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Catalog of rank-4 temperaments: Difference between revisions

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Badness (Sintel): 0.505
Badness (Sintel): 0.505
==== Commas 2080/2079, 3250/3249, 4096/4095 ====
Subgroup: 2.3.5.7.11.13.19
Comma list: 2080/2079, 3250/3249, 4096/4095
Mapping: {{mapping| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}
Optimal tunings:
* WE: ~2 = 1199.9639{{c}}, ~3/2 = 702.0643{{c}}, ~5/4 = 386.3218{{c}}, ~187/100 = 1084.4676{{c}}
: error map: {{val| -0.036 +0.073 -0.064 +0.073 +0.129 -0.166 -0.004 }}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0887{{c}}, ~5/4 = 386.3257{{c}}, ~187/100 = 1084.5006{{c}}
: error map: {{val| 0.000 +0.134 +0.012 +0.175 +0.236 -0.032 +0.135 }}
{{Optimal ET sequence|legend=0| 41, 53, 84, 94, 137, 176, 217, 270, 581, 851, 935, 1205, 2193, 2463, 2774e }}
Badness (Sintel): 0.618
===== 2.3.5.7.11.13.19.29 subgroup =====
Subgroup: 2.3.5.7.11.13.19.29
Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095
Mapping: {{mapping| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}
Optimal tunings:
* WE: ~2 = 1199.9594{{c}}, ~3/2 = 702.0487{{c}}, ~5/4 = 386.3262{{c}}, ~187/100 = 1084.4677{{c}}
: error map: {{val| -0.041 +0.053 -0.069 +0.069 +0.163 -0.170 +0.005 +0.048 }}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0709{{c}}, ~5/4 = 386.3327{{c}}, ~187/100 = 1084.5064{{c}}
: error map: {{val| -0.000 +0.116 +0.019 +0.187 +0.302 -0.015 +0.171 +0.241 }}
{{Optimal ET sequence|legend=0| 41, 53j, 94, 137j, 176, 217, 270, 487, 581j, 718, 894, 935, 988, 1205, 2193, 3398dehj}}
Badness (Sintel): 1.10


==== Metaolympic ====
==== Metaolympic ====
Line 1,068: Line 1,102:


Badness (Sintel): 1.27
Badness (Sintel): 1.27
==== Commas 2080/2079, 3250/3249, 4096/4095 ====
Subgroup: 2.3.5.7.11.13.19
Comma list: 2080/2079, 3250/3249, 4096/4095
Mapping: {{mapping| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}
Optimal tunings:
* WE: ~2 = 1199.9639{{c}}, ~3/2 = 702.0643{{c}}, ~5/4 = 386.3218{{c}}, ~187/100 = 1084.4676{{c}}
: error map: {{val| -0.036 +0.073 -0.064 +0.073 +0.129 -0.166 -0.004 }}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0887{{c}}, ~5/4 = 386.3257{{c}}, ~187/100 = 1084.5006{{c}}
: error map: {{val| 0.000 +0.134 +0.012 +0.175 +0.236 -0.032 +0.135 }}
{{Optimal ET sequence|legend=0| 41, 53, 84, 94, 137, 176, 217, 270, 581, 851, 935, 1205, 2193, 2463, 2774e }}
Badness (Sintel): 0.618
===== 2.3.5.7.11.13.19.29 subgroup =====
Subgroup: 2.3.5.7.11.13.19.29
Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095
Mapping: {{mapping| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}
Optimal tunings:
* WE: ~2 = 1199.9594{{c}}, ~3/2 = 702.0487{{c}}, ~5/4 = 386.3262{{c}}, ~187/100 = 1084.4677{{c}}
: error map: {{val| -0.041 +0.053 -0.069 +0.069 +0.163 -0.170 +0.005 +0.048 }}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0709{{c}}, ~5/4 = 386.3327{{c}}, ~187/100 = 1084.5064{{c}}
: error map: {{val| -0.000 +0.116 +0.019 +0.187 +0.302 -0.015 +0.171 +0.241 }}
{{Optimal ET sequence|legend=0| 41, 53j, 94, 137j, 176, 217, 270, 487, 581j, 718, 894, 935, 988, 1205, 2193, 3398dehj}}
Badness (Sintel): 1.10


== Alphaxenic (131769/131072) ==
== Alphaxenic (131769/131072) ==
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