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Breedsmic temperaments: Difference between revisions

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m Units & misc. cleanup
Switch to Sintel's badness, WE & CWE tunings
Line 41: Line 41:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.4464{{c}}
* [[WE]]: ~2 = 1199.7412{{c}}, ~49/40 = 351.4016{{c}}
: [[error map]]: {{val| -0.259 +0.590 +0.021 -0.346 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.4671{{c}}
: error map: {{val| 0.000 +0.979 +0.364 +0.246 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.4464{{c}}
: [[error map]]: {{val| 0.0000 +0.9379 -0.1531 -0.0224 }}
: [[error map]]: {{val| 0.0000 +0.9379 -0.1531 -0.0224 }}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.4774{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.4774{{c}}
: error map: {{val| 0.0000 +0.9999 +0.6221 +0.0307 }}
: error map: {{val| 0.0000 +0.9999 +0.6221 +0.0307 }} -->


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 53: Line 57:
[[Algebraic generator]]: (2 + sqrt(2))/2
[[Algebraic generator]]: (2 + sqrt(2))/2


{{Optimal ET sequence|legend=1| 41, 58, 99, 239, 338 }}
{{Optimal ET sequence|legend=1| 17c, 41, 58, 99, 239, 338 }}


[[Badness]] (Smith): 0.022243
[[Badness]] (Sintel): 0.563


=== 11-limit ===
=== 11-limit ===
Line 65: Line 69:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4289{{c}}
* WE: ~2 = 1199.2845{{c}}, ~11/9 = 351.3110{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.5206{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4956{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4289{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.5206{{c}} -->


{{Optimal ET sequence|legend=0| 17c, 41, 58, 99e }}
{{Optimal ET sequence|legend=0| 17c, 41, 58, 99e }}


Badness (Smith): 0.023498
Badness (Sintel): 0.777


==== 13-limit ====
==== 13-limit ====
Line 80: Line 86:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4331{{c}}
* WE: ~2 = 1198.8875{{c}}, ~11/9 = 351.2475{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.5734{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.5438{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.4331{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~11/9 = 351.5734{{c}} -->


{{Optimal ET sequence|legend=0| 17c, 41, 58, 99ef, 157eff }}
{{Optimal ET sequence|legend=0| 17c, 41, 58, 99ef, 157eff }}


Badness (Smith): 0.019090
Badness (Sintel): 0.789


=== Semihemi ===
=== Semihemi ===
Line 96: Line 104:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~49/40 = 351.4722{{c}}
* WE: ~99/70 = 599.8556{{c}}, ~400/231 = 951.2757{{c}}
* POTE: ~99/70 = 600.0000{{c}}, ~49/40 = 351.5047{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~400/231 = 951.4939{{c}}
<!-- * CTE: ~99/70 = 600.0000{{c}}, ~400/231 = 951.4722{{c}}
* POTE: ~99/70 = 600.0000{{c}}, ~400/231 = 951.5047{{c}} -->


{{Optimal ET sequence|legend=0| 58, 140, 198 }}
{{Optimal ET sequence|legend=0| 58, 140, 198 }}


Badness (Smith): 0.042487
Badness (Sintel): 1.40


==== 13-limit ====
==== 13-limit ====
Line 111: Line 121:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~49/40 = 351.4674{{c}}
* WE: ~99/70 = 599.8513{{c}}, ~26/15 = 951.2662{{c}}
* POTE: ~99/70 = 600.0000{{c}}, ~49/40 = 351.5019{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~26/15 = 951.4905{{c}}
<!-- * CTE: ~99/70 = 600.0000{{c}}, ~26/15 = 951.4674{{c}}
* POTE: ~99/70 = 600.0000{{c}}, ~26/15 = 951.5019{{c}} -->


{{Optimal ET sequence|legend=0| 58, 140, 198, 536f }}
{{Optimal ET sequence|legend=0| 58, 140, 198, 536f }}


Badness (Smith): 0.021188
Badness (Sintel): 0.876


=== Quadrafifths ===
=== Quadrafifths ===
Line 126: Line 138:


Mapping: {{mapping| 1 1 -5 -1 8 | 0 4 50 26 -31 }}
Mapping: {{mapping| 1 1 -5 -1 8 | 0 4 50 26 -31 }}
: Mapping generators: ~2, ~243/220
: mapping generators: ~2, ~243/220


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~243/220 = 175.7284{{c}}
* WE: ~2 = 1199.7520{{c}}, ~243/220 = 175.7015{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~243/220 = 175.7378{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~243/220 = 175.7360{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~243/220 = 175.7284{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~243/220 = 175.7378{{c}} -->


