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Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)
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Line 26: Line 26:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.2194{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.2194{{c}}
: error map: {{val| 0.000 -0.858 -6.094 }}
: 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 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 380.058{{c}}
: error map: {{val| 0.000 -1.663 -6.255 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 76: Line 72:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.4576{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.4576{{c}}
: error map: {{val| 0.000 +0.333 -5.856 -3.335 }}
: 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 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 380.352{{c}}
: error map: {{val| 0.000 -0.195 -5.962 -4.602 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 105: Line 97:
* WE: ~2 = 1200.1372{{c}}, ~5/4 = 380.7399{{c}}
* WE: ~2 = 1200.1372{{c}}, ~5/4 = 380.7399{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7008{{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 132: Line 122:
* WE: ~2 = 1200.0331{{c}}, ~5/4 = 380.4377{{c}}
* WE: ~2 = 1200.0331{{c}}, ~5/4 = 380.4377{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.4284{{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 153: Line 141:
* WE: ~2 = 1199.3584{{c}}, ~5/4 = 380.4006{{c}}
* WE: ~2 = 1199.3584{{c}}, ~5/4 = 380.4006{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.5896{{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 }}
Line 160: Line 146:
Badness (Sintel): 1.05
Badness (Sintel): 1.05


====== 19-limit ======
====== Magicus ======
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 170: Line 156:
* WE: ~2 = 1199.7173{{c}}, ~5/4 = 380.3808{{c}}
* WE: ~2 = 1199.7173{{c}}, ~5/4 = 380.3808{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.4680{{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 }}
Line 186: Line 171:
* WE: ~2 = 1199.3670{{c}}, ~5/4 = 380.4681{{c}}
* WE: ~2 = 1199.3670{{c}}, ~5/4 = 380.4681{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.6541{{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 }}
Line 202: Line 186:
* WE: ~2 = 1200.1727{{c}}, ~5/4 = 380.2982{{c}}
* WE: ~2 = 1200.1727{{c}}, ~5/4 = 380.2982{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.2483{{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 }}
Line 218: Line 201:
* WE: ~2 = 1200.2179{{c}}, ~5/4 = 380.3942{{c}}
* WE: ~2 = 1200.2179{{c}}, ~5/4 = 380.3942{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.3314{{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 }}
Line 236: Line 218:
* WE: ~2 = 1200.2802{{c}}, ~5/4 = 380.5053{{c}}
* WE: ~2 = 1200.2802{{c}}, ~5/4 = 380.5053{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.4258{{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 }}
Line 253: Line 233:
* WE: ~2 = 1201.2397{{c}}, ~5/4 = 380.8698{{c}}
* WE: ~2 = 1201.2397{{c}}, ~5/4 = 380.8698{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.5080{{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 (Sintel): 1.07
Badness (Sintel): 1.07
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 52/51, 65/64, 78/77, 91/90, 100/99
Mapping: {{mapping| 1 0 2 -1 6 4 6 | 0 5 1 12 -8 -1 -6 }}
Optimal tunings:
* WE: ~2 = 1200.4822{{c}}, ~5/4 = 380.8818{{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 }}
Badness (Sintel): 1.21
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 52/51, 65/64, 78/77, 91/90, 100/99, 133/132
Mapping: {{mapping| 1 0 2 -1 6 4 6 9 | 0 5 1 12 -8 -1 -6 -15 }}
Optimal tunings:
* WE: ~2 = 1200.6684{{c}}, ~5/4 = 380.8328{{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 }}
Badness (Sintel): 1.41


==== Necromancy ====
==== Necromancy ====
Line 303: Line 248:
* WE: ~2 = 1199.9675{{c}}, ~5/4 = 380.7770{{c}}
* WE: ~2 = 1199.9675{{c}}, ~5/4 = 380.7770{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7874{{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 }}
Line 320: Line 263:
* WE: ~2 = 1199.6176{{c}}, ~5/4 = 380.7053{{c}}
* WE: ~2 = 1199.6176{{c}}, ~5/4 = 380.7053{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.8280{{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 (Sintel): 1.12
Badness (Sintel): 1.12
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 120/119, 133/132, 154/153, 209/208, 225/224
Mapping: {{mapping| 1 0 2 -1 6 11 6 9 | 0 5 1 12 -8 -23 -6 -15 }}
Optimal tunings:
* WE: ~2 = 1199.6176{{c}}, ~5/4 = 380.6981{{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 }}
Badness (Sintel): 1.28


