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Syntonic–diatonic equivalence continuum: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings. Comment out unnamed temps
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 709.8213{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 709.8213{{c}}
: error map: {{val| 0.000 +7.866 +2.078 }}
: error map: {{val| 0.000 +7.866 +2.078 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 709.393{{c}}
: [[error map]]: {{val| 0.000 +7.438 -1.774 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 710.078{{c}}
: error map: {{val| 0.000 +8.123 +4.385 }} -->


{{Optimal ET sequence|legend=1| 5, 17, 22, 49, 120b, 169bbc }}
{{Optimal ET sequence|legend=1| 5, 17, 22, 49, 120b, 169bbc }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 733.721{{c}}
: [[error map]]: {{val| 0.000 +31.766 +11.362 }} -->
* [[WE]]: ~2 = 1189.7544{{c}}, ~3/2 = 724.6670{{c}}
* [[WE]]: ~2 = 1189.7544{{c}}, ~3/2 = 724.6670{{c}}
: [[error map]]: {{val| -10.246 +12.466 +4.210 }}
: [[error map]]: {{val| -10.246 +12.466 +4.210 }}
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 713.5968{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 713.5968{{c}}
: error map: {{val| 0.000 +11.642 +4.041 }}
: error map: {{val| 0.000 +11.642 +4.041 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 713.185{{c}}
: [[error map]]: {{val| 0.000 +11.230 -1.722 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 713.829{{c}}
: error map: {{val| 0.000 +11.874 +7.289 }} -->


{{Optimal ET sequence|legend=1| 5, 27c, 32, 37, 79bc, 116bbc }}
{{Optimal ET sequence|legend=1| 5, 27c, 32, 37, 79bc, 116bbc }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 714.992{{c}}
: [[error map]]: {{val| 0.000 +13.037 -1.473 }} -->
* [[WE]]: ~2 = 1195.8566{{c}}, ~3/2 = 713.0611{{c}}
* [[WE]]: ~2 = 1195.8566{{c}}, ~3/2 = 713.0611{{c}}
: [[error map]]: {{val| -4.143 +6.963 -0.863 }}
: [[error map]]: {{val| -4.143 +6.963 -0.863 }}
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: ''For extensions, see [[Gamelismic clan #Rodan]].''
: ''For extensions, see [[Gamelismic clan #Rodan]].''


The 5-limit version of rodan tempers out the [[rodan comma]], which is the difference between a stack of three [[729/640|retroptolemaic whole tones (729/640)]] and a perfect fifth (3/2). The only 7-limit extension that makes any sense to use is to add the gamelisma to the comma list. It corresponds to {{nowrap| ''n'' {{=}} 3 }}.  
The 5-limit version of rodan tempers out the [[rodan comma]], which is the difference between a stack of three [[729/640|retroptolemaic whole tones (729/640)]] and a perfect fifth (3/2). The only 7-limit extension that makes any sense to use is to add the gamelisma to the comma list, whereby the generator represents [[8/7]]. It corresponds to {{nowrap| ''n'' {{=}} 3 }}.  


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
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* [[CWE]]: ~2 = 1200.000{{c}}, ~729/640 = 234.4999{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~729/640 = 234.4999{{c}}
: error map: {{val| 0.000 +1.545 +0.185 }}
: error map: {{val| 0.000 +1.545 +0.185 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~729/640 = 234.457{{c}}
: [[error map]]: {{val| 0.000 +1.417 -0.537 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~729/640 = 234.528{{c}}
: error map: {{val| 0.000 +1.629 +0.663 }} -->


{{Optimal ET sequence|legend=1| 5, …, 41, 46, 87, 220, 307 }}
{{Optimal ET sequence|legend=1| 5, …, 41, 46, 87, 220, 307 }}
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* [[CWE]]: ~2 = 1200.000{{c}}, ~10/9 = 228.0128{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~10/9 = 228.0128{{c}}
: error map: {{val| 0.000 -17.917 +9.776 }}
: error map: {{val| 0.000 -17.917 +9.776 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 228.700{{c}}
: [[error map]]: {{val| 0.000 -15.856 +14.584 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~10/9 = 227.426{{c}}
: error map: {{val| 0.000 -19.679 +5.664 }} -->


{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37b }}
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37b }}
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* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 231.4822{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 231.4822{{c}}
: error map: {{val| 0.000 -7.509 +76.651 }}
: error map: {{val| 0.000 -7.509 +76.651 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 226.980{{c}}
: [[error map]]: {{val| 0.000 -21.014 +67.647 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 235.442{{c}}
: error map: {{val| 0.000 +4.370 +84.569 }} -->


{{Optimal ET sequence|legend=1| 1b, …, 4bc, 5 }}
{{Optimal ET sequence|legend=1| 1b, …, 4bc, 5 }}
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/160 = 716.7671{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/160 = 716.7671{{c}}
: error map: {{val| 0.000 -1.352 -0.067 }}
: error map: {{val| 0.000 -1.352 -0.067 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~243/160 = 716.753{{c}} -->


{{Optimal ET sequence|legend=1| 5, …, 72, 149, 221, 370, 591b }}
{{Optimal ET sequence|legend=1| 5, …, 72, 149, 221, 370, 591b }}
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* [[CWE]]: ~729/640 = 240.0000{{c}}, ~3/2 = 704.4446{{c}}
* [[CWE]]: ~729/640 = 240.0000{{c}}, ~3/2 = 704.4446{{c}}
: error map: {{val| 0.000 +2.490 +0.354 }}
: error map: {{val| 0.000 +2.490 +0.354 }}
<!-- * [[POTE]]: ~729/640 = 240.000{{c}}, ~3/2 = 704.572{{c}} -->


{{Optimal ET sequence|legend=1| 5, …, 75, 80, 155, 390b, 545bbc }}
{{Optimal ET sequence|legend=1| 5, …, 75, 80, 155, 390b, 545bbc }}
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~177147/102400 = 957.5367{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~177147/102400 = 957.5367{{c}}
: error map: {{val| 0.000 +0.802 +0.082 }}
: error map: {{val| 0.000 +0.802 +0.082 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~177147/102400 = 957.543{{c}} -->


{{Optimal ET sequence|legend=1| 5, …, 94, 99, 193, 292, 391, 1074b, 1465bb }}
{{Optimal ET sequence|legend=1| 5, …, 94, 99, 193, 292, 391, 1074b, 1465bb }}
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