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Syntonic–diatonic equivalence continuum: Difference between revisions

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[[Comma list]]: {{monzo| -76 67 -13 }}
[[Comma list]]: {{monzo| -76 67 -13 }}


{{Mapping|legend=1| 1 12 56 | 0 -13 -67 }}
{{Mapping|legend=1| 1 -1 -11 | 0 13 67 }}
 
: mapping generators: ~2, ~{{monzo| -35 31 -6 }}
: mapping generators: ~2, ~{{monzo| 36 -31 6 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.0377{{c}}, ~{{monzo| 36 -31 6 }} = 961.4293{{c}}
* [[WE]]: ~2 = 1200.0377{{c}}, ~{{monzo| -35 31 -6 }} = 238.6084{{c}}
: [[error map]]: {{val| +0.038 -0.083 +0.035 }}
: [[error map]]: {{val| +0.038 -0.083 +0.035 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| 36 -31 6 }} = 961.3985{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -35 31 -6 }} = 238.6015{{c}}
: error map: {{val| 0.000 -0.135 -0.011 }}
: error map: {{val| 0.000 -0.135 -0.011 }}


{{Optimal ET sequence|legend=1| 5, …, 166, 171, 860, 1031, 1202, 1373, 1544 }}
{{Optimal ET sequence|legend=1| 5, …, 166, 171, 860, 1031, 1202, 1373, 1544, 3259, 4803b, 6347b }}


[[Badness]] (Sintel): 20.9
[[Badness]] (Sintel): 20.9
Line 452: Line 451:


{{Mapping|legend=1| 1 -2 -16 | 0 9 46 }}
{{Mapping|legend=1| 1 -2 -16 | 0 9 46 }}
: mapping generators: ~2, ~320/243
: mapping generators: ~2, ~320/243


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{{Optimal ET sequence|legend=1| 5, 108c, 113, 118, 1057, 1175, 1293, 1411, 1529, 1647, 1765, 1883, 2001b, 3884b }}
{{Optimal ET sequence|legend=1| 5, 108c, 113, 118, 1057, 1175, 1293, 1411, 1529, 1647, 1765, 1883, 2001b, 3884b }}


[[Badness]] (Smith): 0.617683
[[Badness]] (Sintel): 14.5


== Tribilalegu (5 & 137) ==
== Tribilalegu (5 & 137) ==
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[[Comma list]]: {{Monzo| -60 54 -11 }}
[[Comma list]]: {{Monzo| -60 54 -11 }}


{{Mapping|legend=1| 1 6 24 | 0 -11 -54 }}
{{Mapping|legend=1| 1 -5 -30 | 0 11 54 }}
 
: mapping generators: ~2, ~243/160
: mapping generators: ~2, ~320/243


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.000{{c}}, ~320/243 = 481.742{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~243/160 = 718.258{{c}}


{{Optimal ET sequence|legend=1| 5, 127c, 132, 137, 553, 690b, 827b, 964b }}
{{Optimal ET sequence|legend=1| 5, 127c, 132, 137, 553, 690b, 827b, 964b }}


[[Badness]] (Smith): 3.620981
[[Badness]] (Sintel): 84.9
 
[http://x31eq.com/cgi-bin/rt.cgi?ets=5_137&limit=5 The temperament finder - 5-limit 5 & 137]


== 559 & 2513 ==
== 559 & 2513 ==
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[[Comma list]]: {{monzo| -124 109 -21 }}
[[Comma list]]: {{monzo| -124 109 -21 }}


{{Mapping|legend=1| 1 10 46 | 0 -21 -109 }}
{{Mapping|legend=1| 1 -11 -63 | 0 21 109 }}
 
: mapping generators: ~2, ~{{monzo| -29 26 -5 }}
: mapping generators: ~2, ~3355443200000/2541865828329


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1200.0000{{c}}, ~3355443200000/2541865828329 = 480.8595{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -29 26 -5 }} = 719.1405{{c}}
 
{{Optimal ET sequence|legend=1| 5, 267c, 272c, 277, 559, 1395, 1954, 2513, 40767, 43280, 45793, 48306, 50819, 53332, 55845, 58358, 60871, 63384, 65897, 68410, 70923, 73436, 75949, 78462 }}


[[Badness]] (Smith): 0.134523
{{Optimal ET sequence|legend=1| 5, …, 277, 559, 1395, 1954, 2513, 40767, 43280, 45793, 48306, 50819, 53332, 55845, 58358, 60871, 63384, 65897, 68410, 70923, 73436, 75949, 78462, 154411b }}


[http://x31eq.com/cgi-bin/rt.cgi?ets=2513_559&limit=5 The temperament finder - 5-limit 2513 & 559]
[[Badness]] (Sintel): 3.16
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[[Category:5edo]]
[[Category:5edo]]
[[Category:Equivalence continua]]
[[Category:Equivalence continua]]
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