==== Soothsaying ====
==== Soothsaying ====
Line 353: Line 278:
* WE: ~55/39 = 600.2918{{c}}, ~5/4 = 380.6928{{c}}
* WE: ~55/39 = 600.2918{{c}}, ~5/4 = 380.6928{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~5/4 = 380.5121{{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 }}
Line 370: Line 293:
* WE: ~17/12 = 600.2918{{c}}, ~5/4 = 380.6927{{c}}
* WE: ~17/12 = 600.2918{{c}}, ~5/4 = 380.6927{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~5/4 = 380.5135{{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 }}
Line 387: Line 308:
* WE: ~17/12 = 600.3301{{c}}, ~5/4 = 380.6797{{c}}
* WE: ~17/12 = 600.3301{{c}}, ~5/4 = 380.6797{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~5/4 = 380.4704{{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 }}
Line 404: Line 323:
* WE: ~2 = 1200.7724{{c}}, ~5/4 = 381.2641{{c}}
* WE: ~2 = 1200.7724{{c}}, ~5/4 = 381.2641{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 381.0913{{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 }}
Line 421: Line 338:
* WE: ~2 = 1202.5634{{c}}, ~5/4 = 381.3348{{c}}
* WE: ~2 = 1202.5634{{c}}, ~5/4 = 381.3348{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.6886{{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 (Sintel): 1.05
Badness (Sintel): 1.05
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 55/54, 65/64, 85/84, 91/90, 99/98
Mapping: {{mapping| 1 0 2 -1 -1 4 -1 | 0 5 1 12 14 -1 16 }}
Optimal tunings:
* WE: ~2 = 1202.5560{{c}}, ~5/4 = 381.4295{{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 }}
Badness (Sintel): 1.03
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 55/54, 57/56, 65/64, 76/75, 85/84, 99/98
Mapping: {{mapping| 1 0 2 -1 -1 4 -1 2 | 0 5 1 12 14 -1 16 7 }}
Optimal tunings:
* WE: ~2 = 1203.4043{{c}}, ~5/4 = 381.5989{{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 }}
Badness (Sintel): 1.16


==== Intuition ====
==== Intuition ====
Line 471: Line 353:
* WE: ~2 = 1201.3172{{c}}, ~5/4 = 380.9004{{c}}
* WE: ~2 = 1201.3172{{c}}, ~5/4 = 380.9004{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.5942{{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 (Sintel): 1.08
Badness (Sintel): 1.08
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 55/54, 66/65, 85/84, 99/98, 105/104
Mapping: {{mapping| 1 0 2 -1 -1 -2 -1 | 0 5 1 12 14 18 16 }}
Optimal tunings:
* WE: ~2 = 1201.3593{{c}}, ~5/4 = 381.0356{{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 }}
Badness (Sintel): 1.03
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 55/54, 66/65, 77/76, 85/84, 99/98, 105/104
Mapping: {{mapping| 1 0 2 -1 -1 -2 -1 -4 | 0 5 1 12 14 18 16 26 }}
Optimal tunings:
* WE: ~2 = 1201.5266{{c}}, ~5/4 = 381.0019{{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 }}
Badness (Sintel): 1.19


