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Aberschismic temperaments: 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/)
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: mapping generators: ~50/49, ~5
: mapping generators: ~50/49, ~5


[[Optimal tuning]] ([[POTE]]): ~50/49 = 41.379{{c}}, ~5/4 = 388.646{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~50/49 = 41.3652{{c}}, ~5/4 = 388.5128{{c}}
: [[error map]]: {{val| -0.410 +0.842 +1.378 -2.022 }}
* [[CWE]]: ~50/49 = 41.3793{{c}}, ~5/4 = 388.3030{{c}}
: error map: {{val| 0.000 +1.493 +1.989 -1.213 }}
<!-- * [[POTE]]: ~50/49 = 41.379{{c}}, ~5/4 = 388.646{{c}} -->


{{Optimal ET sequence|legend=1| 29, 58, 87, 145 }}
{{Optimal ET sequence|legend=1| 29, 58, 87, 145 }}


[[Badness]] (Smith): 0.103734
[[Badness]] (Sintel): 2.63


=== 11-limit ===
=== 11-limit ===
Line 320: Line 325:
Mapping: {{mapping| 29 46 0 14 33 | 0 0 1 1 1 }}
Mapping: {{mapping| 29 46 0 14 33 | 0 0 1 1 1 }}


Optimal tuning (POTE): ~45/44 = 41.379{{c}}, ~5/4 = 388.460{{c}}
Optimal tunings:
* WE: ~50/49 = 41.3637{{c}}, ~5/4 = 388.3136{{c}}
* CWE: ~50/49 = 41.3793{{c}}, ~5/4 = 388.0598{{c}}
<!-- * POTE: ~45/44 = 41.379{{c}}, ~5/4 = 388.460{{c}} -->


{{Optimal ET sequence|legend=0| 29, 58, 87, 145 }}
{{Optimal ET sequence|legend=0| 29, 58, 87, 145 }}


Badness (Smith): 0.034291
Badness (Sintel): 1.13


=== 13-limit ===
=== 13-limit ===
Line 333: Line 341:
Mapping: {{mapping| 29 46 0 14 33 40 | 0 0 1 1 1 1 }}
Mapping: {{mapping| 29 46 0 14 33 40 | 0 0 1 1 1 1 }}


Optimal tuning (POTE): ~45/44 = 41.379{{c}}, ~5/4 = 388.354{{c}}
Optimal tunings:
* WE: ~50/49 = 41.3623{{c}}, ~5/4 = 388.1942{{c}}
* CWE: ~50/49 = 41.3793{{c}}, ~5/4 = 387.9017{{c}}
<!-- * POTE: ~45/44 = 41.379{{c}}, ~5/4 = 388.354{{c}} -->


{{Optimal ET sequence|legend=0| 29, 58, 87, 145, 232, 377cef }}
{{Optimal ET sequence|legend=0| 29, 58, 87, 145, 232 }}


Badness (Smith): 0.018591
Badness (Sintel): 0.768


== Quanic ==
== Quanic ==
Line 347: Line 358:
: mapping generators: ~2, ~160/147
: mapping generators: ~2, ~160/147


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~160/147 = 140.493{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.6159{{c}}, ~160/147 = 140.4483{{c}}
: [[error map]]: {{val| -0.384 -0.098 -0.570 +1.933 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~160/147 = 140.4862{{c}}
: error map: {{val| 0.000 +0.476 -0.061 +2.842 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~160/147 = 140.493{{c}} -->


{{Optimal ET sequence|legend=1| 94, 111, 205 }}
{{Optimal ET sequence|legend=1| 94, 111, 205 }}


[[Badness]] (Smith): 0.179475
[[Badness]] (Sintel): 4.54


=== 11-limit ===
=== 11-limit ===
Line 360: Line 376:
Mapping: {{mapping| 1 1 -4 0 1 | 0 5 54 24 21 }}
Mapping: {{mapping| 1 1 -4 0 1 | 0 5 54 24 21 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~88/81 = 140.489{{c}}
Optimal tunings:
* WE: ~2 = 1199.7834{{c}}, ~88/81 = 140.4635{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~88/81 = 140.4850{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~88/81 = 140.489{{c}} -->


{{Optimal ET sequence|legend=0| 94, 111, 205 }}
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


Badness (Smith): 0.058678
Badness (Sintel): 1.94


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 1 -4 0 1 3 | 0 5 54 24 21 6 }}
Mapping: {{mapping| 1 1 -4 0 1 3 | 0 5 54 24 21 6 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 140.496{{c}}
Optimal tunings:
* WE: ~2 = 1199.6639{{c}}, ~13/12 = 140.4562{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.4904{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~13/12 = 140.496{{c}} -->


