Magic family: Difference between revisions

Review optimal GPV sequences; +missing CTE and CWE tunings, +error maps, and misc. cleanup (1/2)
Review optimal GPV sequences; +missing CTE and CWE tunings, +error maps, and misc. cleanup (2/2)
Line 719: Line 719:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/4 = 378.744
* [[CTE]]: ~2 = 1200.000, ~5/4 = 378.744
: [[error map]]: {{val| 0.000 -8.235 -7.570 -20.034 }}
* [[POTE]]: ~2 = 1200.000, ~5/4 = 378.479
* [[POTE]]: ~2 = 1200.000, ~5/4 = 378.479
: error map: {{val| 0.000 -9.558 -7.834 -18.181 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 745: Line 747:
* 11-odd-limit diamond tradeoff: ~5/4 = [347.408, 386.314]
* 11-odd-limit diamond tradeoff: ~5/4 = [347.408, 386.314]


{{Optimal ET sequence|legend=0| 16, 19, 54bd }}
{{Optimal ET sequence|legend=0| 16, 19, 35, 54bd }}


Badness (Smith): 0.048038
Badness (Smith): 0.048038
Line 760: Line 762:
* POTE: ~2 = 1200.000, ~5/4 = 377.653
* POTE: ~2 = 1200.000, ~5/4 = 377.653


{{Optimal ET sequence|legend=0| 16, 19, 54bdf }}
{{Optimal ET sequence|legend=0| 16, 19, 35f, 54bdf }}


Badness (Smith): 0.030386
Badness (Smith): 0.030386
Line 775: Line 777:
* POTE: ~2 = 1200.000, ~5/4 = 377.832
* POTE: ~2 = 1200.000, ~5/4 = 377.832


{{Optimal ET sequence|legend=0| 3, 10bd, 13bd, 16, 19e, 35ee }}
{{Optimal ET sequence|legend=0| 3, 16, 19e, 35ee, 54bdeee }}


Badness (Smith): 0.046970
Badness (Smith): 0.046970
Line 790: Line 792:
* POTE: ~2 = 1200.000, ~5/4 = 377.838
* POTE: ~2 = 1200.000, ~5/4 = 377.838


{{Optimal ET sequence|legend=0| 3, 10bd, 13bd, 16, 19e, 35eef }}
{{Optimal ET sequence|legend=0| 3, 16, 19e, 35eef }}


Badness (Smith): 0.028732
Badness (Smith): 0.028732
Line 807: Line 809:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/4 = 377.385
* [[CTE]]: ~2 = 1200.000, ~5/4 = 377.385
: [[error map]]: {{val| 0.000 -15.028 -8.928 +27.643 }}
* [[CWE]]: ~2 = 1200.000, ~5/4 = 376.963
: error map: {{val| 0.000 -18.198 -9.562 +21.937 }}


{{Optimal ET sequence|legend=1| 3d, …, 13b, 16, 19d, 35d }}
{{Optimal ET sequence|legend=1| 3d, …, 13b, 16 }}


[[Badness]] (Smith): 0.084213
[[Badness]] (Smith): 0.084213
Line 821: Line 826:
Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 377.388
* CTE: ~2 = 1200.000, ~5/4 = 377.388
* CWE: ~2 = 1200.000, ~5/4 = 376.973


{{Optimal ET sequence|legend=0| 3de, …, 13be, 16, 19d, 35d }}
{{Optimal ET sequence|legend=0| 3de, 13be, 16 }}


Badness (Smith): 0.046775
Badness (Smith): 0.046775
Line 835: Line 841:
Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 376.914
* CTE: ~2 = 1200.000, ~5/4 = 376.914
* CWE: ~2 = 1200.000, ~5/4 = 376.422


{{Optimal ET sequence|legend=0| 3def, , 16, 35d }}
{{Optimal ET sequence|legend=0| 3def, 13beff, 16 }}


