Syntonic–chromatic equivalence continuum: Difference between revisions

- CTE & POTE tunings
+ error map. Review optimal ET sequence. Unify precision
 
(2 intermediate revisions by 2 users not shown)
Line 94: Line 94:
| {{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 209: 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 228: 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


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{{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 }}


{{Optimal ET sequence|legend=1| 6b, 7 }}
{{Optimal ET sequence|legend=1| 6b, 7 }}
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{{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


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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


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{{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 335: 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 356: 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


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{{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


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{{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


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[[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]]