Kalismic temperaments: Difference between revisions
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== Hnoss == | == Hnoss == | ||
To the wizma {{monzo| -6 -8 2 5 }} = 420175/419904, the kalisma is a natural complement, as their product is the [[tinge]]. | To the [[wizma]] {{monzo| -6 -8 2 5 }} = 420175/419904, the kalisma is a natural complement, as their product is the [[tinge]]. | ||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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Badness: 0.391 × 10<sup>-3</sup> | Badness: 0.391 × 10<sup>-3</sup> | ||
== Linus == | |||
{{Main| Linus }} | |||
Linus [[tempering out|tempers out]] the [[linus comma]], {{monzo| 11 -10 -10 10 }} in the 7-limit and can be described as the 80 & 130 & 270 temperament. It tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99. | |||
=== 7-limit === | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 578509309952/576650390625 | |||
{{Mapping|legend=1| 10 0 0 -11 | 0 1 0 1 | 0 0 1 1 }} | |||
: mapping generators: ~15/14, ~3, ~5 | |||
[[Optimal tuning]] ([[CTE]]): ~15/14 = 1\10, ~3/2 = 702.0437, ~5/4 = 386.5040 | |||
{{Optimal ET sequence|legend=1| 50, 60, 80, 130, 270, 1270, 1540, 1810, 1940, 2080, 2210c, 2480c }} | |||
[[Badness]]: 1.12 × 10<sup>-3</sup> | |||
=== 11-limit === | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 9801/9800, 391314/390625 | |||
{{Mapping|legend=1| 10 0 0 -11 4 | 0 1 0 1 -1 | 0 0 1 1 2 }} | |||
[[Optimal tuning]] ([[CTE]]): ~15/14 = 1\10, ~3/2 = 702.0010, ~5/4 = 386.5927 | |||
{{Optimal ET sequence|legend=1| 50, 60e, 80, 130, 190, 270, 670, 940, 1130, 1400, 1800c, 2070c, 2340c }} | |||
[[Badness]]: 1.12 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1001/1000, 4225/4224, 4459/4455 | |||
Mapping: {{mapping| 10 0 0 -11 4 37 | 0 1 0 1 -1 0 | 0 0 1 1 2 0 }} | |||
Optimal tuning (CTE): ~15/14 = 1\10, ~3/2 = 702.0010, ~5/4 = 386.5928 | |||
Optimal ET sequence: {{Optimal ET sequence| 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def }} | |||
Badness: 0.771 × 10<sup>-3</sup> | |||
== Rishi == | == Rishi == | ||