Xenharmonic Wiki

Aberschismic temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Switch to Sintel's badness, WE & CWE tunings, per community consensus (2/)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (3/3)
Line 491: Line 491:
[[Comma list]]: 5120/5103, 7558272/7503125
[[Comma list]]: 5120/5103, 7558272/7503125


{{Mapping|legend=1| 1 6 19 -7 | 0 -9 -34 20 }}
{{Mapping|legend=1| 1 -3 -15 13 | 0 9 34 -20 }}
: mapping generators: ~2, ~1728/1225
: mapping generators: ~2, ~1225/864


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~1728/1225 = 588.582{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.4179{{c}}, ~1225/864 = 611.1213{{c}}
: [[error map]]: {{val| -0.582 -0.117 +0.541 +1.181 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1225/864 = 611.4120{{c}}
: error map: {{val| 0.000 +0.753 +1.695 +2.934 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~1225/864 = 611.418{{c}} -->


{{Optimal ET sequence|legend=1| 53, 157, 210 }}
{{Optimal ET sequence|legend=1| 51c, 53, 157, 210, 473cdd }}


[[Badness]] (Smith): 0.131191
[[Badness]] (Sintel): 3.32


=== 11-limit ===
=== 11-limit ===
Line 505: Line 510:
Comma list: 176/175, 5120/5103, 41503/41472
Comma list: 176/175, 5120/5103, 41503/41472


Mapping: {{mapping| 1 6 19 -7 27 | 0 -9 -34 20 -48 }}
Mapping: {{mapping| 1 -3 -15 13 -21 | 0 9 34 -20 48 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~108/77 = 588.545{{c}}
Optimal tunings:
* WE: ~2 = 1199.5178{{c}}, ~77/54 = 611.2097{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/54 = 611.4495{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~77/54 = 611.455{{c}} -->


{{Optimal ET sequence|legend=0| 53, 104c, 157 }}
{{Optimal ET sequence|legend=0| 51ce, 53, 104c, 157 }}


Badness (Smith): 0.084782
Badness (Sintel): 2.80


=== 13-limit ===
=== 13-limit ===
Line 518: Line 526:
Comma list: 176/175, 351/350, 847/845, 2197/2187
Comma list: 176/175, 351/350, 847/845, 2197/2187


Mapping: {{mapping| 1 6 19 -7 27 14 | 0 -9 -34 20 -48 -21 }}
Mapping: {{mapping| 1 -3 -15 13 -21 -7 | 0 9 34 -20 48 21 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~108/77 = 588.544{{c}}
Optimal tunings:
* WE: ~2 = 1199.5944{{c}}, ~77/54 = 611.2491{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/54 = 611.4506{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~77/54 = 588.544{{c}} -->


{{Optimal ET sequence|legend=0| 53, 104c, 157 }}
{{Optimal ET sequence|legend=0| 51ce, 53, 104c, 157 }}


Badness (Smith): 0.042321
Badness (Sintel): 1.75


== Artoneutral ==
== Artoneutral ==
Line 533: Line 544:
[[Comma list]]: 5120/5103, 3828125/3779136
[[Comma list]]: 5120/5103, 3828125/3779136


{{Mapping|legend=1| 1 8 18 -20 | 0 -9 -22 32 }}
{{Mapping|legend=1| 1 -1 -4 12 | 0 9 22 -32 }}
: mapping generators: ~2, ~105/64
: mapping generators: ~2, ~128/105


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~105/64 = 855.2452{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1400{{c}}, ~128/105 = 344.7929{{c}}
: [[error map]]: {{val| +0.140 +1.041 -1.430 -0.518 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 344.7531{{c}}
: error map: {{val| 0.000 +0.823 -1.746 -0.925 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~128/105 = 344.7548{{c}} -->


{{Optimal ET sequence|legend=1| 87, 94, 181 }}
{{Optimal ET sequence|legend=1| 87, 94, 181 }}