{{Optimal ET sequence|legend=0| 41, 157, 198, 239, 676b, 915be }}
{{Optimal ET sequence|legend=0| 41, 157, 198, 239, 676b, 915be }}


Badness (Smith): 0.040170
Badness (Sintel): 1.33


==== 13-limit ====
==== 13-limit ====
Line 144: Line 158:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~72/65 = 175.7412{{c}}
* WE: ~2 = 1199.6502{{c}}, ~72/65 = 175.6957{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~72/65 = 175.7470{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~72/65 = 175.7461{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~72/65 = 175.7412{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~72/65 = 175.7470{{c}} -->


{{Optimal ET sequence|legend=0| 41, 157, 198, 437f, 635bcff }}
{{Optimal ET sequence|legend=0| 41, 157, 198, 437f, 635bcff }}


Badness (Smith): 0.031144
Badness (Sintel): 1.29


== Tertiaseptal ==
== Tertiaseptal ==
Line 160: Line 176:
[[Comma list]]: 2401/2400, 65625/65536
[[Comma list]]: 2401/2400, 65625/65536


{{Mapping|legend=1| 1 3 2 3 | 0 -22 5 -3 }}
{{Mapping|legend=1| 1 -19 7 0 | 0 22 -5 3 }}
: mapping generators: ~2, ~256/245
: mapping generators: ~2, ~245/128


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~256/245 = 77.191{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1004{{c}}, ~245/128 = 1122.9024{{c}} (~256/245 = 77.1979)
: [[error map]]: {{val| +0.100 -0.008 -0.123 -0.119 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~245/128 = 1122.8101{{c}} (~256/245 = 77.1899)
: error map: {{val| 0.000 -0.133 -0.364 -0.396 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~256/245 = 77.191{{c}} -->


{{Optimal ET sequence|legend=1| 31, 109, 140, 171 }}
{{Optimal ET sequence|legend=1| 31, 109, 140, 171 }}


[[Badness]] (Smith): 0.012995
[[Badness]] (Sintel): 0.329


=== 11-limit ===
=== 11-limit ===
Line 174: Line 195:
Comma list: 243/242, 441/440, 65625/65536
Comma list: 243/242, 441/440, 65625/65536


Mapping: {{mapping| 1 3 2 3 7 | 0 -22 5 -3 -55 }}
Mapping: {{mapping| 1 -19 7 0 -48 | 0 22 -5 3 55 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~256/245 = 77.227{{c}}
Optimal tunings:
* WE: ~2 = 1200.1034{{c}}, ~245/128 = 1122.8694{{c}} (~256/245 = 77.2340{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~245/128 = 1122.7743{{c}} (~256/245 = 77.2257{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~256/245 = 77.227{{c}} -->


{{Optimal ET sequence|legend=0| 31, 109e, 140e, 171, 202 }}
{{Optimal ET sequence|legend=0| 31, 109e, 140e, 171, 202 }}


Badness (Smith): 0.035576
Badness (Sintel): 1.18


==== 13-limit ====
==== 13-limit ====
Line 187: Line 211:
Comma list: 243/242, 441/440, 625/624, 3584/3575
Comma list: 243/242, 441/440, 625/624, 3584/3575


Mapping: {{mapping| 1 3 2 3 7 1 | 0 -22 5 -3 -55 42 }}
Mapping: {{mapping| 1 -19 7 0 -48 43 | 0 22 -5 3 55 -42 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~117/112 = 77.203{{c}}
Optimal tunings:
* WE: ~2 = 1199.8783{{c}}, ~224/117 = 1122.6835{{c}} (~117/112 = 77.1948{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~224/117 = 1122.7968{{c}} (~117/112 = 77.2032{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~117/112 = 77.203{{c}} -->


{{Optimal ET sequence|legend=0| 31, 109e, 140e, 171 }}
{{Optimal ET sequence|legend=0| 31, 140e, 171, 373ef }}


Badness (Smith): 0.036876
Badness (Sintel): 1.52


==== 17-limit ====
==== 17-limit ====
Line 200: Line 227:
Comma list: 243/242, 375/374, 441/440, 625/624, 3584/3575
Comma list: 243/242, 375/374, 441/440, 625/624, 3584/3575


Mapping: {{mapping| 1 3 2 3 7 1 1 | 0 -22 5 -3 -55 42 48 }}
Mapping: {{mapping| 1 -19 7 0 -48 43 49 | 0 22 -5 3 55 -42 -48 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~68/65 = 77.201{{c}}
Optimal tunings:
* WE: ~2 = 1199.8677{{c}}, ~65/34 = 1122.6748{{c}} (~68/65 = 77.1929{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~65/34 = 1122.7985{{c}} (~68/65 = 77.2015{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~68/65 = 77.201{{c}} -->


