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Septischismic family: Difference between revisions

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Created page with "The '''garischismic family''' of rank-3 temperaments tempers out the garischisma, {{monzo| 25 -14 0 -1 }} = 33554432/33480783...."
 
Complete the data
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{{Mapping|legend=1| 1 0 0 25 | 0 1 0 -14 | 0 0 1 0 }}
{{Mapping|legend=1| 1 0 0 25 | 0 1 0 -14 | 0 0 1 0 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2224, ~5/4 = 386.3137
: mapping generators: ~2, ~3, ~5
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.2224, ~5/4 = 386.3137
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.2124, ~5/4 = 386.4496


{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}
{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}
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{{Mapping|legend=1| 1 0 0 25 -33 | 0 1 0 -14 23 | 0 0 1 0 0 }}
{{Mapping|legend=1| 1 0 0 25 -33 | 0 1 0 -14 23 | 0 0 1 0 0 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2280, ~5/4 = 386.3137
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.2280, ~5/4 = 386.3137
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.2290, ~5/4 = 386.3819


{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851, 1121 }}
{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851, 1121 }}
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Mapping: {{mapping| 1 0 0 25 -33 -13 | 0 1 0 -14 23 12 | 0 0 1 0 0 -1 }}
Mapping: {{mapping| 1 0 0 25 -33 -13 | 0 1 0 -14 23 12 | 0 0 1 0 0 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2289, ~5/4 = 386.2869
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 702.2289, ~5/4 = 386.2869
* CWE: ~2 = 1\1, ~3/2 = 702.2303, ~5/4 = 386.3031


{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851, 2283b }}
{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851, 2283b }}
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== Androschismic ==
== Androschismic ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 151263/151250, [[Reef comma|200704/200475]]
 
{{Mapping|legend=1| 1 0 0 25 62 | 0 1 0 -14 -34 | 0 0 1 0 -2 }}


Comma list: 151263/151250, [[Reef comma|200704/200475]]
[[Optimal tuning]]s:
* CTE: ~2 = 1\1, ~3/2 = 702.2308, ~5/4 = 386.3806
* CWE: ~2 = 1\1, ~3/2 = 702.2178, ~5/4 = 386.5048


Mapping: {{mapping| 1 0 0 25 62 | 0 1 0 -14 -34 | 0 0 1 0 -2 }}
{{Optimal ET sequence|legend=1| 12, 29, 41, …, 229, 270, 581, 822, 851, 863e, 1133, 1403, 3117bce, 3387bce, 4520bcdee, 4790bbcdee, 5923bbccddeee }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.231, ~5/4 = 386.381
[[Badness]]: 1.64 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 0 0 25 62 82 | 0 1 0 -14 -34 -43 | 0 0 1 0 -2 -3 }}
Mapping: {{mapping| 1 0 0 25 62 82 | 0 1 0 -14 -34 -43 | 0 0 1 0 -2 -3 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.230, ~5/4 = 386.375
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 702.2305, ~5/4 = 386.3748
* CWE: ~2 = 1\1, ~3/2 = 702.2174, ~5/4 = 386.4968
 
Optimal ET sequence: {{Optimal ET sequence| 12f, 29, 41, …, 229, 241, 270, 552, 581, 822, 851, 863ef, 1133, 1403, 2536bcdef, 3117bcef, 4250bcdeeff, 4520bcdeeff, 5653bbccddeeeff }}
 
Badness: 1.01 × 10<sup>-3</sup>


[[Category:Temperament families]]
[[Category:Temperament families]]
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