[[Badness]] (Smith): 0.157120
[[Badness]] (Sintel): 3.98


=== 11-limit ===
=== 11-limit ===
Line 547: Line 563:
Comma list: 385/384, 2200/2187, 4000/3993
Comma list: 385/384, 2200/2187, 4000/3993


Mapping: {{mapping| 1 8 18 -20 17 | 0 -9 -22 32 -19 }}
Mapping: {{mapping| 1 -1 -4 12 -2 | 0 9 22 -32 19 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~18/11 = 855.2397{{c}}
Optimal tunings:
* WE: ~2 = 1200.1668{{c}}, ~11/9 = 344.8027{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7557{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7603{{c}} -->


{{Optimal ET sequence|legend=0| 87, 181 }}
{{Optimal ET sequence|legend=0| 87, 181 }}


Badness (Smith): 0.045920
Badness (Sintel): 1.52


=== 13-limit ===
=== 13-limit ===
Line 560: Line 579:
Comma list: 325/324, 352/351, 385/384, 1575/1573
Comma list: 325/324, 352/351, 385/384, 1575/1573


Mapping: {{mapping| 1 8 18 -20 17 -2 | 0 -9 -22 32 -19 8 }}
Mapping: {{mapping| 1 -1 -4 12 -2 6 | 0 9 22 -32 19 -8 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~18/11 = 855.2369{{c}}
Optimal tunings:
* WE: ~2 = 1200.0662{{c}}, ~11/9 = 344.7804{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7617{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7631{{c}} -->


{{Optimal ET sequence|legend=0| 87, 181 }}
{{Optimal ET sequence|legend=0| 87, 181 }}


Badness (Smith): 0.026257
Badness (Sintel): 1.08


=== 17-limit ===
=== 17-limit ===
Line 573: Line 595:
Comma list: 325/324, 352/351, 375/374, 385/384, 595/594
Comma list: 325/324, 352/351, 375/374, 385/384, 595/594


Mapping: {{mapping| 1 8 18 -20 17 -2 44 | 0 -9 -22 32 -19 8 -56 }}
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 | 0 9 22 -32 19 -8 56 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~18/11 = 855.2495{{c}}
Optimal tunings:
* WE: ~2 = 1200.0346{{c}}, ~11/9 = 344.7589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7492{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7505{{c}} -->


{{Optimal ET sequence|legend=0| 87, 94, 181 }}
{{Optimal ET sequence|legend=0| 87, 94, 181 }}


Badness (Smith): 0.022749
Badness (Sintel): 1.16


=== 19-limit ===
=== 19-limit ===
Line 586: Line 611:
Comma list: 325/324, 352/351, 375/374, 385/384, 400/399, 595/594
Comma list: 325/324, 352/351, 375/374, 385/384, 400/399, 595/594


Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 | 0 -9 -22 32 -19 8 -56 -67 }}
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 -15 | 0 9 22 -32 19 -8 56 67 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~18/11 = 855.2534{{c}}
Optimal tunings:
* WE: ~2 = 1200.0282{{c}}, ~11/9 = 344.7532{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7453{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~18/11 = 855.2534{{c}} -->


{{Optimal ET sequence|legend=0| 87, 94, 181 }}
{{Optimal ET sequence|legend=0| 87, 94, 181 }}


Badness (Smith): 0.019585
Badness (Sintel): 1.19


=== 23-limit ===
=== 23-limit ===
Line 599: Line 627:
Comma list: 300/299, 325/324, 352/351, 375/374, 385/384, 400/399, 484/483
Comma list: 300/299, 325/324, 352/351, 375/374, 385/384, 400/399, 484/483


Mapping: {{mapping| 1 8 18 -20 17 -2 44 52 48 | 0 -9 -22 32 -19 8 -56 -67 -61 }}
Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 -15 -13 | 0 9 22 -32 19 -8 56 67 61 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~18/11 = 855.2576{{c}}
Optimal tunings:
* WE: ~2 = 1200.0163{{c}}, ~11/9 = 344.7461{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 344.7416{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~18/11 = 855.2576{{c}} -->


{{Optimal ET sequence|legend=0| 87, 94, 181 }}
{{Optimal ET sequence|legend=0| 87, 94, 181 }}


