3/11-comma meantone: Difference between revisions
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{{ | {{Mathematical interest}} | ||
'''3/11-comma meantone''' is a tuning of [[meantone]] temperament where the [[3/2|fifth]] is flattened by 3/11 of the [[81/80|syntonic comma]], producing a fifth of 696.090 cents. This is approximated well by [[50edo]]. | '''3/11-comma meantone''' is a tuning of [[meantone]] temperament where the [[3/2|fifth]] is flattened by 3/11 of the [[81/80|syntonic comma]], producing a fifth of 696.090 cents. This is approximated well by [[50edo]]. Its [[eigenmonzo]] is [[125/96]]. | ||
The fifth of 3/11-comma meantone is a good generator for mainline 5- and 7-limit meantone. The most natural way to extend 3/11-comma meantone into the 11, 13, 17 and 19-limits is [[meanenneadecal]] temperament. | The fifth of 3/11-comma meantone is a good generator for mainline 5- and 7-limit meantone. The most natural way to extend 3/11-comma meantone into the 11, 13, 17 and 19-limits is [[meanenneadecal]] temperament. | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||
Latest revision as of 11:53, 6 November 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. |
3/11-comma meantone is a tuning of meantone temperament where the fifth is flattened by 3/11 of the syntonic comma, producing a fifth of 696.090 cents. This is approximated well by 50edo. Its eigenmonzo is 125/96.
The fifth of 3/11-comma meantone is a good generator for mainline 5- and 7-limit meantone. The most natural way to extend 3/11-comma meantone into the 11, 13, 17 and 19-limits is meanenneadecal temperament.