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Ragismic microtemperaments: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (7/)
Switch to Sintel's badness, WE & CWE tunings (8/)
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: mapping generators: ~2, ~{{monzo| 21 3 1 -10 }}
: mapping generators: ~2, ~{{monzo| 21 3 1 -10 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~{{monzo| 21 3 1 -10 }} = 4.4465{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0068{{c}}, ~{{monzo| 21 3 1 -10 }} = 4.4467{{c}}
: [[error map]]: {{val| +0.007 +0.031 -0.035 -0.032 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| 21 3 1 -10 }} = 4.4466{{c}}
: error map: {{val| 0.000 +0.025 -0.043 -0.050 }}


{{Optimal ET sequence|legend=1| 270, 1079, 1349, 1619, 1889, 2159, 4048, 18081cd }}
{{Optimal ET sequence|legend=1| 270, 1079, 1349, 1619, 1889, 2159, 4048, 18081cd }}


[[Badness]] (Sintel): 2.172
[[Badness]] (Sintel): 2.17


=== 11-limit ===
=== 11-limit ===
Line 885: Line 889:
Mapping: {{mapping| 1 2 3 3 3 | 0 -112 -183 -52 124 }}
Mapping: {{mapping| 1 2 3 3 3 | 0 -112 -183 -52 124 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~385/384 = 4.4465{{c}}
Optimal tunings:
* WE: ~2 = 1199.9970{{c}}, ~385/384 = 4.4465{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~385/384 = 4.4465{{c}}


{{Optimal ET sequence|legend=0| 270, 1349, 1619, 1889, 2159, 11065, 13224 }}
{{Optimal ET sequence|legend=0| 270, 1349, 1619, 1889, 2159, 11065, 13224 }}


Badness (Sintel): 1.020
Badness (Sintel): 1.02


=== 13-limit ===
=== 13-limit ===
Line 898: Line 904:
Mapping: {{mapping| 1 2 3 3 3 3 | 0 -112 -183 -52 124 189 }}
Mapping: {{mapping| 1 2 3 3 3 3 | 0 -112 -183 -52 124 189 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~385/384 = 4.4466{{c}}
Optimal tunings:
* WE: ~2 = 1200.0065{{c}}, ~385/384 = 4.4467{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~385/384 = 4.4467{{c}}


{{Optimal ET sequence|legend=0| 270, 1079, 1349, 1619, 1889, 4048 }}
{{Optimal ET sequence|legend=0| 270, 1079, 1349, 1619, 1889, 4048 }}
Line 916: Line 924:
: Mapping generators: ~135/128, ~3
: Mapping generators: ~135/128, ~3


[[Optimal tuning]] ([[CTE]]): ~135/128 = 92.3077{{c}}, ~3/2 = 702.0024{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~135/128 = 92.3072{{c}}, ~3/2 = 701.9995{{c}}
: [[error map]]: {{val| -0.006 +0.038 -0.030 -0.013 }}
* [[CWE]]: ~135/128 = 92.3077{{c}}, ~3/2 = 702.0030{{c}}
: error map: {{val| 0.000 +0.048 -0.015 +0.001 }}


{{Optimal ET sequence|legend=1| 494, 1053, 1547, 8788, 10335, 11882, 13429b, 14976b }}
{{Optimal ET sequence|legend=1| 494, 1053, 1547, 8788, 10335, 11882, 13429b, 14976b }}


[[Badness]] (Sintel): 3.201
[[Badness]] (Sintel): 3.20


=== 11-limit ===
=== 11-limit ===
Line 929: Line 941:
Mapping: {{mapping| 13 0 92 -355 148 | 0 1 -3 19 -5 }}
Mapping: {{mapping| 13 0 92 -355 148 | 0 1 -3 19 -5 }}


Optimal tuning (CTE): ~135/128 = 92.3077{{c}}, ~3/2 = 702.0042{{c}}
Optimal tunings:
* WE: ~135/128 = 92.3062{{c}}, ~3/2 = 701.9946{{c}}
* CWE: ~135/128 = 92.3077{{c}}, ~3/2 = 702.0056{{c}}


