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Consolidate existing info on 11-limit magic. Address 13-limit magic.
Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)
Line 22: Line 22:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 380.499{{c}}
* [[WE]]: ~2 = 1201.2449{{c}}, ~5/4 = 380.4527{{c}}
: [[error map]]: {{val| +1.245 +0.309 -3.371 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.2194{{c}}
: error map: {{val| 0.000 -0.858 -6.094 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 380.499{{c}}
: [[error map]]: {{val| 0.000 +0.542 -5.814 }}
: [[error map]]: {{val| 0.000 +0.542 -5.814 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 380.058{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 380.058{{c}}
: error map: {{val| 0.000 -1.663 -6.255 }}
: error map: {{val| 0.000 -1.663 -6.255 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 39: Line 43:
{{Optimal ET sequence|legend=1| 3, 13b, 16, 19, 41, 60, 221cc, 281cc }}
{{Optimal ET sequence|legend=1| 3, 13b, 16, 19, 41, 60, 221cc, 281cc }}


[[Badness]] (Smith): 0.039163
[[Badness]] (Sintel): 0.919


=== Overview to extensions ===
=== Overview to extensions ===
Line 68: Line 72:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 380.651{{c}}
* [[WE]]: ~2 = 1201.0786{{c}}, ~5/4 = 380.6939{{c}}
: [[error map]]: {{val| +1.079 +1.514 -3.463 -1.578 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.4576{{c}}
: error map: {{val| 0.000 +0.333 -5.856 -3.335 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 380.651{{c}}
: [[error map]]: {{val| 0.000 +1.301 -5.662 -1.011 }}
: [[error map]]: {{val| 0.000 +1.301 -5.662 -1.011 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 380.352{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 380.352{{c}}
: error map: {{val| 0.000 -0.195 -5.962 -4.602 }}
: error map: {{val| 0.000 -0.195 -5.962 -4.602 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 85: Line 93:
{{Optimal ET sequence|legend=1| 19, 41, 142cd, 183cd, 224ccd }}
{{Optimal ET sequence|legend=1| 19, 41, 142cd, 183cd, 224ccd }}


[[Badness]] (Smith): 0.018918
[[Badness]] (Sintel): 0.479


=== 11-limit ===
=== 11-limit ===
Line 95: Line 103:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.720{{c}}
* WE: ~2 = 1200.1372{{c}}, ~5/4 = 380.7399{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.696{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7008{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.720{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.696{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 108: Line 118:
{{Optimal ET sequence|legend=0| 19, 22, 41, 104 }}
{{Optimal ET sequence|legend=0| 19, 22, 41, 104 }}


Badness (Smith): 0.020352
Badness (Sintel): 0.673


==== 13-limit ====
==== 13-limit ====
Line 120: Line 130:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.435{{c}}
* WE: ~2 = 1200.0331{{c}}, ~5/4 = 380.4377{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.427{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.4284{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.435{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.427{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 129: Line 141:
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}


Badness (Smith): 0.021509
Badness (Sintel): 0.889


===== Magical =====
===== Magical =====
Line 139: Line 151:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.510{{c}}
* WE: ~2 = 1199.3584{{c}}, ~5/4 = 380.4006{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.604{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.5896{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.510{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.604{{c}} -->


{{Optimal ET sequence|legend=0| 19, 22f, 41 }}
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}


Badness (Smith): 0.020633
Badness (Sintel): 1.05


====== 19-limit ======
====== 19-limit ======
Line 154: Line 168:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.451{{c}}
* WE: ~2 = 1199.7173{{c}}, ~5/4 = 380.3808{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.4680{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.451{{c}} -->


{{Optimal ET sequence|legend=0| 19, 41 }}
{{Optimal ET sequence|legend=0| 19, 41 }}


Badness (Smith): 0.020881
Badness (Sintel): 1.27


====== Magica ======
====== Magica ======
Line 168: Line 184:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.573{{c}}
* WE: ~2 = 1199.3670{{c}}, ~5/4 = 380.4681{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.6541{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.573{{c}} -->


{{Optimal ET sequence|legend=0| 22fh, 41 }}
{{Optimal ET sequence|legend=0| 22fh, 41 }}