=== Horcrux ===
=== Horcrux ===
Line 521: Line 368:
* WE: ~2 = 1200.4670{{c}}, ~5/4 = 379.7895{{c}}
* WE: ~2 = 1200.4670{{c}}, ~5/4 = 379.7895{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 379.6889{{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 }}
Line 538: Line 383:
* WE: ~2 = 1200.2953{{c}}, ~5/4 = 379.8842{{c}}
* WE: ~2 = 1200.2953{{c}}, ~5/4 = 379.8842{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 379.8165{{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 }}
Line 555: Line 398:
* WE: ~2 = 1200.2484{{c}}, ~5/4 = 380.2053{{c}}
* WE: ~2 = 1200.2484{{c}}, ~5/4 = 380.2053{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.1482{{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 }}
Line 571: Line 413:
* WE: ~2 = 1199.5457{{c}}, ~5/4 = 379.4681{{c}}
* WE: ~2 = 1199.5457{{c}}, ~5/4 = 379.4681{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 379.5713{{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 }}
Line 587: Line 428:
* WE: ~2 = 1202.2187{{c}}, ~5/4 = 379.8171{{c}}
* WE: ~2 = 1202.2187{{c}}, ~5/4 = 379.8171{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 379.2709{{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 }}
Line 604: Line 443:
* WE: ~2 = 1201.2634{{c}}, ~5/4 = 380.6321{{c}}
* WE: ~2 = 1201.2634{{c}}, ~5/4 = 380.6321{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.2849{{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 }}
Line 621: Line 458:
* WE: ~2 = 1201.0424{{c}}, ~5/4 = 380.5193{{c}}
* WE: ~2 = 1201.0424{{c}}, ~5/4 = 380.5193{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.2349{{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 }}
Line 638: Line 473:
* WE: ~2 = 1201.1638{{c}}, ~5/4 = 380.4827{{c}}
* WE: ~2 = 1201.1638{{c}}, ~5/4 = 380.4827{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.1599{{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 (Sintel): 1.06
Badness (Sintel): 1.06
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 105/104, 133/132, 154/153, 170/169, 171/169, 196/195
Mapping: {{mapping| 1 0 2 -1 -7 -2 -7 -4 | 0 5 1 12 33 18 35 26 }}
Optimal tunings:
* WE: ~2 = 1201.2528{{c}}, ~5/4 = 380.5518{{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 }}
Badness (Sintel): 1.13


=== Divination ===
=== Divination ===
Line 671: Line 488:
* WE: ~99/70 = 600.8306{{c}}, ~5/4 = 380.7598{{c}}
* WE: ~99/70 = 600.8306{{c}}, ~5/4 = 380.7598{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~5/4 = 380.3800{{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 }}
Line 688: Line 503:
* WE: ~99/70 = 600.9624{{c}}, ~5/4 = 380.5297{{c}}
* WE: ~99/70 = 600.9624{{c}}, ~5/4 = 380.5297{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~5/4 = 380.0614{{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 }}
Line 705: Line 518:
* WE: ~17/12 = 600.8921{{c}}, ~5/4 = 380.5094{{c}}
* WE: ~17/12 = 600.8921{{c}}, ~5/4 = 380.5094{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~5/4 = 380.0672{{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 }}
Line 721: Line 533:
* WE: ~2 = 1201.0749{{c}}, ~11/7 = 790.7980{{c}}
* WE: ~2 = 1201.0749{{c}}, ~11/7 = 790.7980{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 790.1429{{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 }}
Line 738: Line 548:
* WE: ~2 = 1201.2830{{c}}, ~11/7 = 790.8409{{c}}
* WE: ~2 = 1201.2830{{c}}, ~11/7 = 790.8409{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 790.0516{{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 }}
Line 755: Line 563:
* WE: ~2 = 1201.1557{{c}}, ~11/7 = 790.7157{{c}}
* WE: ~2 = 1201.1557{{c}}, ~11/7 = 790.7157{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 790.0057{{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 }}
Line 771: Line 578:
* WE: ~2 = 1201.3558{{c}}, ~11/7 = 790.8266{{c}}
* WE: ~2 = 1201.3558{{c}}, ~11/7 = 790.8266{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 789.9880{{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 }}
Line 789: Line 595:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 378.744{{c}}
* [[WE]]: ~2 = 1203.9554{{c}}, ~5/4 = 379.7269{{c}}
: [[error map]]: {{val| 0.000 -8.235 -7.570 -20.034 }}
: [[error map]]: {{val| +3.955 -3.321 +1.324 -7.137 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 378.479{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 378.5328{{c}}
: error map: {{val| 0.000 -9.558 -7.834 -18.181 }}
: error map: {{val| 0.000 -9.291 -7.781 -18.555 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 801: Line 607:
{{Optimal ET sequence|legend=1| 16, 19, 73bcd, 92bcdd, 111bcddd }}
{{Optimal ET sequence|legend=1| 16, 19, 73bcd, 92bcdd, 111bcddd }}


[[Badness]] (Smith): 0.056206
[[Badness]] (Sintel): 1.42


=== 11-limit ===
=== 11-limit ===
Line 811: Line 617:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 378.228{{c}}
* WE: ~2 = 1203.0804{{c}}, ~5/4 = 378.6936{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 377.724{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 377.8174{{c}}


