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Landscape microtemperaments: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (2/). - domain (covered in minortonic family)
Switch to Sintel's badness, WE & CWE tunings (3/)
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{{Mapping|legend=1| 3 3 1 0 | 0 5 17 24 }}
{{Mapping|legend=1| 3 3 1 0 | 0 5 17 24 }}
: mapping generators: ~2, ~243/224
: mapping generators: ~63/50, ~243/224


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
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{{Mapping|legend=1| 3 -3 1 12 | 0 13 10 -6 }}
{{Mapping|legend=1| 3 -3 1 12 | 0 13 10 -6 }}
: mapping generators: ~63/50, ~147/128


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
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{{Mapping|legend=1| 3 2 8 16 | 0 8 -3 -22 }}
{{Mapping|legend=1| 3 2 8 16 | 0 8 -3 -22 }}
: mapping generators: ~63/50, ~1024/945


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~63/50 = 400.000{{c}}, ~1024/945 = 137.772{{c}}
* [[WE]]: ~63/50 = 399.9681{{c}}, ~1024/945 = 137.7570{{c}}
* [[POTE]]: ~63/50 = 400.000{{c}}, ~1024/945 = 137.768{{c}}
: [[error map]]: {{val| -0.096 +0.037 +0.160 +0.010 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~1024/945 = 137.7689{{c}}
: error map: {{val| 0.000 +0.196 +0.380 +0.259 }}


{{Optimal ET sequence|legend=1| 87, 183, 270, 723, 993, 1263, 2796cd, 4059bccd }}
{{Optimal ET sequence|legend=1| 87, 183, 270, 723, 993, 1263, 2796cd, 4059bccd }}


[[Badness]] (Smith): 0.062187
[[Badness]] (Sintel): 1.57


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~63/50 = 400.000{{c}}, ~693/640 = 137.773{{c}}
* WE: ~63/50 = 399.9798{{c}}, ~693/640 = 137.7643{{c}}
* POTE: ~63/50 = 400.000{{c}}, ~693/640 = 137.771{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~693/640 = 137.7716{{c}}


{{Optimal ET sequence|legend=0| 87, 183, 270, 1263, 1533, 1803c }}
{{Optimal ET sequence|legend=0| 87, 183, 270, 1263, 1533, 1803c }}


Badness (Smith): 0.023085
Badness (Sintel): 0.763


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~63/50 = 400.000{{c}}, ~13/12 = 137.777{{c}}
* WE: ~63/50 = 399.9921{{c}}, ~13/12 = 137.7743{{c}}
* POTE: ~63/50 = 400.000{{c}}, ~13/12 = 137.777{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~13/12 = 137.7770{{c}}


{{Optimal ET sequence|legend=0| 87, 183, 270 }}
{{Optimal ET sequence|legend=0| 87, 183, 270 }}


Badness (Smith): 0.015557
Badness (Sintel): 0.643


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 676/675, 715/714, 1001/1000, 3025/3024, 4096/4095
Comma list: 676/675, 715/714, 936/935, 1001/1000, 4096/4095


Mapping: {{mapping| 3 2 8 16 9 8 4 | 0 8 -3 -22 4 9 24 }}
Mapping: {{mapping| 3 2 8 16 9 8 4 | 0 8 -3 -22 4 9 24 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~63/50 = 400.000{{c}}, ~13/12 = 137.758{{c}}
* WE: ~34/27 = 399.9776{{c}}, ~13/12 = 137.7535{{c}}
* POTE: ~63/50 = 400.000{{c}}, ~13/12 = 137.761{{c}}
* CWE: ~34/27 = 400.0000{{c}}, ~13/12 = 137.7608{{c}}


{{Optimal ET sequence|legend=0| 87, 183, 270, 453 }}
{{Optimal ET sequence|legend=0| 87, 183, 270, 453 }}


Badness (Smith): 0.0171
Badness (Sintel): 0.869


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 676/675, 715/714, 1001/1000, 1216/1215, 1729/1728, 3025/3024
Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1729/1728


Mapping: {{mapping| 3 2 8 16 9 8 4 0 | 0 8 -3 -22 4 9 24 37 }}
Mapping: {{mapping| 3 2 8 16 9 8 4 0 | 0 8 -3 -22 4 9 24 37 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~63/50 = 400.000{{c}}, ~13/12 = 137.763{{c}}
* WE: ~34/27 = 399.9804{{c}}, ~13/12 = 137.7602{{c}}
* POTE: ~63/50 = 400.000{{c}}, ~13/12 = 137.767{{c}}
* CWE: ~34/27 = 400.0000{{c}}, ~13/12 = 137.7664{{c}}


{{Optimal ET sequence|legend=0| 87, 183, 270 }}
{{Optimal ET sequence|legend=0| 87, 183, 270 }}


Badness (Smith): 0.0153
Badness (Sintel): 0.928


== Terture ==
== Terture ==
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[[Comma list]]: 250047/250000, 359661568/358722675
[[Comma list]]: 250047/250000, 359661568/358722675


{{Mapping|legend=1| 3 4 3 2 | 0 4 21 34 }}
{{Mapping|legend=1| 3 0 -18 -32 | 0 4 21 34 }}
: mapping generators: ~63/50, ~320/243