{{Optimal ET sequence|legend=0| 31, 109eg, 140e, 171 }}
{{Optimal ET sequence|legend=0| 31, 140e, 171 }}


Badness (Smith): 0.027398
Badness (Sintel): 1.40


=== Tertia ===
=== Tertia ===
Line 213: Line 243:
Comma list: 385/384, 1331/1323, 1375/1372
Comma list: 385/384, 1331/1323, 1375/1372


Mapping: {{mapping| 1 3 2 3 5 | 0 -22 5 -3 -24 }}
Mapping: {{mapping| 1 -19 7 0 -19 | 0 22 -5 3 24 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~22/21 = 77.173{{c}}
Optimal tunings:
* WE: ~2 = 1200.2336{{c}}, ~21/11 = 1123.0454{{c}} (~22/21 = 77.1882{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1122.8311{{c}} (~22/21 = 77.1689{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.173{{c}} -->


{{Optimal ET sequence|legend=0| 31, 109, 140, 171e, 311e }}
{{Optimal ET sequence|legend=0| 31, 109, 140, 171e, 311e }}


Badness (Smith): 0.030171
Badness (Sintel): 0.997


==== 13-limit ====
==== 13-limit ====
Line 226: Line 259:
Comma list: 352/351, 385/384, 625/624, 1331/1323
Comma list: 352/351, 385/384, 625/624, 1331/1323


Mapping: {{mapping| 1 3 2 3 5 1 | 0 -22 5 -3 -24 42 }}
Mapping: {{mapping| 1 -19 7 0 -19 43 | 0 22 -5 3 24 -42 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~22/21 = 77.158{{c}}
Optimal tunings:
* WE: ~2 = 1200.1395{{c}}, ~21/11 = 1122.9727{{c}} (~22/21 = 77.1669{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1122.8426{{c}} (~22/21 = 77.1574{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.158{{c}} -->


{{Optimal ET sequence|legend=0| 31, 109, 140, 311e, 451ee }}
{{Optimal ET sequence|legend=0| 31, 78f, 109, 140 }}


Badness (Smith): 0.028384
Badness (Sintel): 1.17


==== 17-limit ====
==== 17-limit ====
Line 239: Line 275:
Comma list: 352/351, 385/384, 561/560, 625/624, 715/714
Comma list: 352/351, 385/384, 561/560, 625/624, 715/714


Mapping: {{mapping| 1 3 2 3 5 1 1 | 0 -22 5 -3 -24 42 48 }}
Mapping: {{mapping| 1 -19 7 0 -19 43 49 | 0 22 -5 3 24 -42 -48 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~22/21 = 77.162{{c}}
Optimal tunings:
* WE: ~2 = 1200.1655{{c}}, ~21/11 = 1122.9926{{c}} (~22/21 = 77.1729{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1122.8376{{c}} (~22/21 = 77.1624{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.162{{c}} -->


{{Optimal ET sequence|legend=0| 31, 109g, 140, 311e, 451ee }}
{{Optimal ET sequence|legend=0| 31, 78fg, 109g, 140 }}


Badness (Smith): 0.022416
Badness (Sintel): 1.14


=== Tertiaseptia ===
=== Tertiaseptia ===
Line 252: Line 291:
Comma list: 2401/2400, 6250/6237, 65625/65536
Comma list: 2401/2400, 6250/6237, 65625/65536


Mapping: {{mapping| 1 3 2 3 -4 | 0 -22 5 -3 116 }}
Mapping: {{mapping| 1 -19 7 0 112 | 0 22 -5 3 -116 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~256/245 = 77.169{{c}}
Optimal tunings:
* WE: ~2 = 1200.0053{{c}}, ~245/128 = 1122.8357{{c}} (~256/245 = 77.1696{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~245/128 = 1122.8308{{c}} (~256/245 = 77.1692{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~256/245 = 77.169{{c}} -->


{{Optimal ET sequence|legend=0| 140, 171, 311, 1695c, 2006bcd, 2317bcd, 2628bccde, 2939bccde, 3250bccde }}
{{Optimal ET sequence|legend=0| 31e, 140, 171, 311 }}


Badness (Smith): 0.056926
Badness (Sintel): 1.88


==== 13-limit ====
==== 13-limit ====
Line 265: Line 307:
Comma list: 625/624, 2080/2079, 2200/2197, 2401/2400
Comma list: 625/624, 2080/2079, 2200/2197, 2401/2400


