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Aberschismic family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (2/2)
Line 339: Line 339:
: mapping generators: ~2, ~3, ~128/99
: mapping generators: ~2, ~3, ~128/99


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.8776{{c}}, ~128/99 = 441.7516{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7125{{c}}, ~3/2 = 702.6631{{c}}, ~128/99 = 441.8973{{c}}
: [[error map]]: {{val| -0.287 +0.421 -0.143 +0.216 +0.021 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8413{{c}}, ~128/99 = 441.9493{{c}}
: error map: {{val| 0.000 +0.886 +0.426 +0.866 +1.050 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8776{{c}}, ~128/99 = 441.7516{{c}} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]:  
* [[11-odd-limit]]:  
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/5 2/5 0 -1/15 -2/15 }}, {{monzo| 14/5 6/5 0 7/15 -16/15 }}, {{monzo| 16/5 -6/5 0 13/15 -4/15 }}, {{monzo| 16/5 -6/5 0 -2/15 11/15 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/5 2/5 0 -1/15 -2/15 }}, {{monzo| 14/5 6/5 0 7/15 -16/15 }}, {{monzo| 16/5 -6/5 0 13/15 -4/15 }}, {{monzo| 16/5 -6/5 0 -2/15 11/15 }}]
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7.11/9
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7.11/9


{{Optimal ET sequence|legend=1| 41, 87, 111, 152, 239, 391 }}
{{Optimal ET sequence|legend=1| 41, 65d, 87, 111, 152, 239, 391, 980bcde, 1132bcdde, 1371bbcddee }}


[[Badness]] (Smith): 0.994 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.19


== Namaka ==
== Namaka ==
Line 358: Line 363:
: mapping generators: ~2, ~400/231, ~5
: mapping generators: ~2, ~400/231, ~5


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~400/231 = 951.4956{{c}}, ~5/4 = 386.7868{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7179{{c}}, ~400/231 = 951.2909{{c}}, ~5/4 = 387.4982{{c}}
: [[error map]]: {{val| -0.282 +0.627 +0.620 -0.203 -1.074 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~400/231 = 951.5081{{c}}, ~5/4 = 387.3182{{c}}
: error map: {{val| 0.000 +1.061 +1.004 +0.395 -0.426 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~400/231 = 951.4956{{c}}, ~5/4 = 386.7868{{c}} -->


{{Optimal ET sequence|legend=1| 29, 53, 58, 87, 111, 140, 198 }}
{{Optimal ET sequence|legend=1| 29, 53, 58, 87, 111, 140, 198 }}


[[Badness]] (Smith): 1.74 × 10<sup>-3</sup>
[[Badness]] (Sintel): 2.09


=== 13-limit ===
=== 13-limit ===
Line 371: Line 381:
Mapping: {{mapping| 1 0 0 10 -6 -1 | 0 2 0 -12 9 3 | 0 0 1 1 1 1 }}
Mapping: {{mapping| 1 0 0 10 -6 -1 | 0 2 0 -12 9 3 | 0 0 1 1 1 1 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~26/15 = 951.4871{{c}}, ~5/4 = 386.6606{{c}}
Optimal tunings:
* WE: ~2 = 1199.7072{{c}}, ~26/15 = 951.2767{{c}}, ~5/4 = 387.4314{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.5016{{c}}, ~5/4 = 387.2360{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4871{{c}}, ~5/4 = 386.6606{{c}} -->


{{Optimal ET sequence|legend=0| 29, 53, 58, 87, 111, 140, 198 }}
{{Optimal ET sequence|legend=0| 29, 53, 58, 87, 111, 140, 198, 536f }}


Badness (Smith): 0.781 × 10<sup>-3</sup>
Badness (Sintel): 0.731


== Kahoupokane ==
== Kahoupokane ==
Line 385: Line 398:
: mapping generators: ~2, ~3, ~11/10
: mapping generators: ~2, ~3, ~11/10


[[Optimal tuning]] ([[CWE]]): ~2 = 1200.000{{c}}, ~3 = 1903.042{{c}}, ~11/10 = 157.992{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1911{{c}}, ~3/2 = 703.1412{{c}}, ~11/10 = 158.1068{{c}}
: [[error map]]: {{val| +0.191 +1.377 +0.996 +0.401 -5.710 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.0417{{c}}, ~11/10 = 157.9917{{c}}
: error map: {{val| 0.000 +1.087 +0.744 -0.018 -6.268 }}


Badness (Sintel): 2.734
{{Optimal ET sequence|legend=1| 7, 17c, 24d, 29, 46, 53, 82e, 99 }}
 
[[Badness]] (Sintel): 2.73


=== 13-limit ===
=== 13-limit ===
[[Subgroup]]: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
 
Comma list: 121/120, 169/168, 352/351


[[Comma list]]: 121/120, 169/168, 352/351
Mapping: {{mapping| 1 0 1 11 2 7 | 0 1 1 -5 1 -2 | 0 0 -2 -2 -1 -1 }}


{{Mapping|legend=1| 1 0 1 11 2 7 | 0 1 1 -5 1 -2 | 0 0 -2 -2 -1 -1 }}
Optimal tunings:
* WE: ~2 = 1200.4435{{c}}, ~3/2 = 703.1443{{c}}, ~11/10 = 158.4176{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9013{{c}}, ~11/10 = 158.1657{{c}}


[[Optimal tuning]] ([[CWE]]): ~2 = 1200.000{{c}}, ~3 = 1902.901{{c}}, ~11/10 = 158.166{{c}}
{{Optimal ET sequence|legend=0| 7, 17c, 24d, 29, 46, 53, 82e, 99, 181eef }}


Badness (Sintel): 1.269
Badness (Sintel): 1.27


== References ==
== References ==
Retrieved from "https://en.xen.wiki/w/Aberschismic_family"