Badness (Smith): 0.019945
Badness (Sintel): 1.21


===== Magia =====
===== Magia =====
Line 182: Line 200:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.271{{c}}
* WE: ~2 = 1200.1727{{c}}, ~5/4 = 380.2982{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.2483{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.271{{c}} -->


{{Optimal ET sequence|legend=0| 19g, 41, 60 }}
{{Optimal ET sequence|legend=0| 19g, 41, 60 }}


Badness (Smith): 0.026232
Badness (Sintel): 1.34


====== 19-limit ======
====== 19-limit ======
Line 196: Line 216:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.360{{c}}
* WE: ~2 = 1200.2179{{c}}, ~5/4 = 380.3942{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.3314{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.360{{c}} -->


{{Optimal ET sequence|legend=0| 19gh, 41 }}
{{Optimal ET sequence|legend=0| 19gh, 41 }}


Badness (Smith): 0.023709
Badness (Sintel): 1.44


===== Evening =====
===== Evening =====
Evening is a remarkable subgroup temperament of 19 &amp; 41 with prime harmonics of 29 and 31.  
Evening is a remarkable subgroup temperament of {{nowrap| 19 & 22f }} with prime harmonics of 29 and 31.  


Subgroup: 2.3.5.7.11.13.29.31
Subgroup: 2.3.5.7.11.13.29.31
Line 209: Line 231:
Comma list: 100/99, 105/104, 144/143, 145/144, 155/154, 196/195
Comma list: 100/99, 105/104, 144/143, 145/144, 155/154, 196/195


Sval mapping: {{mapping| 1 0 2 -1 6 -2 2 4 | 0 5 1 12 -8 18 9 3 }}
Subgroup-val mapping: {{mapping| 1 0 2 -1 6 -2 2 4 | 0 5 1 12 -8 18 9 3 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.478{{c}}
* WE: ~2 = 1200.2802{{c}}, ~5/4 = 380.5053{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.416{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.4258{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.478{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.416{{c}} -->


{{Optimal ET sequence|legend=0| 19, 22f, 41 }}
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}
Badness (Sintel): 0.807


==== Sorcery ====
==== Sorcery ====
Line 225: Line 251:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.674{{c}}
* WE: ~2 = 1201.2397{{c}}, ~5/4 = 380.8698{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.477{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.5080{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.674{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.477{{c}} -->


{{Optimal ET sequence|legend=0| 19, 22, 41f }}
{{Optimal ET sequence|legend=0| 19, 22, 41f }}


Badness (Smith): 0.025829
Badness (Sintel): 1.07


===== 17-limit =====
===== 17-limit =====
Line 240: Line 268:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.784{{c}}
* WE: ~2 = 1200.4822{{c}}, ~5/4 = 380.8818{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.729{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7356{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.784{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.729{{c}} -->


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


Badness (Smith): 0.023768
Badness (Sintel): 1.21


===== 19-limit =====
===== 19-limit =====
Line 255: Line 285:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.625{{c}}
* WE: ~2 = 1200.6684{{c}}, ~5/4 = 380.8328{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 380.621{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.6212{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.625{{c}} -->


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


Badness (Smith): 0.023232
Badness (Sintel): 1.41


==== Necromancy ====
==== Necromancy ====
Line 270: Line 301:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.788{{c}}
* WE: ~2 = 1199.9675{{c}}, ~5/4 = 380.7770{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.787{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7874{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.788{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.787{{c}} -->


{{Optimal ET sequence|legend=0| 19f, 22, 41, 63, 104 }}
{{Optimal ET sequence|legend=0| 19f, 22, 41, 63, 104 }}


Badness (Smith): 0.025275
Badness (Sintel): 1.04


===== 17-limit =====
===== 17-limit =====
Line 285: Line 318:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.837{{c}}
* WE: ~2 = 1199.6176{{c}}, ~5/4 = 380.7053{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.827{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.8280{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.837{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.827{{c}} -->


{{Optimal ET sequence|legend=0| 19f, 22, 41, 63 }}
{{Optimal ET sequence|legend=0| 19f, 22, 41, 63 }}