Mapping: {{mapping| 1 3 2 3 -4 1 | 0 -22 5 -3 116 42 }}
Mapping: {{mapping| 1 -19 7 0 112 43 | 0 22 -5 3 -116 -42 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~117/112 = 77.168{{c}}
Optimal tunings:
* WE: ~2 = 1199.9823{{c}}, ~224/117 = 1122.8150{{c}} (~117/112 = 77.1673{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~224/117 = 1122.8316{{c}} (~117/112 = 77.1684{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~117/112 = 77.168{{c}} -->


{{Optimal ET sequence|legend=0| 140, 171, 311, 1073, 1384cf, 1695cf, 2006bcdf }}
{{Optimal ET sequence|legend=0| 31e, 140, 171, 311, 1073 }}


Badness (Smith): 0.027474
Badness (Sintel): 1.14


==== 17-limit ====
==== 17-limit ====
Line 278: Line 323:
Comma list: 595/594, 625/624, 833/832, 1156/1155, 2200/2197
Comma list: 595/594, 625/624, 833/832, 1156/1155, 2200/2197


Mapping: {{mapping| 1 3 2 3 -4 1 1 | 0 -22 5 -3 116 42 48 }}
Mapping: {{mapping| 1 -19 7 0 112 43 49 | 0 22 -5 3 -116 -42 -48 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~68/65 = 77.169{{c}}
Optimal tunings:
* WE: ~2 = 1200.0092{{c}}, ~65/34 = 1122.8392{{c}} (~68/65 = 77.1700{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~65/34 = 1122.8305{{c}} (~68/65 = 77.1695{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~68/65 = 77.169{{c}} -->


{{Optimal ET sequence|legend=0| 140, 171, 311 }}
{{Optimal ET sequence|legend=0| 31e, 140, 171, 311 }}


Badness (Smith): 0.018773
Badness (Sintel): 0.956


==== 19-limit ====
==== 19-limit ====
Line 291: Line 339:
Comma list: 595/594, 625/624, 833/832, 1156/1155, 1216/1215, 2200/2197
Comma list: 595/594, 625/624, 833/832, 1156/1155, 1216/1215, 2200/2197


Mapping: {{mapping| 1 3 2 3 -4 1 1 11 | 0 -22 5 -3 116 42 48 -105 }}
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 | 0 22 -5 3 -116 -42 -48 105 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~68/65 = 77.169{{c}}
Optimal tunings:
* WE: ~2 = 1200.0187{{c}}, ~65/34 = 1122.8489{{c}} (~68/65 = 77.1698{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~65/34 = 1122.8313{{c}} (~68/65 = 77.1687{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~68/65 = 77.169{{c}} -->


{{Optimal ET sequence|legend=0| 140, 171, 311, 1384cfgg, 1695cfgg, 2006bcdfgg }}
{{Optimal ET sequence|legend=0| 140, 171, 311 }}


Badness (Smith): 0.017653
Badness (Sintel): 1.07


==== 23-limit ====
==== 23-limit ====
Line 304: Line 355:
Comma list: 595/594, 625/624, 833/832, 875/874, 1105/1104, 1156/1155, 1216/1215
Comma list: 595/594, 625/624, 833/832, 875/874, 1105/1104, 1156/1155, 1216/1215


Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 | 0 -22 5 -3 116 42 48 -105 117 }}
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 | 0 22 -5 3 -116 -42 -48 105 -117 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~23/22 = 77.168{{c}}
Optimal tunings:
* WE: ~2 = 1200.0101{{c}}, ~44/23 = 1122.8418{{c}} (~23/22 = 77.1683{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8323{{c}} (~23/22 = 77.1677{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~23/22 = 77.168{{c}} -->


{{Optimal ET sequence|legend=0| 140, 311, 762g, 1073g, 1384cfgg }}
{{Optimal ET sequence|legend=0| 140, 311, 762g }}


Badness (Smith): 0.015123
Badness (Sintel): 1.08


==== 29-limit ====
==== 29-limit ====
Line 317: Line 371:
Comma list: 595/594, 625/624, 784/783, 833/832, 875/874, 1015/1014, 1105/1104, 1156/1155
Comma list: 595/594, 625/624, 784/783, 833/832, 875/874, 1015/1014, 1105/1104, 1156/1155


Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 | 0 -22 5 -3 116 42 48 -105 117 60 }}
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 | 0 22 -5 3 -116 -42 -48 105 -117 -60 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~23/22 = 77.167{{c}}
Optimal tunings:
* WE: ~2 = 1200.0007{{c}}, ~44/23 = 1122.8332{{c}} (~23/22 = 77.1675{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8326{{c}} (~23/22 = 77.1674{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~23/22 = 77.167{{c}} -->


{{Optimal ET sequence|legend=0| 140, 311, 762g, 1073g, 1384cfggj }}
{{Optimal ET sequence|legend=0| 140, 311, 762g }}


Badness (Smith): 0.012181
Badness (Sintel): 1.02


==== 31-limit ====
==== 31-limit ====
Line 330: Line 387:
Comma list: 595/594, 625/624, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014
Comma list: 595/594, 625/624, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014


Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 11 | 0 -22 5 -3 116 42 48 -105 117 60 -94 }}
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~23/22 = 77.169{{c}}
Optimal tunings:
* WE: ~2 = 1199.9721{{c}}, ~44/23 = 1122.8047{{c}} (~23/22 = 77.1673{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8309{{c}} (~23/22 = 77.1691{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~23/22 = 77.169{{c}} -->


{{Optimal ET sequence|legend=0| 140, 171, 311 }}
{{Optimal ET sequence|legend=0| 140, 171, 311 }}


Badness (Smith): 0.012311
Badness (Sintel): 1.18


==== 37-limit ====
==== 37-limit ====
Line 343: Line 403:
Comma list: 595/594, 625/624, 703/702, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014
Comma list: 595/594, 625/624, 703/702, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014


Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 11 0 | 0 -22 5 -3 116 42 48 -105 117 60 -94 81 }}
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 81 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~23/22 = 77.170{{c}}
Optimal tunings:
* WE: ~2 = 1199.9824{{c}}, ~44/23 = 1122.8139{{c}} (~23/22 = 77.1685{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8304{{c}} (~23/22 = 77.1696{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~23/22 = 77.170{{c}} -->


{{Optimal ET sequence|legend=0| 140, 171, 311 }}
{{Optimal ET sequence|legend=0| 140, 171, 311 }}


Badness (Smith): 0.010949
Badness (Sintel): 1.19


==== 41-limit ====
==== 41-limit ====
Line 356: Line 419:
Comma list: 595/594, 625/624, 697/696, 703/702, 714/713, 784/783, 820/819, 833/832, 875/874, 900/899, 931/930
Comma list: 595/594, 625/624, 697/696, 703/702, 714/713, 784/783, 820/819, 833/832, 875/874, 900/899, 931/930


Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 11 0 6 | 0 -22 5 -3 116 42 48 -105 117 60 -94 81 -10 }}
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 81 -4 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 10 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~23/22 = 77.169{{c}}
Optimal tunings:
* WE: ~2 = 1199.9957{{c}}, ~44/23 = 1122.8266{{c}} (~23/22 = 77.1691{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8306{{c}} (~23/22 = 77.1694{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~23/22 = 77.169{{c}} -->


{{Optimal ET sequence|legend=0| 140, 171, 311 }}
{{Optimal ET sequence|legend=0| 140, 171, 311 }}


Badness (Smith): 0.009825
Badness (Sintel): 1.20


=== Hemitert ===
=== Hemitert ===
Line 369: Line 435:
Comma list: 2401/2400, 3025/3024, 65625/65536
Comma list: 2401/2400, 3025/3024, 65625/65536


Mapping: {{mapping| 1 3 2 3 6 | 0 -44 10 -6 -79 }}
Mapping: {{mapping| 1 -41 12 -3 -73 | 0 44 -10 6 79 }}
: mapping generators: ~2, ~45/44
: mapping generators: ~2, ~88/45


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 38.596{{c}}
Optimal tunings:
* WE: ~2 = 1200.1008{{c}}, ~88/45 = 1161.5020{{c}} (~45/44 = 38.5988{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~88/45 = 1161.4053{{c}} (~45/44 = 38.5947{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~45/44 = 38.596{{c}} -->


{{Optimal ET sequence|legend=0| 31, 280, 311, 342 }}
{{Optimal ET sequence|legend=0| 31, …, 280, 311, 342, 2021cde, 2363cde, …, 3389ccddee, 3731ccddee }}


Badness (Smith): 0.015633
Badness (Sintel): 0.517


==== 13-limit ====
==== 13-limit ====
Line 383: Line 452:
Comma list: 625/624, 1575/1573, 2401/2400, 4096/4095
Comma list: 625/624, 1575/1573, 2401/2400, 4096/4095


