Ragismic family: Difference between revisions
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The '''ragismic family''' of temperaments are rank-3 microtemperaments which temper out [[4375/4374]]. | The '''ragismic family''' of temperaments are rank-3 microtemperaments which temper out [[4375/4374]]. | ||
== Ragismic == | == Ragismic == | ||
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Scales: [[Ragismic19]], [[Ragismic chromatic]] | Scales: [[Ragismic19]], [[Ragismic chromatic]] | ||
=== Overview to extensions === | |||
Temperaments discussed elsewhere include: | |||
* ''[[Sensigh]]'' → [[Sengic family #Sensigh|Sengic family]] | |||
* ''[[Catakleismoid]]'' → [[Kleismic rank-3 family #Catakleismoid|Kleismic rank-3 family]] | |||
* ''[[Ennealimmic]]'' → [[Breed family #Ennealimmic|Breed family]] | |||
Considered below are beyla, ulmo, raglympic, thor, heimdall, bragi, vidar. | |||
== Beyla == | == Beyla == | ||
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Badness (Sintel): 0.871 | Badness (Sintel): 0.871 | ||
== Raglympic == | |||
Named by [[Eufalesio]] in 2026, raglympic is the intersection of [[olympic]] and ragismic, as its name implies. It is also a detemperament of [[ponta]], achieved by observing the schisma. As such, the 5 generator can be taken to be a schisma. | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 4375/4374, 131072/130977 | |||
{{Mapping|legend=1| 1 0 0 1 15 | 0 1 0 7 −19 | 0 0 1 −4 8 }} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.9495{{c}}, ~3/2 = 702.0619{{c}}, ~5/4 = 386.3920{{c}} | |||
: [[error map]]: {{val| -0.0505 +0.0565 -0.0226 +0.0395 +0.0362 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0892{{c}}, ~5/4 = 386.4019{{c}} | |||
: error map: {{val| 0.0000 +0.1342 +0.0882 +0.1909 +0.2024 }} | |||
{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 99, 171, 217, 224, 270, 494, 764, 1205, 1475, 1969, 2239, 4208de, 9891bbcddeee }} | |||
[[Badness]] (Sintel): 0.957 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 2080/2079, 4096/4095, 4375/4374 | |||
{{Mapping|legend=0| 1 0 0 1 15 11 | 0 1 0 7 −19 -9 | 0 0 1 −4 8 3 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.9615{{c}}, ~3/2 = 702.0459{{c}}, ~5/4 = 386.3501{{c}} | |||
: error map: {{val| -0.0385 +0.0523 -0.0407 +0.0949 +0.1485 -0.1987 }} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0686{{c}}, ~5/4 = 386.3614{{c}} | |||
: error map: {{val| 0.0000 +0.1136 +0.0477 +0.2089 +0.2692 -0.0612 }} | |||
{{Optimal ET sequence|legend=0| 7, 39, 46, 53, 99, 171, 217, 224, 270, 494, 764, 935, 1205, 1699 }} | |||
Badness (Sintel): 0.431 | |||
== Thor == | == Thor == | ||
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[[Category:Ragismic family| ]] <!-- main article --> | [[Category:Ragismic family| ]] <!-- main article --> | ||
[[Category:Ragismic| ]] <!-- key article --> | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Catalogs of rank-3 temperaments]] | [[Category:Catalogs of rank-3 temperaments]] | ||