1/11-comma meantone: Difference between revisions
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{{ | {{Mathematical interest}} | ||
'''1/11-comma meantone''' is a tuning of meantone where the [[3/2|fifth]] is flattened by 1/11 of the [[81/80|syntonic comma]], producing a fifth of 699.9998836 cents. This is approximated well by [[12edo]]. | '''1/11-comma meantone''' is a tuning of meantone where the [[3/2|fifth]] is flattened by 1/11 of the [[81/80|syntonic comma]], producing a fifth of 699.9998836 cents. This is approximated well by [[12edo]], differing only by 1/132 of [[Kirnberger's atom]]. Its [[eigenmonzo]] is [[10935/8192]], which is a [[schisma]]-raised [[4/3]]. This means that 1/11 of a syntonic comma is very close to the value of a schisma. | ||
In the [[7-limit]], 1/11-comma’s fifth is a good [[sharptone]] generator. In the [[11-limit]], it becomes a good [[meanertone]] generator. | In the [[7-limit]], 1/11-comma’s fifth is a good [[sharptone]] generator. In the [[11-limit]], it becomes a good [[meanertone]] generator. | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||
Latest revision as of 11:44, 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. |
1/11-comma meantone is a tuning of meantone where the fifth is flattened by 1/11 of the syntonic comma, producing a fifth of 699.9998836 cents. This is approximated well by 12edo, differing only by 1/132 of Kirnberger's atom. Its eigenmonzo is 10935/8192, which is a schisma-raised 4/3. This means that 1/11 of a syntonic comma is very close to the value of a schisma.
In the 7-limit, 1/11-comma’s fifth is a good sharptone generator. In the 11-limit, it becomes a good meanertone generator.