma meantone’s fifth is almost exactly the optimal CTE generator for 11-limit flattone — less than 0.2 cents different.