[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000{{c}}, ~392/375 = 75.555{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 399.9723{{c}}, ~320/243 = 475.5221{{c}} (~392/375 = 75.5499{{c}})
: [[error map]]: {{val| -0.083 +0.134 +0.151 -0.185 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~320/243 = 475.5519{{c}} (~392/375 = 75.5519{{c}})
: error map: {{val| 0.000 +0.253 +0.276 -0.061 }}


{{Optimal ET sequence|legend=1| 111, 159, 270 }}
{{Optimal ET sequence|legend=1| 111, 159, 270 }}


[[Badness]] (Smith): 0.087156
[[Badness]] (Sintel): 2.21


=== 11-limit ===
=== 11-limit ===
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Comma list: 3025/3024, 19712/19683, 102487/102400
Comma list: 3025/3024, 19712/19683, 102487/102400


Mapping: {{mapping| 3 4 3 2 10 | 0 4 21 34 2 }}
Mapping: {{mapping| 3 0 -18 -32 8 | 0 4 21 34 2 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~392/375 = 75.550{{c}}
Optimal tunings:
* WE: ~63/50 = 399.9902{{c}}, ~320/243 = 475.5383{{c}} (~392/375 = 75.5481{{c}})
* CWE: ~63/50 = 400.0000{{c}}, ~320/243 = 475.5490{{c}} (~392/375 = 75.5490{{c}})


{{Optimal ET sequence|legend=0| 111, 159, 270, 1239, 1509, 1779, 2049, 2319 }}
{{Optimal ET sequence|legend=0| 111, 159, 270, 1239, 1509, 1779, 2049, 2319 }}


Badness (Smith): 0.029326
Badness (Sintel): 0.969


=== 13-limit ===
=== 13-limit ===
Line 368: Line 379:
Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976
Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976


Mapping: {{mapping| 3 4 3 2 10 6 | 0 4 21 34 2 27 }}
Mapping: {{mapping| 3 0 -18 -32 8 -21 | 0 4 21 34 2 27 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~117/112 = 75.553{{c}}
Optimal tunings:
* WE: ~63/50 = 399.9958{{c}}, ~154/117 = 475.5485{{c}} (~117/112 = 75.5527{{c}})
* CWE: ~63/50 = 400.0000{{c}}, ~154/117 = 475.5531{{c}} (~117/112 = 75.5531{{c}})


{{Optimal ET sequence|legend=0| 111, 159, 270 }}
{{Optimal ET sequence|legend=0| 111, 159, 270 }}


Badness (Smith): 0.018647
Badness (Sintel): 0.771


=== 17-limit ===
=== 17-limit ===
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Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913
Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913


Mapping: {{mapping| 3 4 3 2 10 6 10 | 0 4 21 34 2 27 12 }}
Mapping: {{mapping| 3 0 -18 -32 8 -21 -2 | 0 4 21 34 2 27 12 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~117/112 = 75.560{{c}}
Optimal tunings:
* WE: ~34/27 = 399.9664{{c}}, ~112/85 = 475.5198{{c}} (~117/112 = 75.5534{{c}})
* CWE: ~34/27 = 400.0000{{c}}, ~112/85 = 475.5568{{c}} (~117/112 = 75.5568{{c}})


{{Optimal ET sequence|legend=0| 111, 159, 270 }}
{{Optimal ET sequence|legend=0| 111, 159, 270 }}


Badness (Smith): 0.018705
Badness (Sintel): 0.953


=== 19-limit ===
=== 19-limit ===
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Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615
Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615


Mapping: {{mapping| 3 4 3 2 10 6 10 5 | 0 4 21 34 2 27 12 41 }}
Mapping: {{mapping| 3 0 -18 -32 8 -21 -2 -36 | 0 4 21 34 2 27 12 41 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~95/91 = 75.560{{c}}
Optimal tunings:
* WE: ~34/27 = 399.9665{{c}}, ~112/85 = 475.5198{{c}} (~95/91 = 75.5533{{c}})
* CWE: ~34/27 = 400.0000{{c}}, ~112/85 = 475.5568{{c}} (~95/91 = 75.5568{{c}})


{{Optimal ET sequence|legend=0| 111, 159, 270 }}
{{Optimal ET sequence|legend=0| 111, 159, 270 }}


Badness (Smith): 0.013902
Badness (Sintel): 0.846


=== 23-limit ===
=== 23-limit ===
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Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215
Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215


Mapping: {{mapping| 3 4 3 2 10 6 10 5 13 | 0 4 21 34 2 27 12 41 3 }}
Mapping: {{mapping| 3 0 -18 -32 8 -21 -2 -36 10 | 0 4 21 34 2 27 12 41 3 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~24/23 = 75.548{{c}}
Optimal tunings:
* WE: ~34/27 = 400.0026{{c}}, ~112/85 = 475.5510{{c}} (~24/23 = 75.5485{{c}})
* CWE: ~34/27 = 400.0000{{c}}, ~112/85 = 475.5482{{c}} (~24/23 = 75.5482{{c}})


{{Optimal ET sequence|legend=0| 111, 159, 270 }}
{{Optimal ET sequence|legend=0| 111, 159, 270 }}


Badness (Smith): 0.014915
Badness (Sintel): 1.07


== Slendscape ==
== Slendscape ==
Retrieved from "https://en.xen.wiki/w/Landscape_microtemperaments"