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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/)
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: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 703.039{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.6543{{c}}, ~3/2 = 702.8370{{c}}
: [[error map]]: {{val| -0.346 +0.536 +0.423 -0.494 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.0465{{c}}
: error map: {{val| 0.000 +1.092 +0.966 +0.175 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.039{{c}} -->


{{Optimal ET sequence|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc, 1118bbcc, 1217bbcc, 1316bbccd }}
{{Optimal ET sequence|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc }}


[[Badness]] (Smith): 0.094603
[[Badness]] (Sintel): 2.39


== Leapday ==
== Leapday ==
Line 57: Line 62:
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


Optimal tunings:  
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.2257{{c}}
* [[WE]]: ~2 = 1199.7167{{c}}, ~3/2 = 704.0971{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 704.263{{c}}
: [[error map]]: {{val| -0.283 +1.859 +2.559 -5.669 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.2504{{c}}
: error map: {{val| 0.000 +2.295 +2.945 -5.070 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.2257{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 704.263{{c}} -->


{{Optimal ET sequence|legend=1| 17c, 29, 46 }}
{{Optimal ET sequence|legend=1| 17c, 29, 46 }}


[[Badness]] (Smith): 0.096123
[[Badness]] (Sintel): 2.43


=== 11-limit ===
=== 11-limit ===
Line 73: Line 82:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2625{{c}}
* WE: ~2 = 1200.0731{{c}}, ~3/2 = 704.2933{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.250{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2538{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2625{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.250{{c}} -->


{{Optimal ET sequence|legend=0| 17c, 29, 46 }}
{{Optimal ET sequence|legend=0| 17c, 29, 46 }}


Badness (Smith): 0.038624
Badness (Sintel): 1.28


=== 13-limit ===
=== 13-limit ===
Line 88: Line 99:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2924{{c}}
* WE: ~2 = 1200.4758{{c}}, ~3/2 = 704.4930{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.214{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2346{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2924{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.214{{c}} -->


{{Optimal ET sequence|legend=0| 17c, 29, 46, 121def }}
{{Optimal ET sequence|legend=0| 17c, 29, 46, 121def }}


Badness (Smith): 0.024732
Badness (Sintel): 1.02


=== 17-limit ===
=== 17-limit ===
Line 103: Line 116:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.3098{{c}}
* WE: ~2 = 1200.4818{{c}}, ~3/2 = 704.5121{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.229{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2507{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.3098{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.229{{c}} -->


{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 121defg }}
{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 121defg }}


Badness (Smith): 0.017863
Badness (Sintel): 0.910


==== 19-limit ====
==== 19-limit ====
Line 118: Line 133:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2990{{c}}
* WE: ~2 = 1201.0192{{c}}, ~3/2 = 704.7333{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.135{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1680{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2990{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.135{{c}} -->


{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}
{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}


Badness (Smith): 0.017356
Badness (Sintel): 1.06


===== 23-limit =====
===== 23-limit =====
Line 133: Line 150:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.3035{{c}}
* WE: ~2 = 1200.9738{{c}}, ~3/2 = 704.7120{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.141{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1695{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.3035{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.141{{c}} -->


{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}
{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}


Badness (Smith): 0.014065
Badness (Sintel): 1.01


==== Leapling ====
==== Leapling ====
Line 148: Line 167:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2037{{c}}
* WE: ~2 = 1200.4745{{c}}, ~3/2 = 704.4016{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.123{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1442{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2037{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.123{{c}} -->


{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}
{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}


Badness (Smith): 0.019065
Badness (Sintel): 1.16


===== 23-limit =====
===== 23-limit =====
Line 163: Line 184:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2082{{c}}
* WE: ~2 = 1200.5425{{c}}, ~3/2 = 704.4319{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.114{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1349{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2082{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.114{{c}} -->


{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}
{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}


Badness (Smith): 0.016067
Badness (Sintel): 1.15


== Hemidromeda ==
== Hemidromeda ==
Line 180: Line 203:
: mapping generator: ~2, ~12500/7203
: mapping generator: ~2, ~12500/7203


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~7203/6250 = 248.581{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7236{{c}}, ~12500/7203 = 951.1864{{c}}
: [[error map]]: {{val| -0.276 +0.418 -0.205 +0.282 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~12500/7203 = 951.4098{{c}}
: error map: {{val| 0.000 +0.865 +0.243 +0.813 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~12500/7203 = 951.419{{c}} -->