Mapping: {{mapping| 1 3 2 3 6 1 | 0 -44 10 -6 -79 84 }}
Mapping: {{mapping| 1 -41 12 -3 -73 85 | 0 44 -10 6 79 -84 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 38.588{{c}}
Optimal tunings:
* WE: ~2 = 1199.9822{{c}}, ~88/45 = 1161.3952{{c}} (~45/44 = 38.5871{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~88/45 = 1161.4123{{c}} (~45/44 = 38.5877{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~45/44 = 38.588{{c}} -->


{{Optimal ET sequence|legend=0| 31, 280, 311, 964f, 1275f, 1586cff }}
{{Optimal ET sequence|legend=0| 31, 280, 311 }}


Badness (Smith): 0.033573
Badness (Sintel): 1.39


==== 17-limit ====
==== 17-limit ====
Line 396: Line 468:
Comma list: 625/624, 833/832, 1225/1224, 1575/1573, 4096/4095
Comma list: 625/624, 833/832, 1225/1224, 1575/1573, 4096/4095


Mapping: {{mapping| 1 3 2 3 6 1 1 | 0 -44 10 -6 -79 84 96 }}
Mapping: {{mapping| 1 -41 12 -3 -73 85 97| 0 44 -10 6 79 -84 -96 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 38.589{{c}}
Optimal tunings:
* WE: ~2 = 1200.0042{{c}}, ~88/45 = 1161.4149{{c}} (~45/44 = 38.5893{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~88/45 = 1161.4109{{c}} (~45/44 = 38.5891{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~45/44 = 38.589{{c}} -->


{{Optimal ET sequence|legend=0| 31, 280, 311, 653f, 964f }}
{{Optimal ET sequence|legend=0| 31, 280, 311, 653f }}


Badness (Smith): 0.025298
Badness (Sintel): 1.29


=== Semitert ===
=== Semitert ===
Line 409: Line 484:
Comma list: 2401/2400, 9801/9800, 65625/65536
Comma list: 2401/2400, 9801/9800, 65625/65536


Mapping: {{mapping| 2 6 4 6 1 | 0 -22 5 -3 46 }}
Mapping: {{mapping| 2 -16 9 3 47 | 0 22 -5 3 -46 }}
: mapping generators: ~99/70, ~256/245
: mapping generators: ~99/70, ~693/512


Optimal tuning (POTE): ~99/70 = 1200.000{{c}}, ~256/245 = 77.193{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0548{{c}}, ~693/512 = 522.8547{{c}} (~256/245 = 77.2002{{c}})
* CWE: ~99/70 = 600.0000{{c}}, ~693/512 = 522.8069{{c}} (~256/245 = 77.1931{{c}})
<!-- * POTE: ~99/70 = 600.000{{c}}, ~256/245 = 77.193{{c}} -->


{{Optimal ET sequence|legend=0| 62e, 140, 202, 342 }}
{{Optimal ET sequence|legend=0| 62e, 140, 202, 342 }}


Badness (Smith): 0.025790
Badness (Sintel): 0.853


== Quasiorwell ==
== Quasiorwell ==
Line 427: Line 505:
[[Comma list]]: 2401/2400, 29360128/29296875
[[Comma list]]: 2401/2400, 29360128/29296875


{{Mapping|legend=1| 1 31 0 9 | 0 -38 3 -8 }}
{{Mapping|legend=1| 1 -7 3 1 | 0 38 -3 8 }}
: mapping generators: ~2, ~875/512
: mapping generators: ~2, ~1024/875


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~1024/875 = 271.107{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9403{{c}}, ~1024/875 = 271.0935{{c}}
: [[error map]]: {{val| -0.060 +0.018 +0.226 -0.137 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1024/875 = 271.1064{{c}}
: error map: {{val| 0.000 +0.087 +0.367 +0.025 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~1024/875 = 271.107{{c}} -->


{{Optimal ET sequence|legend=1| 31, 177, 208, 239, 270, 571, 841, 1111 }}
{{Optimal ET sequence|legend=1| 31, …, 177, 208, 239, 270, 571, 841, 1111 }}


[[Badness]] (Smith): 0.035832
[[Badness]] (Sintel): 0.907


=== 11-limit ===
=== 11-limit ===
Line 441: Line 524:
Comma list: 2401/2400, 3025/3024, 5632/5625
Comma list: 2401/2400, 3025/3024, 5632/5625


Mapping: {{mapping| 1 31 0 9 53 | 0 -38 3 -8 -64 }}
Mapping: {{mapping| 1 -7 3 1 -11 | 0 38 -3 8 64 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~90/77 = 271.111{{c}}
Optimal tunings:
* WE: ~2 = 1199.9484{{c}}, ~90/77 = 271.0989{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~90/77 = 271.1099{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~90/77 = 271.111{{c}} -->