Badness (Smith): 0.038328
Badness (Smith): 0.038328
Line 851: Line 858:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/4 = 381.955
* [[CTE]]: ~2 = 1200.000, ~5/4 = 381.955
: [[error map]]: {{val| 0.000 +7.818 -4.359 +11.627 }}
* [[CWE]]: ~2 = 1200.000, ~5/4 = 381.956
: error map: {{val| 0.000 +7.826 -4.358 +11.613 }}


{{Optimal ET sequence|legend=1| 3, …, 19d, 22 }}
{{Optimal ET sequence|legend=1| 3, 19d, 22 }}


[[Badness]] (Smith): 0.088072
[[Badness]] (Smith): 0.088072
Line 865: Line 875:
Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 381.790
* CTE: ~2 = 1200.000, ~5/4 = 381.790
* CWE: ~2 = 1200.000, ~5/4 = 381.712


{{Optimal ET sequence|legend=0| 3, …, 19d, 22 }}
{{Optimal ET sequence|legend=0| 3, 19d, 22 }}


Badness (Smith): 0.047379
Badness (Smith): 0.047379
Line 879: Line 890:
Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 381.732
* CTE: ~2 = 1200.000, ~5/4 = 381.732
* CWE: ~2 = 1200.000, ~5/4 = 381.736


{{Optimal ET sequence|legend=0| 3, …, 19d, 22 }}
{{Optimal ET sequence|legend=0| 3, 22 }}


Badness (Smith): 0.039703
Badness (Smith): 0.039703
Line 897: Line 909:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~63/50 = 409.836
* [[CTE]]: ~2 = 1200.000, ~63/50 = 409.836
: [[error map]]: {{val| 0.000 -0.316 -5.986 -1.612 }}
* [[POTE]]: ~2 = 1200.000, ~63/50 = 410.108
* [[POTE]]: ~2 = 1200.000, ~63/50 = 410.108
: error map: {{val| 0.000 -0.437 -6.010 -1.406 }}


{{Optimal ET sequence|legend=1| 3, …, 35d, 38, 41, 202cc, 243cc, 284cc }}
{{Optimal ET sequence|legend=1| 3, 38, 41, 161c }}


[[Badness]] (Smith): 0.107115
[[Badness]] (Smith): 0.107115
Line 918: Line 932:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~147/100 = 673.187
* [[CTE]]: ~2 = 1200.000, ~147/100 = 673.187
: [[error map]]: {{val| 0.000 +0.240 -5.875 -2.891 }}
* [[POTE]]: ~2 = 1200.000, ~147/100 = 673.290
* [[POTE]]: ~2 = 1200.000, ~147/100 = 673.290
: error map: {{val| 0.000 -0.932 -6.109 -2.500 }}


{{Optimal ET sequence|legend=1| 16, 25, 41 }}
{{Optimal ET sequence|legend=1| 16, 25, 41, 139c, 180c, 221cc, 262ccd }}


[[Badness]] (Smith): 0.098334
[[Badness]] (Smith): 0.098334
Line 935: Line 951:
* POTE: ~2 = 1200.000, ~22/15 = 673.340
* POTE: ~2 = 1200.000, ~22/15 = 673.340


{{Optimal ET sequence|legend=0| 16, 25e, 41, 221cc, 262ccde }}
{{Optimal ET sequence|legend=0| 16, 25e, 41, 98c }}


Badness (Smith): 0.045623
Badness (Smith): 0.045623
Line 950: Line 966:
* POTE: ~2 = 1200.000, ~22/15 = 673.359
* POTE: ~2 = 1200.000, ~22/15 = 673.359


{{Optimal ET sequence|legend=0| 16, 25e, 41, 139cf, 180cf, 221ccf }}
{{Optimal ET sequence|legend=0| 16, 25e, 41, 98c }}


Badness (Smith): 0.033081
Badness (Smith): 0.033081
Line 961: Line 977:
{{Mapping|legend=1| 1 5 3 4 | 0 -20 -4 -7 }}
{{Mapping|legend=1| 1 5 3 4 | 0 -20 -4 -7 }}