Tuning ranges:  
Tuning ranges:  
Line 820: Line 626:
{{Optimal ET sequence|legend=0| 16, 19, 35, 54bd }}
{{Optimal ET sequence|legend=0| 16, 19, 35, 54bd }}


Badness (Smith): 0.048038
Badness (Sintel): 1.59


==== 13-limit ====
==== 13-limit ====
Line 830: Line 636:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 378.176{{c}}
* WE: ~2 = 1203.4291{{c}}, ~5/4 = 378.7321{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 377.653{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 377.7336{{c}}


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


Badness (Smith): 0.030386
Badness (Sintel): 1.26


=== Muggloid ===
=== Muggloid ===
Line 845: Line 651:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 377.724{{c}}
* WE: ~2 = 1205.6044{{c}}, ~5/4 = 379.5966{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 377.832{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 377.8142{{c}}


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


Badness (Smith): 0.046970
Badness (Sintel): 1.55


==== 13-limit ====
==== 13-limit ====
Line 860: Line 666:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 377.652{{c}}
* WE: ~2 = 1205.4897{{c}}, ~5/4 = 379.5667{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 377.838{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 377.8118{{c}}


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


Badness (Smith): 0.028732
Badness (Sintel): 1.19


== Darkstone ==
== Brightstone ==
Darkstone (16 & 19d) is a low-accuacy temperament which tempers out 36/35 and 1875/1792. It makes the major third and the fifth even flatter than those of muggles. In [http://www.tonalsoft.com/enc/m/magic.aspx ''Encyclopedia of Microtonal Music Theory'', Tonalsoft], this temperament is given a name ''witch''.
Brightstone tempers out 64/63 and may be described as {{nowrap| 22 & 25 }}. 22edo itself is a good tuning, in which case it is identical to magic. Brightstone can be extended to the 11- and 13-limit in a similar way to muggles.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 1875/1792
[[Comma list]]: 64/63, 3125/3024


{{Mapping|legend=1| 1 0 2 0 | 0 5 1 9 }}
{{Mapping|legend=1| 1 0 2 6 | 0 5 1 -10 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 377.385{{c}}
* [[WE]]: ~2 = 1198.1701{{c}}, ~5/4 = 381.3741{{c}}
: [[error map]]: {{val| 0.000 -15.028 -8.928 +27.643 }}
: error map: {{val| -1.830 +4.915 -8.599 +6.454 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 376.963{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 381.9562{{c}}
: error map: {{val| 0.000 -18.198 -9.562 +21.937 }}
: error map: {{val| 0.000 +7.826 -4.358 +11.613 }}


{{Optimal ET sequence|legend=1| 3d, …, 13b, 16 }}
{{Optimal ET sequence|legend=1| 3, 19d, 22 }}


[[Badness]] (Smith): 0.084213
[[Badness]] (Sintel): 2.23


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 36/35, 45/44, 363/343
Comma list: 55/54, 64/63, 625/616


Mapping: {{mapping| 1 0 2 0 0 | 0 5 1 9 11 }}
Mapping: {{mapping| 1 0 2 6 -1 | 0 5 1 -10 14 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 377.388{{c}}
* WE: ~2 = 1198.5372{{c}}, ~5/4 = 381.7556{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 376.973{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 382.1943{{c}}


{{Optimal ET sequence|legend=0| 3de, 13be, 16 }}
{{Optimal ET sequence|legend=0| 22, 69b }}


Badness (Smith): 0.046775
Badness (Sintel): 1.85


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 27/26, 36/35, 45/44, 363/343
Comma list: 40/39, 55/54, 64/63, 625/616


Mapping: {{mapping| 1 0 2 0 0 -1 | 0 5 1 9 11 15 }}
Mapping: {{mapping| 1 0 2 6 6 4 | 0 5 1 -10 14 -4 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 376.914{{c}}
* WE: ~2 = 1197.2300{{c}}, ~5/4 = 381.6164{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 376.422{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 382.4690{{c}}
 
{{Optimal ET sequence|legend=0| 22f, 47bff }}
 
Badness (Sintel): 1.99


{{Optimal ET sequence|legend=0| 3def, 13beff, 16 }}
== Darkstone ==
Darkstone (16 & 19d) is a low-accuracy temperament which tempers out 36/35 and 1875/1792. It makes the major third and the fifth even flatter than those of muggles.


Badness (Smith): 0.038328
This temperament is known as ''witch'' in [http://www.tonalsoft.com/enc/m/magic.aspx Tonalsoft Encyclopedia].  


