Semicathartismic clan: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''semicanousmic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[semicanousma]] ({{monzo|legend=1| -2 -6 -1 0 4 }}, [[ratio]]: 14641/14580). | The '''semicanousmic clan''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[semicanousma]] ({{monzo|legend=1| -2 -6 -1 0 4 }}, [[ratio]]: 14641/14580). | ||
For the rank-4 semicanousmic temperament, see [[Catalog of rank-4 temperaments #Semicanousmic (14641/14580)]]. | For the rank-4 semicanousmic temperament, see [[Catalog of rank-4 temperaments #Semicanousmic (14641/14580)]]. | ||
== Deuteromere == | == Deuteromere == | ||
[[File:Lattice Semicanousmic.png|thumb|Lattice]] | [[File:Lattice Semicanousmic.png|thumb|Lattice for deutermere.]] | ||
[[File:Lattice Semicanousmic Rearranged.png|thumb| | [[File:Lattice Semicanousmic Rearranged.png|thumb|Ditto, but re-arranged into neutral thirds]] | ||
[[Subgroup]]: 2.3.5.11 | [[Subgroup]]: 2.3.5.11 | ||
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[[Badness]] (Sintel): 1.18 | [[Badness]] (Sintel): 1.18 | ||
=== | === Overview to extensions === | ||
Temperaments discussed elsewhere are: | |||
* ''[[Urania]]'' (+81/80 or 121/120) → [[Rastmic rank-3 clan #Urania|Rastmic rank-3 clan]] | |||
* ''[[Triglav]]'' (+3025/3024 or 3136/3125) → [[Hemimean family #Triglav|Hemimean family]] | |||
* ''[[Semicanou]]'' (+9801/9800) → [[Canou family #Semicanou|Canou family]] | |||
* | |||
* | |||
Considered below are syndeute and hemireiwa, in addition to the add-17 extension of deuteromere. | |||
== Syndeute == | == Syndeute == | ||
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Badness (Sintel): 1.78 | Badness (Sintel): 1.78 | ||
== Subgroup extensions == | |||
=== Deuteromere (2.3.5.11.17) === | |||
Subgroup: 2.3.5.11.17 | |||
Comma list: 1089/1088, 14641/14580 | |||
Subgroup-val mapping: {{mapping| 1 0 -2 0 -6 | 0 1 2 2 6 | 0 0 4 1 2 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1200.0291{{c}}, ~3/2 = 702.3333{{c}}, ~11/9 = 345.4465{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3266{{c}}, ~11/9 = 345.4394{{c}} | |||
{{Optimal ET sequence|legend=0| 24, 31g, 55g, 56gg, 63, 70c, 80gg, 87, 111, 118, 205, 528e, 733e }} | |||
Badness (Sintel): 1.01 | |||
==== 2.3.5.11.17.19 subgroup ==== | |||
Subgroup: 2.3.5.11.17.19 | |||
Comma list: 1089/1088, 1216/1215, 1445/1444 | |||
Subgroup-val mapping: {{mapping| 1 0 -2 0 -6 -8 | 0 1 2 2 6 7 | 0 0 4 1 2 4 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1200.0556{{c}}, ~3/2 = 702.2904{{c}}, ~11/9 = 345.4565{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2728{{c}}, ~11/9 = 345.4432{{c}} | |||
{{Optimal ET sequence|legend=0| 24, 55gh, 63, 70c, 80gghh, 87, 94, 111, 118, 205, 323, 528e }} | |||
Badness (Sintel): 0.630 | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Semicanousmic clan| ]] <!-- main article --> | [[Category:Semicanousmic clan| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||