{{Optimal ET sequence|legend=0| 31, 208, 239, 270 }}
{{Optimal ET sequence|legend=0| 31, …, 177e, 208, 239, 270 }}


Badness (Smith): 0.017540
Badness (Sintel): 0.580


=== 13-limit ===
=== 13-limit ===
Line 454: Line 540:
Comma list: 1001/1000, 1716/1715, 3025/3024, 4096/4095
Comma list: 1001/1000, 1716/1715, 3025/3024, 4096/4095


Mapping: {{mapping| 1 31 0 9 53 -59 | 0 -38 3 -8 -64 81 }}
Mapping: {{mapping| 1 -7 3 1 -11 22 | 0 38 -3 8 64 -81 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~90/77 = 271.107{{c}}
Optimal tunings:
* WE: ~2 = 1199.9916{{c}}, ~90/77 = 271.1051{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~90/77 = 271.1070{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~90/77 = 271.107{{c}} -->


{{Optimal ET sequence|legend=0| 31, 239, 270, 571, 841, 1111 }}
{{Optimal ET sequence|legend=0| 31, 239, 270, 571, 841, 1111 }}


Badness (Smith): 0.017921
Badness (Sintel): 0.741


== Neominor ==
== Neominor ==
Line 469: Line 558:
[[Comma list]]: 2401/2400, 177147/175616
[[Comma list]]: 2401/2400, 177147/175616


{{Mapping|legend=1| 1 3 12 8 | 0 -6 -41 -22 }}
{{Mapping|legend=1| 1 -3 -29 -14 | 0 6 41 22 }}
: mapping generators: ~2, ~189/160
: mapping generators: ~2, ~320/189


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[TE]]: ~2 = 1200.428{{c}}, ~189/160 = 283.381{{c}}
* [[WE]]: ~2 = 1200.4276{{c}}, ~320/189 = 917.0471{{c}}
* [[CTE]]: ~2 = 1200.000{{c}}, ~189/160 = 283.247{{c}}
: [[error map]]: {{val| +0.428 -0.955 +0.216 +0.224 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~320/189 = 916.7320{{c}}
: error map: {{val| 0.000 -1.563 -0.301 -0.722 }}
<!-- * [[TE]]: ~2 = 1200.428{{c}}, ~320/189 = 916.619{{c}}
* [[CTE]]: ~2 = 1200.000{{c}}, ~320/189 = 916.753{{c}} -->


{{Optimal ET sequence|legend=1| 72, 161, 233, 305 }}
{{Optimal ET sequence|legend=1| 17c, 55c, 72, 161, 233, 305 }}


[[Badness]] (Sintel): 2.233
[[Badness]] (Sintel): 2.23


=== 11-limit ===
=== 11-limit ===
Line 485: Line 578:
Comma list: 243/242, 441/440, 35937/35840
Comma list: 243/242, 441/440, 35937/35840


Mapping: {{mapping| 1 3 12 8 7 | 0 -6 -41 -22 -15 }}
Mapping: {{mapping| 1 -3 -29 -14 -8 | 0 6 41 22 15 }}


Optimal tunings:  
Optimal tunings:  
* TE: ~2 = 1200.347{{c}}, ~33/28 = 283.358{{c}}
* WE: ~2 = 1200.3466{{c}}, ~56/33 = 916.9889{{c}}
* CTE: ~2 = 1200.000{{c}}, ~33/28 = 283.247{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~56/33 = 916.7330{{c}}
<!-- * TE: ~2 = 1200.347{{c}}, ~56/33 = 916.642{{c}}
* CTE: ~2 = 1200.000{{c}}, ~56/33 = 916.753{{c}} -->


{{Optimal ET sequence|legend=0| 72, 161, 233, 305 }}
{{Optimal ET sequence|legend=0| 17c, 55c, 72, 161, 233, 305 }}


Badness (Sintel): 0.924
Badness (Sintel): 0.924
Line 500: Line 595:
Comma list: 169/168, 243/242, 364/363, 441/440
Comma list: 169/168, 243/242, 364/363, 441/440


Mapping: {{mapping| 1 3 12 8 7 7 | 0 -6 -41 -22 -15 -14 }}
Mapping: {{mapping| 1 -3 -29 -14 -8 -7 | 0 6 41 22 15 14 }}


