Kalismic temperaments: Difference between revisions
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Document diaspheric |
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* ''[[Odin]]'' (+151263/151250) → [[Landscape family #Odin|Landscape family]] | * ''[[Odin]]'' (+151263/151250) → [[Landscape family #Odin|Landscape family]] | ||
Considered below are lycoris, van gogh, sif, and linus, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Kalismic (9801/9800)]]. | Considered below are lycoris, van gogh, sif, diaspheric, and linus, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Kalismic (9801/9800)]]. | ||
== Lycoris == | == Lycoris == | ||
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{{Mapping|legend=1| 2 0 1 7 11 | 0 1 0 1 -1 | 0 0 4 -5 -1 }} | {{Mapping|legend=1| 2 0 1 7 11 | 0 1 0 1 -1 | 0 0 4 -5 -1 }} | ||
: mapping generators: ~99/70, ~3 | : mapping generators: ~99/70, ~3, ~48/35 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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Badness (Sintel): 0.317 | Badness (Sintel): 0.317 | ||
== Diaspheric == | |||
Diaspheric is notable for detempering [[diaschismic family #Septimal diaschismic|diaschismic]]. It was named by [[Eufalesio]] in 2026 as a variant of ''diaschismic''. | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 9801/9800, 2252800/2250423 | |||
{{Mapping|legend=1| 2 0 1 16 20 | 0 1 0 -5 -7 | 0 0 2 3 5 }} | |||
: mapping generators: ~99/70, ~3, ~1323/704 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~99/70 = 599.9742{{c}}, ~3/2 = 702.0681{{c}}, ~1323/704 = 1093.1024{{c}} | |||
: [[error map]]: {{val| -0.052 +0.061 -0.015 +0.166 -0.138 }} | |||
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0803{{c}}, ~1323/704 = 1093.1807{{c}} | |||
: error map: {{val| 0.000 +0.133 +0.048 +0.275 -0.033 }} | |||
{{Optimal ET sequence|legend=1| 46, 58, 104c, 154ce, 166, 212, 224, 270, 494, 764 }} | |||
[[Badness]] (Sintel): 0.950 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1716/1715, 2080/2079, 10648/10647 | |||
{{Mapping|legend=0| 2 0 1 16 20 25 | 0 1 0 -5 -7 -9 | 0 0 2 3 5 6 }} | |||
Optimal tunings: | |||
* WE: ~99/70 = 599.9720{{c}}, ~3/2 = 702.0544{{c}}, ~1014/539 = 1093.1699{{c}} | |||
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0759{{c}}, ~1014/539 = 1093.1900{{c}} | |||
{{Optimal ET sequence|legend=0| 46, 58, 104c, 154cef, 166, 212, 224, 270, 494, 764, 1258, 1810d, 2304d, 2574d }} | |||
Badness (Sintel): 0.454 | |||
== Linus == | == Linus == | ||