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Very high accuracy temperaments: Difference between revisions

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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 27 -18 1 }} = 950.981427{{c}}
* [[WE]]: ~2 = 1199.997524{{c}}, ~{{monzo| 27 -18 1 }} = 950.979631{{c}}
* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 27 -18 1 }} = 950.981594{{c}}
: [[error map]]: {{val| -0.0025 +0.0043 -0.0005 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 27 -18 1 }} = 950.981535{{c}}
: error map: {{val| 0.0000 +0.0081 +0.0031 }}
<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 27 -18 1 }} = 950.981427{{c}}
* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 27 -18 1 }} = 950.981594{{c}} -->


{{Optimal ET sequence|legend=1| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}
{{Optimal ET sequence|legend=1| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}
Line 115: Line 119:
[[Comma list]]: {{monzo| -36 -52 51 }}
[[Comma list]]: {{monzo| -36 -52 51 }}


{{Mapping|legend=1| 1 15 16 | 0 -51 -52 }}
{{Mapping|legend=1| 1 -36 -36 | 0 51 52 }}
: mapping generators: ~2, ~6/5
: mapping generators: ~2, ~5/3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000{{c}}, ~6/5 = 315.647899{{c}}
* [[WE]]: ~2 = 1200.000553{{c}}, ~5/3 = 884.352488{{c}}
* [[POTE]]: ~2 = 1200.000000{{c}}, ~6/5 = 315.647919{{c}}
: [[error map]]: {{val| +0.0006 +0.0020 -0.0042 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~5/3 = 844.352090{{c}}
: error map: {{val| 0.0000 +0.0016 -0.0050 }}
<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~5/3 = 884.352101{{c}}
* [[POTE]]: ~2 = 1200.000000{{c}}, ~5/3 = 884.352081{{c}} -->


{{Optimal ET sequence|legend=1| 19, …, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}
{{Optimal ET sequence|legend=1| 19, …, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}
Line 131: Line 139:
Comma list: 78125000/78121827, {{monzo| -48 0 11 8 }}
Comma list: 78125000/78121827, {{monzo| -48 0 11 8 }}


Mapping: {{mapping| 1 15 16 -16 | 0 -102 -104 143 }}
Mapping: {{mapping| 1 -87 -88 127 | 0 102 104 -143 }}
: mapping generators: ~2, ~67108864/36756909


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000000{{c}}, ~36756909/33554432 = 157.823952{{c}}
* WE: ~2 = 1200.000308{{c}}, ~67108864/36756909 = 1042.176313{{c}}
* CWE: ~2 = 1200.000000{{c}}, ~36756909/33554432 = 157.823954{{c}}
* CWE: ~2 = 1200.000000{{c}}, ~67108864/36756909 = 1042.176046{{c}}
<!-- * CTE: ~2 = 1200.000000{{c}}, ~67108864/36756909 = 1042.176048{{c}} -->


{{Optimal ET sequence|legend=0| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
{{Optimal ET sequence|legend=0| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
Line 146: Line 156:
Comma list: [[140625/140608]], {{monzo| -4 20 -9 0 0 -4 }}
Comma list: [[140625/140608]], {{monzo| -4 20 -9 0 0 -4 }}


Mapping: {{mapping| 1 15 16 -16 | 0 -51 -52 -138 }}
Mapping: {{mapping| 1 -36 -36 -98 | 0 51 52 138 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~2 = 1200.0031{{c}}, ~6/5 = 315.6490{{c}}
* WE: ~2 = 1200.000308{{c}}, ~5/3 = 884.354064{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~6/5 = 315.6482{{c}}
* CWE: ~2 = 1200.000000{{c}}, ~5/3 = 884.351835{{c}}
<!-- * CTE: ~2 = 1200.0031{{c}}, ~5/3 = 884.3510{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~5/3 = 884.3518{{c}} -->


{{Optimal ET sequence|legend=0| 19, …, 441, 460, 901, 1342 }}
{{Optimal ET sequence|legend=0| 19, …, 441, 460, 901, 1342 }}
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[[Comma list]]: {{monzo| -107 47 14 }}
[[Comma list]]: {{monzo| -107 47 14 }}


{{Mapping|legend=1| 1 13 -36 | 0 -14 47 }}
{{Mapping|legend=1| 1 -1 11 | 0 14 -47 }}
: mapping generators: ~2, 7381125/4194304
: mapping generators: ~2, ~8388608/7381125


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567861{{c}}
* [[WE]]: ~2 = 1200.000553{{c}}, ~8388608/7381125 = 221.568202{{c}}
* [[POTE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567899{{c}}
: [[error map]]: {{val| +0.0016 -0.0018 -0.0012 }}
* [[CWE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567889{{c}}
: error map: {{val| 0.0000 -0.0046 -0.0045 }}
<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567861{{c}}
* [[POTE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567899{{c}} -->


{{Optimal ET sequence|legend=1| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}
{{Optimal ET sequence|legend=1| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}
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Comma list: 78125000/78121827, {{monzo| -52 17 12 -1 }}
Comma list: 78125000/78121827, {{monzo| -52 17 12 -1 }}


Mapping: {{mapping| 1 13 -36 -263 | 0 -14 47 326 }}
Mapping: {{mapping| 1 -1 11 63 | 0 14 -47 -326 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568013{{c}}
* WE: ~2 = 1200.001970{{c}}, ~8388608/7381125 = 221.568395{{c}}
* POTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568031{{c}}
* CWE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568026{{c}}
<!-- * CTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568013{{c}}
* POTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568031{{c}} -->


{{Optimal ET sequence|legend=0| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}
{{Optimal ET sequence|legend=0| 65d, …, 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}


Badness (Sintel): TBD
Badness (Sintel): TBD
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Comma list: 151263/151250, 21437500/21434787, 369140625/369098752
Comma list: 151263/151250, 21437500/21434787, 369140625/369098752


Mapping: {{mapping| 1 13 -36 -263 -573 | 0 -14 47 326 707 }}
Mapping: {{mapping| 1 -1 11 63 134 | 0 14 -47 -326 -707 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568116{{c}}
* WE: ~2 = 1200.003854{{c}}, ~8388608/7381125 = 221.568850{{c}}
* POTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568139{{c}}
* CWE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568133{{c}}
<!-- * CTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568116{{c}}
* POTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568139{{c}} -->


{{Optimal ET sequence|legend=1| 612, 2513, 3125, 3737, 8086, 19909d }}
{{Optimal ET sequence|legend=0| 65dee, …, 612, 2513, 3125, 3737, 8086, 19909d }}


Badness (Sintel): TBD
Badness (Sintel): TBD
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