Tritikleismic: Difference between revisions
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{{Infobox regtemp | |||
| Title = Tritikleismic | |||
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13.17 | |||
| Comma basis = [[1029/1024]], [[15625/15552]] (7-limit);<br> | |||
| Edo join 1 = 72 | Edo join 2 = 87 | |||
| Mapping = 3; 6 5 -2 3 14 18 | |||
| Generators = 6/5 | |||
| Generators tuning = 316.938 | |||
| Optimization method = CWE | |||
| MOS scales = [[3L 6s]], [[9L 3s]], [[12L 3s]], [[15L 12s]], ... | |||
| Pergen = (P8/3, cP5/6) | |||
| Odd limit 1 = 11 | Mistuning 1 = 2.41 | Complexity 1 = 57 | |||
| Odd limit 2 = 17-limit 21 | Mistuning 2 = 3.34 | Complexity 2 = 72 | |||
}} | |||
'''[[Tritikleismic]]''' is the [[rank]]-2 [[regular temperament|temperament]] that extends [[5-limit]] [[kleismic]] to the [[7-limit]] by [[tempering out]] [[1029/1024]], thus splitting the octave into three. In the 11-limit, it splits the perfect fourth into three [[11/10]]s (tempering out [[4000/3993]]). The mapping for 13 comes from 2.3.5.13 kleismic (sometimes known as ''cata''), which equates [[25/24]], [[26/25]], and [[27/26]]. Finally, the mapping for 17 is reached by equating two [[generator]]s of [[slendric]] to [[17/13]]. | |||
For technical data, see [[Kleismic family #Tritikleismic]]. | |||
== Intervals == | |||
{{Todo|complete section|inline=1}} | |||
== Tunings == | |||
{{Todo|complete section|inline=1}} | |||
[[Category:Rank-2 temperaments]] | |||
[[Category:Kleismic family]] | |||
[[Category:Gamelismic clan]] | |||
[[Category:Landscape microtemperaments]] | |||
Latest revision as of 02:11, 20 May 2026
| Tritikleismic |
17-limit 21-odd-limit: 3.34 ¢
17-limit 21-odd-limit: 72 notes
Tritikleismic is the rank-2 temperament that extends 5-limit kleismic to the 7-limit by tempering out 1029/1024, thus splitting the octave into three. In the 11-limit, it splits the perfect fourth into three 11/10s (tempering out 4000/3993). The mapping for 13 comes from 2.3.5.13 kleismic (sometimes known as cata), which equates 25/24, 26/25, and 27/26. Finally, the mapping for 17 is reached by equating two generators of slendric to 17/13.
For technical data, see Kleismic family #Tritikleismic.
Intervals
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Todo: complete section |
Tunings
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Todo: complete section |