{{Optimal ET sequence|legend=0| 94, 111, 205 }}
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


Badness (Smith): 0.032481
Badness (Sintel): 1.34


=== 17-limit ===
=== 17-limit ===
Line 386: Line 408:
Mapping: {{mapping| 1 1 -4 0 1 3 -2 | 0 5 54 24 21 6 52 }}
Mapping: {{mapping| 1 1 -4 0 1 3 -2 | 0 5 54 24 21 6 52 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 140.497{{c}}
Optimal tunings:
* WE: ~2 = 1199.6699{{c}}, ~13/12 = 140.4586{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.4920{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~13/12 = 140.497{{c}} -->


{{Optimal ET sequence|legend=0| 94, 111, 205 }}
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


Badness (Smith): 0.021112
Badness (Sintel): 1.08


=== 19-limit ===
=== 19-limit ===
Line 399: Line 424:
Mapping: {{mapping| 1 1 -4 0 1 3 -2 -5 | 0 5 54 24 21 6 52 79 }}
Mapping: {{mapping| 1 1 -4 0 1 3 -2 -5 | 0 5 54 24 21 6 52 79 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 140.496{{c}}
Optimal tunings:
* WE: ~2 = 1199.6745{{c}}, ~13/12 = 140.4574{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.4908{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~13/12 = 140.496{{c}} -->


{{Optimal ET sequence|legend=0| 94, 111, 205 }}
{{Optimal ET sequence|legend=0| 94, 111, 205 }}


Badness (Smith): 0.017273
Badness (Sintel): 1.05


== Septiquarter ==
== Septiquarter ==
Line 410: Line 438:
[[Comma list]]: 5120/5103, 420175/419904
[[Comma list]]: 5120/5103, 420175/419904


{{Mapping|legend=1| 1 3 10 2 | 0 -7 -38 4 }}
{{Mapping|legend=1| 1 -4 -28 6 | 0 7 38 -4 }}
: mapping generators: ~2, ~147/128
: mapping generators: ~2, ~243/140


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~147/128 = 242.453{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7212{{c}}, ~243/140 = 957.3250{{c}}
: [[error map]]: {{val| -0.279 +0.435 -0.158 +0.201 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/140 = 957.5424{{c}}
: error map: {{val| 0.000 +0.842 +0.298 +1.004 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~243/140 = 957.547{{c}} -->


{{Optimal ET sequence|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }}
{{Optimal ET sequence|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }}


[[Badness]] (Smith): 0.053760
[[Badness]] (Sintel): 1.36


=== Semiseptiquarter ===
=== Semiseptiquarter ===
Line 424: Line 457:
Comma list: 5120/5103, 9801/9800, 14641/14580
Comma list: 5120/5103, 9801/9800, 14641/14580


Mapping: {{mapping| 2 6 20 4 15 | 0 -7 -38 4 -20 }}
Mapping: {{mapping| 2 -8 -56 12 -25 | 0 7 38 -4 20 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~121/105 = 242.4511{{c}}
Optimal tunings:
* WE: ~99/70 = 599.8953{{c}}, ~210/121 = 957.3819{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~210/121 = 957.5449{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~210/121 = 957.5489{{c}} -->


{{Optimal ET sequence|legend=0| 94, 198, 292, 490 }}
{{Optimal ET sequence|legend=0| 94, 198, 292, 490 }}


Badness (Smith): 0.064160
Badness (Sintel): 2.12


==== 13-limit ====
==== 13-limit ====
Line 437: Line 473:
Comma list: 352/351, 847/845, 1716/1715, 14641/14580
Comma list: 352/351, 847/845, 1716/1715, 14641/14580


Mapping: {{mapping| 2 6 20 4 15 7 | 0 -7 -38 4 -20 1 }}
Mapping: {{mapping| 2 -8 -56 12 -25 9 | 0 7 38 -4 20 -1 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~121/105 = 242.4448{{c}}
Optimal tunings:
* WE: ~99/70 = 599.8565{{c}}, ~210/121 = 957.3261{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~210/121 = 957.5508{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~210/121 = 957.5552{{c}} -->


{{Optimal ET sequence|legend=0| 94, 198, 490f }}
{{Optimal ET sequence|legend=0| 94, 198, 490f }}


Badness (Smith): 0.034834
Badness (Sintel): 1.44


== Countriton ==
== Countriton ==
Retrieved from "https://en.xen.wiki/w/Aberschismic_temperaments"