== Brightstone ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 64/63, 3125/3024
[[Comma list]]: 36/35, 1875/1792


{{Mapping|legend=1| 1 0 2 6 | 0 5 1 -10 }}
{{Mapping|legend=1| 1 0 2 0 | 0 5 1 9 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 381.955{{c}}
* [[WE]]: ~2 = 1201.7458{{c}}, ~5/4 = 377.2996{{c}}
: [[error map]]: {{val| 0.000 +7.818 -4.359 +11.627 }}
: [[error map]]: {{val| +1.746 -15.457 -5.523 +26.870 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 381.956{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 376.9630{{c}}
: error map: {{val| 0.000 +7.826 -4.358 +11.613 }}
: error map: {{val| 0.000 -17.140 -9.351 +23.841 }}


{{Optimal ET sequence|legend=1| 3, 19d, 22 }}
{{Optimal ET sequence|legend=1| 3d, …, 13b, 16 }}


[[Badness]] (Smith): 0.088072
[[Badness]] (Sintel): 2.13


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 64/63, 100/99, 605/588
Comma list: 36/35, 45/44, 363/343


Mapping: {{mapping| 1 0 2 6 6 | 0 5 1 -10 -8 }}
Mapping: {{mapping| 1 0 2 0 0 | 0 5 1 9 11 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 381.790{{c}}
* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 381.712{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.9735{{c}}


{{Optimal ET sequence|legend=0| 3, 19d, 22 }}
{{Optimal ET sequence|legend=0| 3de, 13be, 16 }}


Badness (Smith): 0.047379
Badness (Sintel): 1.55


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 64/63, 65/63, 100/99, 169/165
Comma list: 27/26, 36/35, 45/44, 363/343


Mapping: {{mapping| 1 0 2 6 6 4 | 0 5 1 -10 -8 -1 }}
Mapping: {{mapping| 1 0 2 0 0 -1 | 0 5 1 9 11 15 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~5/4 = 381.732{{c}}
* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 381.736{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.4221{{c}}
 
{{Optimal ET sequence|legend=0| 3def, 13beff, 16 }}


{{Optimal ET sequence|legend=0| 3, 22 }}
Badness (Sintel): 1.58


Badness (Smith): 0.039703
Scales: [[User:BudjarnLambeth/Volcanic glass]]
 
Music: [https://www.youtube.com/watch?v=oXy_RXrBVWA ''Rain in the crystal mirror caves''] - [[Budjarn Lambeth]] (2026)


== Hocum ==
== Hocum ==
Line 968: Line 782:
[[Comma list]]: 3125/3072, 4000/3969
[[Comma list]]: 3125/3072, 4000/3969


{{Mapping|legend=1| 1 5 3 -3 | 0 -10 -2 17 }}
{{Mapping|legend=1| 1 -5 1 14 | 0 10 2 -17 }}


: mapping generators: ~2, ~63/50
: mapping generators: ~2, ~63/40


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~63/50 = 409.836{{c}}
* [[WE]]: ~2 = 1200.8375{{c}}, ~63/40 = 790.7032{{c}}
: [[error map]]: {{val| 0.000 -0.316 -5.986 -1.612 }}
: [[error map]]: {{val| +0.838 +0.890 -4.070 +0.944 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~63/50 = 410.108{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~63/40 = 790.1542{{c}}
: error map: {{val| 0.000 -0.437 -6.010 -1.406 }}
: error map: {{val| 0.000 -0.413 -6.005 -1.447 }}


{{Optimal ET sequence|legend=1| 3, 38, 41, 161c }}
{{Optimal ET sequence|legend=1| 3, 38, 41, 161c }}


[[Badness]] (Smith): 0.107115
[[Badness]] (Sintel): 2.71


== Trismegistus ==
== Trismegistus ==
{{See also| No-threes subgroup temperaments #Mabilic }}{{Main|Mabilic and trismegistus}}
{{Main| Mabilic and trismegistus }}
{{See also| No-threes subgroup temperaments #Mabilic }}


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 989: Line 804:
[[Comma list]]: 1029/1024, 3125/3072
[[Comma list]]: 1029/1024, 3125/3072


{{Mapping|legend=1| 1 10 4 0 | 0 -15 -3 5 }}
{{Mapping|legend=1| 1 -5 1 5 | 0 15 3 -5 }}