Badness (Smith): 0.016332
Badness (Sintel): 1.17


== Ketchup ==
== Ketchup ==
Line 613: Line 644:


{{Mapping|legend=1| 2 3 4 6 | 0 4 15 -9 }}
{{Mapping|legend=1| 2 3 4 6 | 0 4 15 -9 }}
: mapping generators: ~1225/864, ~64/63


[[Optimal tuning]] ([[POTE]]): ~1225/864 = 600.000{{c}}, ~64/63 = 25.719{{c}}
[[Optimal tuning]]s:
: mapping generators: ~1225/864, ~64/63
* [[WE]]: ~1225/864 = 599.9685{{c}}, ~64/63 = 25.7181{{c}}
: [[error map]]: {{val| -0.063 +0.823 -0.668 -0.478 }}
* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~64/63 = 25.7181{{c}}
: error map: {{val| 0.000 +0.917 -0.543 -0.288 }}
<!-- * [[POTE]]: ~1225/864 = 600.000{{c}}, ~64/63 = 25.719{{c}} -->


{{Optimal ET sequence|legend=1| 46, 94, 140 }}
{{Optimal ET sequence|legend=1| 46, 94, 140 }}


[[Badness]] (Smith): 0.084538
[[Badness]] (Sintel): 2.14


=== 11-limit ===
=== 11-limit ===
Line 628: Line 664:
Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}
Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~64/63 = 25.693{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0678{{c}}, ~64/63 = 25.6963{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~64/63 = 25.6956{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~64/63 = 25.693{{c}} -->


{{Optimal ET sequence|legend=0| 46, 94, 140 }}
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


Badness (Smith): 0.039555
Badness (Sintel): 1.31


=== 13-limit ===
=== 13-limit ===
Line 641: Line 680:
Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}
Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~66/65 = 25.697{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0612{{c}}, ~66/65 = 25.7000{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~66/65 = 25.6978{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~66/65 = 25.697{{c}} -->


{{Optimal ET sequence|legend=0| 46, 94, 140 }}
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


Badness (Smith): 0.024824
Badness (Sintel): 1.03


=== 17-limit ===
=== 17-limit ===
Line 654: Line 696:
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~66/65 = 25.701{{c}}
Optimal tunings:
* WE: ~17/12 = 600.0896{{c}}, ~66/65 = 25.7048{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7017{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~66/65 = 25.701{{c}} -->


{{Optimal ET sequence|legend=0| 46, 94, 140 }}
{{Optimal ET sequence|legend=0| 46, 94, 140 }}


Badness (Smith): 0.016591
Badness (Sintel): 0.845


=== 19-limit ===
=== 19-limit ===
Line 667: Line 712:
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 -12 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 -12 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~66/65 = 25.660{{c}}
Optimal tunings:
* WE: ~17/12 = 600.1639{{c}}, ~66/65 = 25.6669{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.6597{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~66/65 = 25.660{{c}} -->


{{Optimal ET sequence|legend=0| 46, 94, 140h, 234eh }}
{{Optimal ET sequence|legend=0| 46, 94, 140h }}


Badness (Smith): 0.018170
Badness (Sintel): 1.11


=== 23-limit ===
=== 23-limit ===
Line 680: Line 728:
Mapping: {{mapping| 2 3 4 6 7 8 8 9 9 | 0 4 15 -9 -2 -14 4 -12 1 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 9 9 | 0 4 15 -9 -2 -14 4 -12 1 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~66/65 = 25.661{{c}}
Optimal tunings:
* WE: ~17/12 = 600.1777{{c}}, ~66/65 = 25.6682{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.6605{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~66/65 = 25.661{{c}} -->


{{Optimal ET sequence|legend=0| 46, 94, 140h, 234ehi }}
{{Optimal ET sequence|legend=0| 46, 94, 140h }}


Badness (Smith): 0.014033
Badness (Sintel): 1.00


[[Category:Temperament collections]]
[[Category:Temperament collections]]
Retrieved from "https://en.xen.wiki/w/Aberschismic_temperaments"