Kleismic rank three family: Difference between revisions
m →Enlil: +alternative name |
This 7-limit rank-3 temperament should not be simply called "kleismic". I put "rank-3 kleismic" as a placeholder |
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The '''kleismic rank-3 family''' of temperaments tempers out the kleisma, [[15625/15552]]. If nothing else is tempered out in the 7-limit, we have a [[planar temperament]]. With an 11-limit comma we get an 11-limit temperament, and so forth. | The '''kleismic rank-3 family''' of temperaments tempers out the kleisma, [[15625/15552]]. If nothing else is tempered out in the 7-limit, we have a [[planar temperament]]. With an 11-limit comma we get an 11-limit temperament, and so forth. | ||
== | == Rank-3 kleismic == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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: [[Eigenmonzo]]s (unchanged intervals): 2, 7/6, 4/3 | : [[Eigenmonzo]]s (unchanged intervals): 2, 7/6, 4/3 | ||
{{Val list|legend=1| 15, 19, 34d, 49, 53, 72, 140, 212 }} | {{Val list|legend=1| 15, 19, 34d, 49, 53, 72, 140, 212, 617c, 829c }} | ||
== Enlil == | == Enlil == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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: [[Eigenmonzo]]s (unchanged intervals): 2, 4/3, 14/11 | : [[Eigenmonzo]]s (unchanged intervals): 2, 4/3, 14/11 | ||
{{Val list|legend=1| 15, 19, 34, 38, 53, 68, 72, 140, 159, 212, 284 }} | {{Val list|legend=1| 15, 19, 34, 38, 53, 68, 72, 140, 159, 212, 284, 496ce, 583cde, 655cde, 867ccdee, 939ccddee }} | ||
[[Badness]]: 0.798 × 10<sup>-3</sup> | [[Badness]]: 0.798 × 10<sup>-3</sup> | ||
=== 13-limit (aka sumatra) === | === 13-limit (aka sumatra) === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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: [[Eigenmonzo]]s (unchanged intervals): 2, 13/11, 14/11 | : [[Eigenmonzo]]s (unchanged intervals): 2, 13/11, 14/11 | ||
Vals: {{Val list| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299 }} | Vals: {{Val list| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 511cdef }} | ||
Badness: 0.680 × 10<sup>-3</sup> | Badness: 0.680 × 10<sup>-3</sup> | ||
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== Enki == | == Enki == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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== Isimud == | == Isimud == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 109: | Line 103: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||