Badness (Smith): 0.022032
Badness (Sintel): 1.12


===== 19-limit =====
===== 19-limit =====
Line 300: Line 335:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.741{{c}}
* WE: ~2 = 1199.6176{{c}}, ~5/4 = 380.6981{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 380.735{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7355{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.741{{c}} -->


{{Optimal ET sequence|legend=0| 19f, 22, 41 }}
{{Optimal ET sequence|legend=0| 19f, 22, 41 }}


Badness (Smith): 0.021101
Badness (Sintel): 1.28


==== Soothsaying ====
==== Soothsaying ====
Line 315: Line 351:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 600.000{{c}}, ~5/4 = 380.539{{c}}
* WE: ~55/39 = 600.2918{{c}}, ~5/4 = 380.6928{{c}}
* POTE: ~55/39 = 600.000{{c}}, ~5/4 = 380.508{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~5/4 = 380.5121{{c}}
<!-- * CTE: ~55/39 = 600.000{{c}}, ~5/4 = 380.539{{c}}
* POTE: ~55/39 = 600.000{{c}}, ~5/4 = 380.508{{c}} -->


{{Optimal ET sequence|legend=0| 22, 60, 82 }}
{{Optimal ET sequence|legend=0| 22, 60, 82 }}


Badness (Smith): 0.055443
Badness (Sintel): 2.29


===== 17-limit =====
===== 17-limit =====
Line 330: Line 368:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600.000{{c}}, ~5/4 = 380.553{{c}}
* WE: ~17/12 = 600.2918{{c}}, ~5/4 = 380.6927{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~5/4 = 380.508{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~5/4 = 380.5135{{c}}
<!-- * CTE: ~17/12 = 600.000{{c}}, ~5/4 = 380.553{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~5/4 = 380.508{{c}} -->


{{Optimal ET sequence|legend=0| 22, 60, 82 }}
{{Optimal ET sequence|legend=0| 22, 60, 82 }}


Badness (Smith): 0.035654
Badness (Sintel): 1.82


===== 19-limit =====
===== 19-limit =====
Line 345: Line 385:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600.000{{c}}, ~5/4 = 380.470{{c}}
* WE: ~17/12 = 600.3301{{c}}, ~5/4 = 380.6797{{c}}
* CWE: ~17/12 = 600.000{{c}}, ~5/4 = 380.470{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~5/4 = 380.4704{{c}}
<!-- * CTE: ~17/12 = 600.000{{c}}, ~5/4 = 380.470{{c}}
* CWE: ~17/12 = 600.000{{c}}, ~5/4 = 380.470{{c}} -->


{{Optimal ET sequence|legend=0| 22, 60, 82 }}
{{Optimal ET sequence|legend=0| 22, 60, 82 }}


Badness (Smith): 0.031291
Badness (Sintel): 1.90


=== Telepathy ===
=== Telepathy ===
Line 360: Line 402:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 381.231{{c}}
* WE: ~2 = 1200.7724{{c}}, ~5/4 = 381.2641{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 381.019{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 381.0913{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 381.231{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 381.019{{c}} -->


{{Optimal ET sequence|legend=0| 19e, 22, 41e, 63e }}
{{Optimal ET sequence|legend=0| 19e, 22, 41e, 63e }}


Badness (Smith): 0.027109
Badness (Sintel): 0.896


==== 13-limit ====
==== 13-limit ====
Line 375: Line 419:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 381.196{{c}}
* WE: ~2 = 1202.5634{{c}}, ~5/4 = 381.3348{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.520{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.6886{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 381.196{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.520{{c}} -->


{{Optimal ET sequence|legend=0| 19e, 22, 41ef }}
{{Optimal ET sequence|legend=0| 19e, 22, 41ef }}


Badness (Smith): 0.025522
Badness (Sintel): 1.05


===== 17-limit =====
===== 17-limit =====
Line 390: Line 436:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 381.288{{c}}
* WE: ~2 = 1202.5560{{c}}, ~5/4 = 381.4295{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.619{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7843{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 381.288{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.619{{c}} -->


{{Optimal ET sequence|legend=0| 19eg, 22, 41efg }}
{{Optimal ET sequence|legend=0| 19eg, 22, 41efg }}