{{Optimal ET sequence|legend=0| 494, 1053, 1547, 3588e, 5135e }}
{{Optimal ET sequence|legend=0| 494, 1053, 1547, 3588e, 5135e }}


Badness (Sintel): 1.393
Badness (Sintel): 1.39


=== 13-limit ===
=== 13-limit ===
Line 942: Line 956:
Mapping: {{mapping| 13 0 92 -355 148 419 | 0 1 -3 19 -5 -18 }}
Mapping: {{mapping| 13 0 92 -355 148 419 | 0 1 -3 19 -5 -18 }}


Optimal tuning (CTE): ~135/128 = 92.3077{{c}}, ~3/2 = 702.0099{{c}}
Optimal tunings:
* WE: ~135/128 = 92.3055{{c}}, ~3/2 = 701.9928{{c}}
* CWE: ~135/128 = 92.3077{{c}}, ~3/2 = 702.0098{{c}}


{{Optimal ET sequence|legend=0| 494, 1547, 2041, 4576def }}
{{Optimal ET sequence|legend=0| 494, 1547, 2041, 4576def }}


Badness (Sintel): 1.180
Badness (Sintel): 1.18


== Countritonic ==
== Countritonic ==
Line 957: Line 973:
[[Comma list]]: 4375/4374, 68719476736/68356598625
[[Comma list]]: 4375/4374, 68719476736/68356598625


{{Mapping|legend=1| 1 6 19 -33 | 0 -9 -34 73 }}
{{Mapping|legend=1| 1 -3 -15 40 | 0 9 34 -73 }}
: mapping generators: ~2, ~45927/32768
: mapping generators: ~2, ~65536/45927


[[Optimal tuning]] (CTE): ~2 = 1200.0000{{c}}, ~45927/32768 = 588.6216{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8189{{c}}, ~65536/45927 = 611.2850{{c}}
: [[error map]]: {{val| -0.181 +0.153 +0.094 +0.123 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~65536/45927 = 611.3775{{c}}
: error map: {{val| 0.000 +0.443 +0.522 +0.615 }}


{{Optimal ET sequence|legend=1| 53, 210d, 263, 316, 369, 422, 791, 1213cd, 2004bcdd }}
{{Optimal ET sequence|legend=1| 53, 210d, 263, 316, 369, 422, 791, 1213cd, 2004bcdd }}


[[Badness]] (Sintel): 3.370
[[Badness]] (Sintel): 3.37


=== 11-limit ===
=== 11-limit ===
Line 971: Line 991:
Comma list: 4375/4374, 5632/5625, 2621440/2614689
Comma list: 4375/4374, 5632/5625, 2621440/2614689


Mapping: {{mapping| 1 6 19 -13 79 | 0 -9 -34 73 154 }}
Mapping: {{mapping| 1 -3 -15 40 -75 | 0 9 34 -73 154 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~539/384 = 588.6258{{c}}
Optimal tunings:
* WE: ~2 = 1199.8147{{c}}, ~768/539 = 611.2822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~768/539 = 611.3762{{c}}


{{Optimal ET sequence|legend=0| 53, 316e, 369, 422, 791e, 1213cde }}
{{Optimal ET sequence|legend=0| 53, 316e, 369, 422, 791e, 1213cde }}


Badness (Sintel): 2.336
Badness (Sintel): 2.34


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13


Comma list: 2080/2079, 2200/2197, 4375/4374, 5632/5625
Comma list: 2080/2079, 2200/2197, 4375/4374, 5632/5625


Mapping: {{mapping| 1 6 19 -13 79 | 0 -9 -34 73 154 -74 }}
Mapping: {{mapping| 1 -3 -15 40 -75 -34 | 0 9 34 -73 154 74 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~128/91 = 588.6277{{c}}
Optimal tunings:
* WE: ~2 = 1199.7916{{c}}, ~768/539 = 611.2698{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~768/539 = 611.3754{{c}}


{{Optimal ET sequence|legend=0| 53, 316ef, 369f, 422, 1213cdeff, 1635bcdefff }}
{{Optimal ET sequence|legend=0| 53, 316ef, 369f, 422, 1213cdeff, 1635bcdefff }}


Badness (Sintel): 1.514
Badness (Sintel): 1.51


== Quatracot ==
== Quatracot ==
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