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Syntonic–chromatic equivalence continuum: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus
+ error map. Review optimal ET sequence. Unify precision
 
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| {{Monzo| -17 21 -7 }}
| {{Monzo| -17 21 -7 }}
|-
|-
| …
| …
| …
| …
| …
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{{Mapping|legend=1| 1 0 -15 | 0 1 11 }}
{{Mapping|legend=1| 1 0 -15 | 0 1 11 }}
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


Line 194: Line 194:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 689.3122{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 689.3122{{c}}
: error map: {{val| 0.000 -12.643 -3.879 }}
: error map: {{val| 0.000 -12.643 -3.879 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 689.879{{c}} -->


{{Optimal ET sequence|legend=1| 7, 33, 40, 47, 54b }}
{{Optimal ET sequence|legend=1| 7, 33, 40, 47, 54b }}
Line 210: Line 209:


{{Mapping|legend=1| 1 0 18 | 0 1 -10 }}
{{Mapping|legend=1| 1 0 18 | 0 1 -10 }}
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


Line 218: Line 216:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 682.6617{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 682.6617{{c}}
: error map: {{val| 0.000 -19.293 -12.931 }}
: error map: {{val| 0.000 -19.293 -12.931 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 681.801{{c}} -->


{{Optimal ET sequence|legend=1| 7, 30b, 37b, 44b, 51b, 58bc, 65bbc }}
{{Optimal ET sequence|legend=1| 7, 30b, 37b, 44b, 51b, 58bc, 65bbc }}
Line 230: Line 227:


{{Mapping|legend=1| 1 1 -1 | 0 2 15 }}
{{Mapping|legend=1| 1 1 -1 | 0 2 15 }}
: mapping generators: ~2, ~2560/2187
: mapping generators: ~2, ~2560/2187


Line 238: Line 234:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~2560/2187 = 345.5992{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~2560/2187 = 345.5992{{c}}
: error map: {{val| 0.000 -10.757 -2.326 }}
: error map: {{val| 0.000 -10.757 -2.326 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~2560/2187 = 345.946{{c}} -->


{{Optimal ET sequence|legend=1| 7, 38c, 45c, 52, 59b, 66b }}
{{Optimal ET sequence|legend=1| 7, 38c, 45c, 52, 59b, 66b }}
Line 252: Line 247:


{{Mapping|legend=1| 1 2 2 | 0 -3 2 }}
{{Mapping|legend=1| 1 2 2 | 0 -3 2 }}
: mapping generators: ~2, ~16/15
: mapping generators: ~2, ~16/15


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1210.1294{{c}}, ~16/15 = 174.5613{{c}}
* [[WE]]: ~2 = 1210.1294{{c}}, ~16/15 = 174.5613{{c}}
: [[error map]]: {{val| +3.120 -6.264 +1.733 }}
: [[error map]]: {{val| +10.129 -5.380 -16.932 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 172.4620{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 172.4620{{c}}
: error map: {{val| 0.000 -10.757 -2.326 }}
: error map: {{val| 0.000 -19.341 -41.390 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~16/15 = 170.671{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~16/15 = 173.101{{c}} -->


{{Optimal ET sequence|legend=1| 6b, 7 }}
{{Optimal ET sequence|legend=1| 6b, 7 }}
Line 273: Line 265:


{{Mapping|legend=1| 1 2 5 | 0 -3 -19 }}
{{Mapping|legend=1| 1 2 5 | 0 -3 -19 }}
: mapping generators: ~2, ~729/640
: mapping generators: ~2, ~729/640


Line 281: Line 272:
* [[CWE]]: ~2 = 1200.000{{c}}, ~729/640 = 169.2234{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~729/640 = 169.2234{{c}}
: error map: {{val| 0.000 -9.625 -1.559 }}
: error map: {{val| 0.000 -9.625 -1.559 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~729/640 = 168.983{{c}} -->


{{Optimal ET sequence|legend=1| 7, 57c, 64, 71b, 78b, 85b }}
{{Optimal ET sequence|legend=1| 7, 57c, 64, 71b, 78b, 85b }}
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{{Mapping|legend=1| 1 3 4 | 0 -5 -6 }}
{{Mapping|legend=1| 1 3 4 | 0 -5 -6 }}
: mapping generators: ~2, ~6/5
: mapping generators: ~2, ~6/5


Line 303: Line 292:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 338.1959{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 338.1959{{c}}
: error map: {{val| 0.000 +7.065 -15.489 }}
: error map: {{val| 0.000 +7.065 -15.489 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 338.005{{c}}
: [[error map]]: {{val| 0.000 +8.020 -14.344 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 338.365{{c}}
: error map: {{val| 0.000 +6.217 -16.507 }} -->


{{Optimal ET sequence|legend=1| 7, 25, 32, 39c }}
{{Optimal ET sequence|legend=1| 7, 25, 32, 39c }}
Line 322: Line 307:


{{Mapping|legend=1| 7 0 -17 | 0 1 3 }}
{{Mapping|legend=1| 7 0 -17 | 0 1 3 }}
: mapping generators: ~800/729, ~3
: mapping generators: ~800/729, ~3


Line 330: Line 314:
* [[CWE]]: ~800/729 = 171.4286{{c}}, ~3/2 = 700.3453{{c}} (~81/80 = 14.6310{{c}})
* [[CWE]]: ~800/729 = 171.4286{{c}}, ~3/2 = 700.3453{{c}} (~81/80 = 14.6310{{c}})
: error map: {{val| 0.000 +7.065 -15.489 }}
: error map: {{val| 0.000 +7.065 -15.489 }}
<!-- * [[CTE]]: ~800/729 = 171.429{{c}}, ~3/2 = 700.538{{c}} (~81/80 = 14.824{{c}})
* [[POTE]]: ~800/729 = 171.429{{c}}, ~3/2 = 700.187{{c}} (~81/80 = 14.473{{c}}) -->