Badness (Smith): 0.020201
Badness (Sintel): 1.03


===== 19-limit =====
===== 19-limit =====
Line 405: Line 453:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 381.464{{c}}
* WE: ~2 = 1203.4043{{c}}, ~5/4 = 381.5989{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 380.735{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7353{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 381.464{{c}} -->


{{Optimal ET sequence|legend=0| 19egh, 22, 41efghh }}
{{Optimal ET sequence|legend=0| 19egh, 22, 41efghh }}


Badness (Smith): 0.019004
Badness (Sintel): 1.16


==== Intuition ====
==== Intuition ====
Line 420: Line 469:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.816{{c}}
* WE: ~2 = 1201.3172{{c}}, ~5/4 = 380.9004{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.483{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.5942{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.816{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.483{{c}} -->


{{Optimal ET sequence|legend=0| 19e, 22f }}
{{Optimal ET sequence|legend=0| 19e, 22f }}


Badness (Smith): 0.026089
Badness (Sintel): 1.08


===== 17-limit =====
===== 17-limit =====
Line 435: Line 486:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.952{{c}}
* WE: ~2 = 1201.3593{{c}}, ~5/4 = 381.0356{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.604{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7204{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.952{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.604{{c}} -->


{{Optimal ET sequence|legend=0| 19eg, 22f }}
{{Optimal ET sequence|legend=0| 19eg, 22f }}


Badness (Smith): 0.020274
Badness (Sintel): 1.03


===== 19-limit =====
===== 19-limit =====
Line 450: Line 503:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.866{{c}}
* WE: ~2 = 1201.5266{{c}}, ~5/4 = 381.0019{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 380.628{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.6275{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.866{{c}} -->


{{Optimal ET sequence|legend=0| 19egh, 22fh }}
{{Optimal ET sequence|legend=0| 19egh, 22fh }}


Badness (Smith): 0.019518
Badness (Sintel): 1.19


=== Horcrux ===
=== Horcrux ===
Line 465: Line 519:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 379.796{{c}}
* WE: ~2 = 1200.4670{{c}}, ~5/4 = 379.7895{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 379.642{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 379.6889{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 379.796{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 379.642{{c}} -->


{{Optimal ET sequence|legend=0| 3de, 16d, 19 }}
{{Optimal ET sequence|legend=0| 3de, 16d, 19 }}


Badness (Smith): 0.039282
Badness (Sintel): 1.30


==== 13-limit ====
==== 13-limit ====
Line 480: Line 536:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 379.885{{c}}
* WE: ~2 = 1200.2953{{c}}, ~5/4 = 379.8842{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 379.791{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 379.8165{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 379.885{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 379.791{{c}} -->


{{Optimal ET sequence|legend=0| 3def, 16dff, 19 }}
{{Optimal ET sequence|legend=0| 3def, 16dff, 19 }}


Badness (Smith): 0.031938
Badness (Sintel): 1.32


===== 17-limit =====
===== 17-limit =====
Line 495: Line 553:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.216{{c}}
* WE: ~2 = 1200.2484{{c}}, ~5/4 = 380.2053{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 380.148{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.1482{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.216{{c}} -->


{{Optimal ET sequence|legend=0| 3defg, 16dffgg, 19g }}
{{Optimal ET sequence|legend=0| 3defg, 16dffgg, 19g }}


Badness (Smith): 0.028074
Badness (Sintel): 1.43


===== Horcruxic =====
===== Horcruxic =====
Line 510: Line 569:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 379.524{{c}}
* WE: ~2 = 1199.5457{{c}}, ~5/4 = 379.4681{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 379.571{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 379.5713{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 379.524{{c}} -->


{{Optimal ET sequence|legend=0| 3defg, 16dff, 19 }}
{{Optimal ET sequence|legend=0| 3defg, 16dff, 19 }}


Badness (Smith): 0.029556
Badness (Sintel): 1.51


==== Glamour ====
==== Glamour ====
Line 525: Line 585:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 379.757{{c}}
* WE: ~2 = 1202.2187{{c}}, ~5/4 = 379.8171{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 379.116{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 379.2709{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 379.757{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 379.116{{c}} -->