: mapping generators: ~2, ~147/100
: mapping generators: ~2, ~168/125


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~147/100 = 673.187{{c}}
* [[WE]]: ~2 = 1201.0799{{c}}, ~168/125 = 527.1841{{c}}
: [[error map]]: {{val| 0.000 +0.240 -5.875 -2.891 }}
: [[error map]]: {{val| +1.080 +0.408 -3.681 +0.653 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~147/100 = 673.290{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~168/125 = 526.7349{{c}}
: error map: {{val| 0.000 -0.932 -6.109 -2.500 }}
: error map: {{val| 0.000 -0.932 -6.109 -2.500 }}


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


[[Badness]] (Smith): 0.098334
[[Badness]] (Sintel): 2.49


=== 11-limit ===
=== 11-limit ===
Line 1,008: Line 823:
Comma list: 385/384, 441/440, 625/616
Comma list: 385/384, 441/440, 625/616


Mapping: {{mapping| 1 10 4 0 13 | 0 -15 -3 5 -17 }}
Mapping: {{mapping| 1 -5 1 5 -4 | 0 15 3 -5 17 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~22/15 = 673.241{{c}}
* WE: ~2 = 1200.8404{{c}}, ~15/11 = 527.0289{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/15 = 673.340{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 526.6826{{c}}


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


Badness (Smith): 0.045623
Badness (Sintel): 1.51


=== 13-limit ===
=== 13-limit ===
Line 1,023: Line 838:
Comma list: 105/104, 144/143, 275/273, 625/616
Comma list: 105/104, 144/143, 275/273, 625/616


Mapping: {{mapping| 1 10 4 0 13 11 | 0 -15 -3 5 -17 -13 }}
Mapping: {{mapping| 1 -5 1 5 -4 -2 | 0 15 3 -5 17 13 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~22/15 = 673.294{{c}}
* WE: ~2 = 1200.4759{{c}}, ~15/11 = 526.8502{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/15 = 673.359{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 526.6548{{c}}


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


Badness (Smith): 0.033081
Badness (Sintel): 1.37


=== 2.3.5.7.11.13.19 subgroup ===
=== 2.3.5.7.11.13.19 subgroup ===
Line 1,038: Line 853:
Comma list: 105/104, 144/143, 441/440, 210/209, 625/616
Comma list: 105/104, 144/143, 441/440, 210/209, 625/616


Subgroup-val mapping: {{mapping| 1 10 4 0 13 11 2 | 0 -15 -3 5 -17 -13 4 }}
Subgroup-val mapping: {{mapping| 1 -5 1 5 -4 -2 6 | 0 15 3 -5 17 13 -4 }}


Optimal tunings:
Optimal tunings:
* CWE: ~2 = 1200.000{{c}}, ~22/15 = 673.363{{c}}
* WE: ~2 = 1200.5832{{c}}, ~15/11 = 526.8804{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 526.6368{{c}}


{{Optimal ET sequence|legend=0| 16, 25e, 41, 98c }}
{{Optimal ET sequence|legend=0| 16, 25e, 41, 98c }}
Badness (Sintel): 1.26


== Quadrimage ==
== Quadrimage ==
Line 1,050: Line 868:
[[Comma list]]: 2401/2400, 3125/3072
[[Comma list]]: 2401/2400, 3125/3072


{{Mapping|legend=1| 1 5 3 4 | 0 -20 -4 -7 }}
{{Mapping|legend=1| 1 -15 -1 -3 | 0 20 4 7 }}


: mapping generators: ~2, ~28/25
: mapping generators: ~2, ~25/14


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~28/25 = 204.860{{c}}
* [[WE]]: ~2 = 1201.2708{{c}}, ~25/14 = 996.0669{{c}}
: [[error map]]: {{val| 0.000 +0.853 -5.752 -2.843 }}
: [[error map]]: {{val| +1.271 +0.322 -3.317 -0.170 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~28/25 = 204.987{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~25/14 = 995.0515{{c}}
: error map: {{val| 0.000 -1.691 -6.261 -3.733 }}
: error map: {{val| 0.000 -0.926 -6.108 -3.466 }}


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


[[Badness]] (Smith): 0.127422
[[Badness]] (Sintel): 3.22


=== 11-limit ===
=== 11-limit ===
Line 1,069: Line 887:
Comma list: 245/242, 385/384, 625/616
Comma list: 245/242, 385/384, 625/616


