Septischismic clan: Difference between revisions
Move gariwizmic here |
Move sextile here |
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* [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]] | * [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]] | ||
* ''[[Newt]]'' (+2401/2400) → [[Breedsmic temperaments #Newt|Breedsmic temperaments]] | * ''[[Newt]]'' (+2401/2400) → [[Breedsmic temperaments #Newt|Breedsmic temperaments]] | ||
* ''[[Alphatrident]]'' (+6144/6125) → [[Alphatricot family #Alphatrident|Alphatricot family]] | * ''[[Alphatrident]]'' (+6144/6125) → [[Alphatricot family #Alphatrident|Alphatricot family]] | ||
* ''[[Vulture]]'' (+4375/4374) → [[Vulture family #Vulture|Vulture family]] | * ''[[Vulture]]'' (+4375/4374) → [[Vulture family #Vulture|Vulture family]] | ||
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* ''[[Garistearn]]'' (+118098/117649) → [[Stearnsmic clan #Garistearn|Stearnsmic clan]] | * ''[[Garistearn]]'' (+118098/117649) → [[Stearnsmic clan #Garistearn|Stearnsmic clan]] | ||
Considered below are cotoneum, gariwizmic, satin, and world calendar. | Considered below are cotoneum, gariwizmic, satin, sextile, and world calendar. | ||
=== 2.3.7.11 subgroup === | === 2.3.7.11 subgroup === | ||
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Badness (Sintel): 0.871 | Badness (Sintel): 0.871 | ||
== Sextile == | |||
: ''For the 5-limit version, see [[Schismic–commatic equivalence continuum #Sextile (5-limit)]].'' | |||
Sextile tempers out the [[landscape comma]] with a 1/6-octave period and is the {{nowrap| 12 & 270 }} temperament. | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 250047/250000, 33554432/33480783 | |||
{{Mapping|legend=1| 6 0 71 150 | 0 1 -6 -14 }} | |||
: mapping generators: ~4096/3645, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~4096/3645 = 199.9828{{c}}, ~3/2 = 702.1521{{c}} | |||
: [[error map]]: {{val| -0.103 +0.094 +0.173 -0.088 }} | |||
* [[CWE]]: ~4096/3645 = 200.0000{{c}}, ~3/2 = 702.2187{{c}} | |||
: error map: {{val| 0.000 +0.264 +0.374 +0.112 }} | |||
{{Optimal ET sequence|legend=1| 12, …, 258, 270, 1362c, 1632c, …, 2442bc, 2712bc }} | |||
[[Badness]] (Sintel): 1.77 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 5632/5625, 9801/9800, 151263/151250 | |||
Mapping: {{mapping| 6 0 71 150 230 | 0 1 -6 -14 -22 }} | |||
Optimal tunings: | |||
* WE: ~55/49 = 199.9817{{c}}, ~3/2 = 702.1383{{c}} | |||
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2080{{c}} | |||
{{Optimal ET sequence|legend=0| 12, …, 258e, 270, 822, 1092, 1362c }} | |||
Badness (Sintel): 0.981 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1716/1715, 2080/2079, 5632/5625, 10648/10647 | |||
Mapping: {{mapping| 6 0 71 150 230 279 | 0 1 -6 -14 -22 -27 }} | |||
Optimal tunings: | |||
* WE: ~55/49 = 199.9804{{c}}, ~3/2 = 702.1260{{c}} | |||
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2001{{c}} | |||
{{Optimal ET sequence|legend=0| 12f, …, 258ef, 270, 552, 822, 1092, 1914cde }} | |||
Badness (Sintel): 0.788 | |||
=== 2.3.5.7.11.13.19 subgroup === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625 | |||
Mapping: {{mapping| 6 0 71 150 230 279 35 | 0 1 -6 -14 -22 -27 -1 }} | |||
Optimal tunings: | |||
* WE: ~55/49 = 199.9826{{c}}, ~3/2 = 702.1359{{c}} | |||
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2003{{c}} | |||
{{Optimal ET sequence|legend=0| 12f, 258ef, 270, 552, 822, 1092 }} | |||
Badness (Sintel): 0.634 | |||
== World calendar == | == World calendar == | ||