{{Optimal ET sequence|legend=0| 3de, 16d, 19 }}
{{Optimal ET sequence|legend=0| 3de, 16d, 19 }}


Badness (Smith): 0.033317
Badness (Sintel): 1.38


=== Witchcraft ===
=== Witchcraft ===
Line 540: Line 602:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.416{{c}}
* WE: ~2 = 1201.2634{{c}}, ~5/4 = 380.6321{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.232{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.2849{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.416{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.232{{c}} -->


{{Optimal ET sequence|legend=0| 19e, 41, 60e, 101cd, 243ccdde }}
{{Optimal ET sequence|legend=0| 19e, 41, 60e, 101cd, 243ccdde }}


Badness (Smith): 0.030706
Badness (Sintel): 1.02


==== 13-limit ====
==== 13-limit ====
Line 555: Line 619:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.352{{c}}
* WE: ~2 = 1201.0424{{c}}, ~5/4 = 380.5193{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.189{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.2349{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.352{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.189{{c}} -->


{{Optimal ET sequence|legend=0| 19e, 41, 60e, 101cd }}
{{Optimal ET sequence|legend=0| 19e, 41, 60e, 101cd }}


Badness (Smith): 0.023547
Badness (Sintel): 0.973


==== 17-limit ====
==== 17-limit ====
Line 570: Line 636:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.281{{c}}
* WE: ~2 = 1201.1638{{c}}, ~5/4 = 380.4827{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.114{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.1599{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.281{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 380.114{{c}} -->


{{Optimal ET sequence|legend=0| 19eg, 41, 60e, 101cd }}
{{Optimal ET sequence|legend=0| 19eg, 41, 60e, 101cd }}


Badness (Smith): 0.020756
Badness (Sintel): 1.06


==== 19-limit ====
==== 19-limit ====
Line 585: Line 653:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.339{{c}}
* WE: ~2 = 1201.2528{{c}}, ~5/4 = 380.5518{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 380.205{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.2052{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 380.339{{c}} -->


{{Optimal ET sequence|legend=0| 19egh, 41, 60eh }}
{{Optimal ET sequence|legend=0| 19egh, 41, 60eh }}


Badness (Smith): 0.018625
Badness (Sintel): 1.13


=== Divination ===
=== Divination ===
Line 600: Line 669:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.000{{c}}, ~5/4 = 380.732{{c}}
* WE: ~99/70 = 600.8306{{c}}, ~5/4 = 380.7598{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~5/4 = 380.223{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~5/4 = 380.3800{{c}}
<!-- * CTE: ~99/70 = 600.000{{c}}, ~5/4 = 380.732{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~5/4 = 380.223{{c}} -->


{{Optimal ET sequence|legend=0| 22, 38d, 60e, 142cdee, 202ccddeee }}
{{Optimal ET sequence|legend=0| 22, 38d, 60e, 142cdee, 202ccddeee }}


Badness (Smith): 0.035864
Badness (Sintel): 1.19


==== 13-limit ====
==== 13-limit ====
Line 615: Line 686:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.000{{c}}, ~5/4 = 380.417{{c}}
* WE: ~99/70 = 600.9624{{c}}, ~5/4 = 380.5297{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~5/4 = 379.920{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~5/4 = 380.0614{{c}}
<!-- * CTE: ~99/70 = 600.000{{c}}, ~5/4 = 380.417{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~5/4 = 379.920{{c}} -->


{{Optimal ET sequence|legend=0| 22f, 38df, 60e }}
{{Optimal ET sequence|legend=0| 22f, 38df, 60e }}


Badness (Smith): 0.034551
Badness (Sintel): 1.43


==== 17-limit ====
==== 17-limit ====
Line 630: Line 703:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600.000{{c}}, ~5/4 = 380.433{{c}}
* WE: ~17/12 = 600.8921{{c}}, ~5/4 = 380.5094{{c}}
* CWE: ~17/12 = 600.000{{c}}, ~5/4 = 380.067{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~5/4 = 380.0672{{c}}
<!-- * CTE: ~17/12 = 600.000{{c}}, ~5/4 = 380.433{{c}} -->


