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Orwellismic 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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[[Comma list]]: 1728/1715, 3645/3584
[[Comma list]]: 1728/1715, 3645/3584


{{Mapping|legend=1| 1 3 -3 6 | 0 -4 15 -9 }}
{{Mapping|legend=1| 1 -1 12 -3 | 0 4 -15 9 }}
: mapping generators: ~2, ~9/7
: mapping generators: ~2, ~14/9


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~9/7 = 425.596{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.8626{{c}}, ~14/9 = 774.9609{{c}}
: [[error map]]: {{val| +0.863 -2.974 -0.376 +3.234 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 774.4021{{c}}
: error map: {{val| 0.000 -4.347 -2.345 +0.793 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~14/9 = 774.404{{c}} -->


{{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b }}


[[Badness]] (Smith): 0.093805
[[Badness]] (Sintel): 2.37


=== 11-limit ===
=== 11-limit ===
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Comma list: 99/98, 243/242, 385/384
Comma list: 99/98, 243/242, 385/384


Mapping: {{mapping| 1 3 -3 6 7 | 0 -4 15 -9 -10 }}
Mapping: {{mapping| 1 -1 12 -3 -3 | 0 4 -15 9 10 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~9/7 = 425.550{{c}}
Optimal tunings:
* WE: ~2 = 1201.0893{{c}}, ~14/9 = 775.1534{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.4564{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~14/9 = 774.450{{c}} -->


{{Optimal ET sequence|legend=0| 14, 17, 31, 79, 110e, 141e }}
{{Optimal ET sequence|legend=0| 14, 17, 31, 79, 110e, 141e }}


Badness (Smith): 0.039595
Badness (Sintel): 1.31


=== 13-limit ===
=== 13-limit ===
Line 185: Line 193:
Comma list: 99/98, 105/104, 144/143, 243/242
Comma list: 99/98, 105/104, 144/143, 243/242


Mapping: {{mapping| 1 3 -3 6 7 3 | 0 -4 15 -9 -10 2 }}
Mapping: {{mapping| 1 -1 12 -3 -3 5 | 0 4 -15 9 10 -2 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~9/7 = 425.501{{c}}
Optimal tunings:
* WE: ~2 = 1200.4045{{c}}, ~14/9 = 774.7596{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.5000{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~14/9 = 774.499{{c}} -->


{{Optimal ET sequence|legend=0| 14, 17, 31, 79f, 110ef, 141ef }}
{{Optimal ET sequence|legend=0| 14, 17, 31 }}


Badness (Smith): 0.037408
Badness (Sintel): 1.55


== Diesic ==
== Diesic ==
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: mapping generators: ~2, ~36/35
: mapping generators: ~2, ~36/35


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~36/35 = 38.567{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1293{{c}}, ~36/35 = 38.5709{{c}}
: [[error map]]: {{val| +0.129 -3.118 +4.086 +0.137 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~36/35 = 38.5603{{c}}
: error map: {{val| 0.000 -3.239 +3.920 -0.188 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~36/35 = 38.567{{c}} -->


{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
{{Optimal ET sequence|legend=1| 1c, 30bc, 31, 156c }}


[[Badness]] (Smith): 0.107348
[[Badness]] (Sintel): 2.72


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }}
Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~36/35 = 38.565{{c}}
Optimal tunings:
* WE: ~2 = 1200.4923{{c}}, ~36/35 = 38.5806{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 38.5397{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~36/35 = 38.565{{c}} -->


{{Optimal ET sequence|legend=0| 31, 156ce, 187ce, 218bcee, 249bcee }}
{{Optimal ET sequence|legend=0| 1ce, 30bce, 31 }}


Badness (Smith): 0.044186
Badness (Sintel): 1.46


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }}
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~36/35 = 38.444{{c}}
Optimal tunings:
* WE: ~2 = 1199.3005{{c}}, ~36/35 = 38.4213{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 38.4764{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~36/35 = 38.444{{c}} -->


{{Optimal ET sequence|legend=0| 31, 94cff, 125cff }}
{{Optimal ET sequence|legend=0| 1ce, 30bce, 31 }}


Badness (Smith): 0.038116
Badness (Sintel): 1.57


== Phillips ==
== Phillips ==
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: mapping generators: ~81/56, ~3
: mapping generators: ~81/56, ~3


[[Optimal tuning]] ([[POTE]]): ~81/56 = 600.000{{c}}, ~3/2 = 691.174{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~81/56 = 601.3944{{c}}, ~3/2 = 692.7807{{c}}
: [[error map]]: {{val| +2.789 -6.385 -0.424 +3.692 }}
* [[CWE]]: ~81/56 = 600.0000{{c}}, ~3/2 = 691.1141{{c}}
: error map: {{val| 0.000 -10.841 -6.340 -4.370 }}
<!-- * [[POTE]]: ~81/56 = 600.000{{c}}, ~3/2 = 691.174{{c}} -->


{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }}
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }}


[[Badness]] (Smith): 0.228602
[[Badness]] (Sintel): 5.79


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }}
Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }}


Optimal tuning (POTE): ~63/44 = 600.000{{c}}, ~3/2 = 691.040{{c}}
Optimal tunings:
* WE: ~63/44 = 601.2349{{c}}, ~3/2 = 692.4623{{c}}
* CWE: ~63/44 = 600.0000{{c}}, ~3/2 = 691.0383{{c}}
<!-- * POTE: ~63/44 = 600.000{{c}}, ~3/2 = 691.040{{c}} -->


{{Optimal ET sequence|legend=0| 14, 26, 40, 66b }}
{{Optimal ET sequence|legend=0| 14, 26, 40, 66b }}


Badness (Smith): 0.095777
Badness (Sintel): 3.17


== Triskaidekic ==
== Triskaidekic ==
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