: Mapping generators: ~2, ~28/25
: mapping generators: ~2, ~28/25


{{Multival|legend=1| 20 4 7 -40 -45 5 }}
{{Multival|legend=1| 20 4 7 -40 -45 5 }}
Line 967: Line 983:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~28/25 = 204.860
* [[CTE]]: ~2 = 1200.000, ~28/25 = 204.860
: [[error map]]: {{val| 0.000 +0.853 -5.752 -2.843 }}
* [[POTE]]: ~2 = 1200.000, ~28/25 = 204.987
* [[POTE]]: ~2 = 1200.000, ~28/25 = 204.987
: error map: {{val| 0.000 -1.691 -6.261 -3.733 }}


{{Optimal ET sequence|legend=1| 6, …, 29b, 35, 41 }}
{{Optimal ET sequence|legend=1| 6, 29b, 35, 41, 158cd, 199ccd, 240ccd, 281ccd }}


[[Badness]] (Smith): 0.127422
[[Badness]] (Smith): 0.127422
Line 984: Line 1,002:
* POTE: ~2 = 1200.000, ~28/25 = 204.956
* POTE: ~2 = 1200.000, ~28/25 = 204.956


{{Optimal ET sequence|legend=0| 6, …, 29b, 35, 41 }}
{{Optimal ET sequence|legend=0| 6, 35, 41 }}


Badness (Smith): 0.061572
Badness (Smith): 0.061572
Line 999: Line 1,017:
* POTE: ~2 = 1200.000, ~28/25 = 205.028
* POTE: ~2 = 1200.000, ~28/25 = 205.028


{{Optimal ET sequence|legend=0| 35f, 41, 199ccdef, 240ccdef, 281ccdeff }}
{{Optimal ET sequence|legend=0| 6f, 35f, 41, 117c }}


Badness (Smith): 0.044047
Badness (Smith): 0.044047
Line 1,009: Line 1,027:


{{Mapping|legend=1| 1 -10 0 -6 | 0 25 5 19 }}
{{Mapping|legend=1| 1 -10 0 -6 | 0 25 5 19 }}
: mapping generators: ~2, ~48/35


{{Multival|legend=1| 25 5 19 -50 -40 30 }}
{{Multival|legend=1| 25 5 19 -50 -40 30 }}
Line 1,014: Line 1,034:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~48/35 = 556.123
* [[CTE]]: ~2 = 1200.000, ~48/35 = 556.123
: [[error map]]: {{val| 0.000 +1.132 -5.696 -2.480 }}
* [[CWE]]: ~2 = 1200.000, ~48/35 = 556.050
: error map: {{val| 0.000 -0.695 -6.062 -3.868 }}


{{Optimal ET sequence|legend=1| 13b, 28b, 41 }}
{{Optimal ET sequence|legend=1| 13b, 28b, 41, 177bcd, 218bccdd, 259bccdd, 300cccdd }}


[[Badness]] (Smith): 0.194548
[[Badness]] (Smith): 0.194548
Line 1,028: Line 1,051:
Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/8 = 556.122
* CTE: ~2 = 1200.000, ~11/8 = 556.122
* CWE: ~2 = 1200.000, ~11/8 = 556.095


{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}
{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}
Line 1,042: Line 1,066:
Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/8 = 556.106
* CTE: ~2 = 1200.000, ~11/8 = 556.106
* CWE: ~2 = 1200.000, ~11/8 = 556.117


{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}
{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}
Line 1,058: Line 1,083:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~8/7 = 240.000, ~5/4 = 380.499 (~256/245 = 99.501)
* [[CTE]]: ~8/7 = 240.000, ~5/4 = 380.499 (~256/245 = 99.501)
* [[POTE]]: ~8/7 = 240.000, ~5/4 = 379.713 (~256/245 = 100.287)
: [[error map]]: {{val| 0.000 +0.542 -5.814 -8.826 }}
* [[CWE]]: ~8/7 = 240.000, ~5/4 = 379.997 (~256/245 = 100.003)
: error map: {{val| 0.000 -1.972 -6.317 -8.826 }}


{{Optimal ET sequence|legend=1| 25, 35, 60 }}
{{Optimal ET sequence|legend=1| 25, 35, 60 }}