{{Optimal ET sequence|legend=1| 29, 82cd, 111, 140, 531, 671, 811b, 951b }}
{{Optimal ET sequence|legend=1| 29, 82cd, 111, 140, 251, 391, 1424bbcdd }}


[[Badness]] (Smith): 0.115803
[[Badness]] (Sintel): 2.93


=== 11-limit ===
=== 11-limit ===
Line 193: Line 221:
Mapping: {{mapping| 1 0 38 48 32 | 0 2 -45 -57 -36 }}
Mapping: {{mapping| 1 0 38 48 32 | 0 2 -45 -57 -36 }}


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~405/352 = 248.589{{c}}
Optimal tunings:
* WE: ~2 = 1199.8767{{c}}, ~400/231 = 951.3065{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~400/231 = 951.4063{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~400/231 = 951.411{{c}} -->


{{Optimal ET sequence|legend=0| 29, 82cd, 111, 140, 251, 391e }}
{{Optimal ET sequence|legend=0| 29, 82cd, 111, 140, 251, 391e }}


Badness (Smith): 0.060808
Badness (Sintel): 2.01


=== 13-limit ===
=== 13-limit ===
Line 206: Line 237:
Mapping: {{mapping| 1 0 38 48 32 37 | 0 2 -45 -57 -36 -42 }}
Mapping: {{mapping| 1 0 38 48 32 37 | 0 2 -45 -57 -36 -42 }}


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~15/13 = 248.588{{c}}
Optimal tunings:
* WE: ~2 = 1199.8753{{c}}, ~26/15 = 951.3054{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4064{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~26/15 = 951.412{{c}} -->


{{Optimal ET sequence|legend=0| 29, 82cdf, 111, 140, 391e, 531e }}
{{Optimal ET sequence|legend=0| 29, 82cdf, 111, 140, 251, 391e }}


Badness (Smith): 0.028632
Badness (Sintel): 1.18


=== 17-limit ===
=== 17-limit ===
Line 219: Line 253:
Mapping: {{mapping| 1 0 38 48 32 37 58 | 0 2 -45 -57 -36 -42 -68 }}
Mapping: {{mapping| 1 0 38 48 32 37 58 | 0 2 -45 -57 -36 -42 -68 }}


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~15/13 = 248.591{{c}}
Optimal tunings:
* WE: ~2 = 1199.8770{{c}}, ~26/15 = 951.3039{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4035{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~26/15 = 951.409{{c}} -->


{{Optimal ET sequence|legend=0| 29g, 82cdfg, 111, 140, 251, 391e }}
{{Optimal ET sequence|legend=0| 29g, 82cdfg, 111, 140, 251, 391e }}


Badness (Smith): 0.019054
Badness (Sintel): 0.971


=== 19-limit ===
=== 19-limit ===
Line 232: Line 269:
Mapping: {{mapping| 1 0 38 48 32 37 58 32 | 0 2 -45 -57 -36 -42 -68 -35 }}
Mapping: {{mapping| 1 0 38 48 32 37 58 32 | 0 2 -45 -57 -36 -42 -68 -35 }}


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~15/13 = 248.587{{c}}
Optimal tunings:
* WE: ~2 = 1199.7534{{c}}, ~26/15 = 951.2024{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4020{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~26/15 = 951.413{{c}} -->


{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140, 391ehh, 531ehh }}
{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140 }}


Badness (Smith): 0.016609
Badness (Sintel): 1.01


=== 23-limit ===
=== 23-limit ===
Line 245: Line 285:
Mapping: {{mapping| 1 0 38 48 32 37 58 32 18 | 0 2 -45 -57 -36 -42 -68 -35 -17 }}
Mapping: {{mapping| 1 0 38 48 32 37 58 32 18 | 0 2 -45 -57 -36 -42 -68 -35 -17 }}


Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~15/13 = 248.588{{c}}
Optimal tunings:
* WE: ~2 = 1199.9128{{c}}, ~26/15 = 951.3371{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.4076{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~26/15 = 951.412{{c}} -->


{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140, 391ehhi, 531ehhii }}
{{Optimal ET sequence|legend=0| 29g, 82cdfgh, 111, 140 }}


Badness (Smith): 0.015361
Badness (Sintel): 1.10


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