385/384: Difference between revisions
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Cmloegcmluin (talk | contribs) add original name, and make it primary name |
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| Monzo = -7 -1 1 1 1 | | Monzo = -7 -1 1 1 1 | ||
| Cents = 4.50256 | | Cents = 4.50256 | ||
| Name = keenanisma | | Name = undecimal kleisma, keenanisma | ||
| Color name = | | Color name = | ||
| FJS name = P1<sup>5, 7, 11</sup> | | FJS name = P1<sup>5, 7, 11</sup> | ||
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}} | }} | ||
The '''keenanisma''' is the [[11-limit]] [[comma]] '''385/384''' = {{Monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s. It is both the interval that separates [[77/64]] and [[6/5]], and, the sum of the [[schisma]] and the [[symbiotic comma]]. Tempering it out leads to a temperament of the 11-limit rank four [[Keenanismic family]]. | The '''undecimal kleisma'''<ref>https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_7286.html#7296</ref><ref>https://www.huygens-fokker.org/docs/intervals.html</ref> or '''keenanisma''' is the [[11-limit]] [[comma]] '''385/384''' = {{Monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s. It is both the interval that separates [[77/64]] and [[6/5]], and, the sum of the [[schisma]] and the [[symbiotic comma]]. Tempering it out leads to a temperament of the 11-limit rank four [[Keenanismic family]]. | ||
In addition to equating [[77/64]] and [[6/5]], tempering out the keenanisma equates [[48/35]] with [[11/8]], [[35/24]] with [[16/11]], and [[12/11]] with [[35/32]], which are [[7-limit]] intervals of low complexity, lying across from 1/1 in the hexanies 8/7-6/5-48/35-8/5-12/7-2 and 7/6-5/4-35/24-5/3-7/4-2. Hence keenanismic tempering allows the hexany to be viewed as containing some 11-limit harmony. The hexany is a fundamental construct in the 3D lattice of [[The_Seven_Limit_Symmetrical_Lattices|7-limit pitch classes]], the "deep holes" of the lattice as opposed to the "holes" represented by major and minor tetrads, and in terms of the [[The Seven Limit Symmetrical Lattices|cubic lattice of 7-limit tetrads]], the otonal tetrad with root 11 (or 11/8) is represented by [-2 0 0]: 1-6/5-48/35-12/7-2. In terms of 7-limit chord relationships, this complexity is as low as possible for an 11-limit projection comma, equaling the [0 1 -1] of 56/55 and less than the other alternatives. Since keenanismic temperament is also quite accurate, this singles it out as being of special interest. | In addition to equating [[77/64]] and [[6/5]], tempering out the keenanisma equates [[48/35]] with [[11/8]], [[35/24]] with [[16/11]], and [[12/11]] with [[35/32]], which are [[7-limit]] intervals of low complexity, lying across from 1/1 in the hexanies 8/7-6/5-48/35-8/5-12/7-2 and 7/6-5/4-35/24-5/3-7/4-2. Hence keenanismic tempering allows the hexany to be viewed as containing some 11-limit harmony. The hexany is a fundamental construct in the 3D lattice of [[The_Seven_Limit_Symmetrical_Lattices|7-limit pitch classes]], the "deep holes" of the lattice as opposed to the "holes" represented by major and minor tetrads, and in terms of the [[The Seven Limit Symmetrical Lattices|cubic lattice of 7-limit tetrads]], the otonal tetrad with root 11 (or 11/8) is represented by [-2 0 0]: 1-6/5-48/35-12/7-2. In terms of 7-limit chord relationships, this complexity is as low as possible for an 11-limit projection comma, equaling the [0 1 -1] of 56/55 and less than the other alternatives. Since keenanismic temperament is also quite accurate, this singles it out as being of special interest. | ||
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* [[Small comma]] | * [[Small comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== References == | |||
<references/> | |||
[[Category:11-limit]] | [[Category:11-limit]] | ||