{{Optimal ET sequence|legend=1| 7, …, 70, 77, 84, 329, 413b, 497b }}
{{Optimal ET sequence|legend=1| 7, …, 70, 77, 84, 329, 413b, 497b }}
Line 347: Line 329:


{{Mapping|legend=1| 7 0 -6 | 0 1 2 }}
{{Mapping|legend=1| 7 0 -6 | 0 1 2 }}
: mapping generators: ~10/9, ~3
: mapping generators: ~10/9, ~3


Line 355: Line 336:
* [[CWE]]: ~10/9 = 171.4286{{c}}, ~3/2 = 705.9119{{c}} (~250/243 = 20.1977{{c}})
* [[CWE]]: ~10/9 = 171.4286{{c}}, ~3/2 = 705.9119{{c}} (~250/243 = 20.1977{{c}})
: error map: {{val| 0.000 +3.957 -3.061 }}
: error map: {{val| 0.000 +3.957 -3.061 }}
<!-- * [[CTE]]: ~10/9 = 171.429{{c}}, ~3/2 = 705.526{{c}} (~250/243 = 19.812{{c}})
* [[POTE]]: ~10/9 = 171.429{{c}}, ~3/2 = 706.288{{c}} (~250/243 = 20.574{{c}}) -->


{{Optimal ET sequence|legend=1| 7, …, 42, 49, 56, 119 }}
{{Optimal ET sequence|legend=1| 7, …, 42, 49, 56, 119 }}
Line 370: Line 349:


{{Mapping|legend=1| 7 0 5 | 0 1 1 }}
{{Mapping|legend=1| 7 0 5 | 0 1 1 }}
: mapping generators: ~125/108, ~3
: mapping generators: ~125/108, ~3


Line 378: Line 356:
* [[CWE]]: ~125/108 = 171.4286{{c}}, ~3/2 = 708.3739{{c}} (~25/24 = 22.6596{{c}})
* [[CWE]]: ~125/108 = 171.4286{{c}}, ~3/2 = 708.3739{{c}} (~25/24 = 22.6596{{c}})
: error map: {{val| 0.000 +6.419 -20.797 }}
: error map: {{val| 0.000 +6.419 -20.797 }}
<!-- * [[CTE]]: ~125/108 = 171.429{{c}}, ~3/2 = 710.606{{c}} (~25/24 = 24.891{{c}})
* [[POTE]]: ~125/108 = 171.429{{c}}, ~3/2 = 706.410{{c}} (~25/24 = 20.696{{c}}) -->


{{Optimal ET sequence|legend=1| 7, 35b, 42c }}
{{Optimal ET sequence|legend=1| 7, 35b, 42c }}
Line 395: Line 371:


{{Mapping|legend=1| 1 -1 -4 | 0 9 22 }}
{{Mapping|legend=1| 1 -1 -4 | 0 9 22 }}
: mapping generators: ~2, ~243/200
: mapping generators: ~2, ~243/200


Line 403: Line 378:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/200 = 344.8041{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/200 = 344.8041{{c}}
: error map: {{val| 0.000 +1.282 -0.624 }}
: error map: {{val| 0.000 +1.282 -0.624 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~400/243 = 855.213{{c}} -->


{{Optimal ET sequence|legend=1| 7, … 73, 80, 87 }}
{{Optimal ET sequence|legend=1| 7, … 73, 80, 87 }}
Line 417: Line 391:


{{Mapping|legend=1| 1 -3 -10 | 0 16 43 }}
{{Mapping|legend=1| 1 -3 -10 | 0 16 43 }}
: mapping generators: ~2, ~8000/6561
: mapping generators: ~2, ~8000/6561


Line 425: Line 398:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8000/6561 = 343.8683{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8000/6561 = 343.8683{{c}}
: error map: {{val| 0.000 -0.062 +0.024 }}
: error map: {{val| 0.000 -0.062 +0.024 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~8000/6561 = 343.868{{c}} -->


{{Optimal ET sequence|legend=1| 7, …, 157, 164, 171, 506, 677, 848 }}
{{Optimal ET sequence|legend=1| 7, …, 157, 164, 171, 506, 677, 848 }}


[[Badness]] (Sintel): 2.78
[[Badness]] (Sintel): 2.78
== Undetrita (5-limit) ==
: ''For extensions, see [[Hemimean clan #Undetrita]].''
[[Subgroup]]: 2.3.5
[[Comma list]]: {{monzo| -22 30 -11 }}
{{Mapping|legend=1| 1 0 -2 | 0 11 30 }}
: mapping generators: ~2, ~177147/160000
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0596{{c}}, ~177147/160000 = 172.8864{{c}}
: [[error map]]: {{val| +0.060 -0.204 +0.161 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~177147/160000 = 172.8804{{c}}
: error map: {{val| 0.000 -0.271 +0.098 }}
{{Optimal ET sequence|legend=1| 7, …, 111, 118, 1541, 1659, 1777, 1895b, …, 2839b, 2957b }}
[[Badness]] (Sintel): 4.09


[[Category:7edo]]
[[Category:7edo]]
[[Category:Equivalence continua]]
[[Category:Equivalence continua]]
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