{{Optimal ET sequence|legend=0| 22f, 38df, 60e }}
{{Optimal ET sequence|legend=0| 22f, 38df, 60e }}


Badness (Smith): 0.023775
Badness (Sintel): 1.21


=== Hocus ===
=== Hocus ===
Line 642: Line 716:
Comma list: 225/224, 243/242, 245/242
Comma list: 225/224, 243/242, 245/242


Mapping: {{mapping| 1 5 3 11 12 | 0 -10 -2 -24 -25 }}
Mapping: {{mapping| 1 -5 1 -13 -13 | 0 10 2 24 25 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~14/11 = 409.760{{c}}
* WE: ~2 = 1201.0749{{c}}, ~11/7 = 790.7980{{c}}
* POTE: ~2 = 1200.000{{c}}, ~14/11 = 409.910{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 790.1429{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 790.240{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/7 = 790.090{{c}} -->


{{Optimal ET sequence|legend=0| 38d, 41, 120cd }}
{{Optimal ET sequence|legend=0| 38d, 41, 120cd }}


Badness (Smith): 0.038519
Badness (Sintel): 1.27


==== 13-limit ====
==== 13-limit ====
Line 657: Line 733:
Comma list: 105/104, 196/195, 243/242, 245/242
Comma list: 105/104, 196/195, 243/242, 245/242


Mapping: {{mapping| 1 5 3 11 12 16 | 0 -10 -2 -24 -25 -36 }}
Mapping: {{mapping| 1 -5 1 -13 -13 -20 | 0 10 2 24 25 36 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~14/11 = 409.842{{c}}
* WE: ~2 = 1201.2830{{c}}, ~11/7 = 790.8409{{c}}
* POTE: ~2 = 1200.000{{c}}, ~14/11 = 410.004{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 790.0516{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 790.158{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/7 = 789.996{{c}} -->


{{Optimal ET sequence|legend=0| 38df, 41, 79d, 120cd }}
{{Optimal ET sequence|legend=0| 38df, 41, 79d, 120cd }}


Badness (Smith): 0.030280
Badness (Sintel): 1.25


==== 17-limit ====
==== 17-limit ====
Line 672: Line 750:
Comma list: 105/104, 154/153, 196/195, 243/242, 245/242
Comma list: 105/104, 154/153, 196/195, 243/242, 245/242


Mapping: {{mapping| 1 5 3 11 12 16 14 | 0 -10 -2 -24 -25 -36 -29 }}
Mapping: {{mapping| 1 -5 1 -13 -13 -20 -15 | 0 10 2 24 25 36 29 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~14/11 = 409.896{{c}}
* WE: ~2 = 1201.1557{{c}}, ~11/7 = 790.7157{{c}}
* CWE: ~2 = 1200.000{{c}}, ~14/11 = 409.994{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 790.0057{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 790.104{{c}} -->


{{Optimal ET sequence|legend=0| 38df, 41, 79d }}
{{Optimal ET sequence|legend=0| 38df, 41, 79d }}


Badness (Smith): 0.025491
Badness (Sintel): 1.30


==== 19-limit ====
==== 19-limit ====
Line 687: Line 766:
Comma list: 105/104, 154/153, 196/195, 243/242, 245/242
Comma list: 105/104, 154/153, 196/195, 243/242, 245/242


Mapping: {{mapping| 1 5 3 11 12 16 14 8 | 0 -10 -2 -24 -25 -36 -29 -11 }}
Mapping: {{mapping| 1 -5 1 -13 -13 -20 -3 | 0 10 2 24 25 36 29 11 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~14/11 = 409.884{{c}}
* WE: ~2 = 1201.3558{{c}}, ~11/7 = 790.8266{{c}}
* CWE: ~2 = 1200.000{{c}}, ~14/11 = 410.012{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 789.9880{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 790.116{{c}} -->


{{Optimal ET sequence|legend=0| 38df, 41, 79dh }}
{{Optimal ET sequence|legend=0| 38df, 41, 79dh }}


Badness (Smith): 0.020277
Badness (Sintel): 1.23


== Muggles ==
== Muggles ==
Retrieved from "https://en.xen.wiki/w/Magic_family"