Mapping: {{mapping| 1 5 3 4 5 | 0 -20 -4 -7 -9 }}
Mapping: {{mapping| 1 -15 -1 -3 -4 | 0 20 4 7 9 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~28/25 = 204.881{{c}}
* WE: ~2 = 1200.6716{{c}}, ~25/14 = 995.6009{{c}}
* POTE: ~2 = 1200.000{{c}}, ~28/25 = 204.956{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/14 = 995.0633{{c}}


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


Badness (Smith): 0.061572
Badness (Sintel): 2.04


=== 13-limit ===
=== 13-limit ===
Line 1,084: Line 902:
Comma list: 105/104, 144/143, 245/242, 625/616
Comma list: 105/104, 144/143, 245/242, 625/616


Mapping: {{mapping| 1 5 3 4 5 9 | 0 -20 -4 -7 -9 -31 }}
Mapping: {{mapping| 1 -15 -1 -3 -22 | 0 20 4 7 9 31 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~28/25 = 204.956{{c}}
* WE: ~2 = 1200.6276{{c}}, ~25/14 = 995.4920{{c}}
* POTE: ~2 = 1200.000{{c}}, ~28/25 = 205.028{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/14 = 994.9901{{c}}


{{Optimal ET sequence|legend=0| 6f, 35f, 41, 117c }}
{{Optimal ET sequence|legend=0| 6f, 35f, 41, 117c }}


Badness (Smith): 0.044047
Badness (Sintel): 1.82


== Quinmage ==
== Quinmage ==
Line 1,104: Line 922:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~48/35 = 556.123{{c}}
* [[WE]]: ~2 = 1201.3334{{c}}, ~48/35 = 556.6311{{c}}
: [[error map]]: {{val| 0.000 +1.132 -5.696 -2.480 }}
: error map: {{val| +1.333 +0.489 -3.158 -0.835 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~48/35 = 556.050{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~48/35 = 556.0504{{c}}
: error map: {{val| 0.000 -0.695 -6.062 -3.868 }}
: error map: {{val| 0.000 -0.695 -6.062 -3.868 }}


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


[[Badness]] (Smith): 0.194548
[[Badness]] (Sintel): 4.92


=== 11-limit ===
=== 11-limit ===
Line 1,121: Line 939:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/8 = 556.122{{c}}
* WE: ~2 = 1200.4252{{c}}, ~11/8 = 556.2831{{c}}
* CWE: ~2 = 1200.000{{c}}, ~11/8 = 556.095{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 556.0951{{c}}


{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}
{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}


Badness (Smith): 0.101724
Badness (Sintel): 3.36


=== 13-limit ===
=== 13-limit ===
Line 1,136: Line 954:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~11/8 = 556.106{{c}}
* WE: ~2 = 1199.8239{{c}}, ~11/8 = 556.0389{{c}}
* CWE: ~2 = 1200.000{{c}}, ~11/8 = 556.117{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 556.1171{{c}}


{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}
{{Optimal ET sequence|legend=0| 13b, 28b, 41 }}


Badness (Smith): 0.067742
Badness (Sintel): 2.80


== Warlock ==
== Warlock ==
Line 1,153: Line 971:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~8/7 = 240.000{{c}}, ~5/4 = 380.499{{c}} (~256/245 = 99.501{{c}})
* [[WE]]: ~8/7 = 240.3877{{c}}, ~5/4 = 380.4267{{c}} (~256/245 = 100.3488{{c}})
: [[error map]]: {{val| 0.000 +0.542 -5.814 -8.826 }}
: error map: {{val| +1.939 +0.178 -2.010 -3.398 }}
* [[CWE]]: ~8/7 = 240.000{{c}}, ~5/4 = 379.997{{c}} (~256/245 = 100.003{{c}})
* [[CWE]]: ~8/7 = 240.0000{{c}}, ~5/4 = 379.9965{{c}} (~256/245 = 100.0035{{c}})
: error map: {{val| 0.000 -1.972 -6.317 -8.826 }}
: 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 }}


[[Badness]] (Smith): 0.287190
[[Badness]] (Sintel): 7.27


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Magic family| ]] <!-- main article -->
[[Category:Magic family| ]] <!-- main article -->
[[Category:Magic| ]] <!-- key article -->
[[Category:Magic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/Magic_family"