Optimal tunings:  
Optimal tunings:  
* TE: ~2 = 1200.689{{c}}, ~13/11 = 283.457{{c}}
* WE: ~2 = 1200.6874{{c}}, ~22/13 = 917.2313{{c}}
* CTE: ~2 = 1200.000{{c}}, ~13/11 = 283.233{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/13 = 916.7228{{c}}
<!-- * TE: ~2 = 1200.689{{c}}, ~22/13 = 916.543{{c}}
* CTE: ~2 = 1200.000{{c}}, ~22/13 = 916.767{{c}} -->


{{Optimal ET sequence|legend=0| 72, 161f, 233ff }}
{{Optimal ET sequence|legend=0| 17c, 55cf, 72 }}


Badness (Sintel): 1.113
Badness (Sintel): 1.11


=== 17-limit ===
=== 17-limit ===
Line 515: Line 612:
Comma list: 169/168, 221/220, 243/242, 273/272, 364/363
Comma list: 169/168, 221/220, 243/242, 273/272, 364/363


Mapping: {{mapping| 1 3 12 8 7 7 14 | 0 -6 -41 -22 -15 -14 -42 }}
Mapping: {{mapping| 1 -3 -29 -14 -8 -7 -28 | 0 6 41 22 15 14 42 }}


Optimal tunings:  
Optimal tunings:  
* TE: ~2 = 1200.692{{c}}, ~13/11 = 283.455{{c}}
* WE: ~2 = 1200.6905{{c}}, ~17/10 = 917.2356{{c}}
* CTE: ~2 = 1200.000{{c}}, ~13/11 = 283.229{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/10 = 916.7252{{c}}
<!-- * TE: ~2 = 1200.692{{c}}, ~17/10 = 916.545{{c}}
* CTE: ~2 = 1200.000{{c}}, ~17/10 = 916.771{{c}} -->


{{Optimal ET sequence|legend=0| 72, 161f, 233ff }}
{{Optimal ET sequence|legend=0| 17cg, 55cfg, 72 }}


Badness (Sintel): 0.918
Badness (Sintel): 0.918
Line 532: Line 631:
[[Comma list]]: 2401/2400, 14348907/14336000
[[Comma list]]: 2401/2400, 14348907/14336000


{{Mapping|legend=1| 1 11 42 25 | 0 -14 -59 -33 }}
{{Mapping|legend=1| 1 -3 -17 -8 | 0 14 59 33 }}
: mapping generators: ~2, ~2187/1372
: mapping generators: ~2, ~2744/2187


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~2744/2187 = 392.988{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0435{{c}}, ~2744/2187 = 393.0021{{c}}
: [[error map]]: {{val| +0.043 -0.057 +0.069 -0.106 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~2744/2187 = 392.9887{{c}}
: error map: {{val| 0.000 -0.113 +0.022 -0.197 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~2744/2187 = 392.988{{c}} -->


{{Optimal ET sequence|legend=1| 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d }}
{{Optimal ET sequence|legend=1| 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d }}


[[Badness]] (Smith): 0.016736
[[Badness]] (Sintel): 0.424


=== 11-limit ===
=== 11-limit ===
Line 546: Line 650:
Comma list: 243/242, 441/440, 1792000/1771561
Comma list: 243/242, 441/440, 1792000/1771561


Mapping: {{mapping| 1 11 42 25 27 | 0 -14 -59 -33 -35 }}
Mapping: {{mapping| 1 -3 -17 -8 -8 | 0 14 59 33 35 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~1372/1089 = 392.991{{c}}
Optimal tunings:
* WE: ~2 = 1199.8090{{c}}, ~1372/1089 = 392.9286{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~1372/1089 = 392.9870{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~1372/1089 = 392.991{{c}} -->


{{Optimal ET sequence|legend=0| 58, 113, 171 }}
{{Optimal ET sequence|legend=0| 58, 113, 171 }}


Badness (Smith): 0.052358
Badness (Sintel): 1.73


=== 13-limit ===
=== 13-limit ===
Line 559: Line 666:
Comma list: 243/242, 364/363, 441/440, 2200/2197
Comma list: 243/242, 364/363, 441/440, 2200/2197


Mapping: {{mapping| 1 11 42 25 27 38 | 0 -14 -59 -33 -35 -51 }}
Mapping: {{mapping| 1 -3 -17 -8 -8 -13 | 0 14 59 33 35 51 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~180/143 = 392.989{{c}}
Optimal tunings:
* WE: ~2 = 1199.7756{{c}}, ~180/143 = 392.9154{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~180/143 = 392.9840{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~180/143 = 392.989{{c}} -->


{{Optimal ET sequence|legend=0| 58, 113, 171 }}
{{Optimal ET sequence|legend=0| 58, 113, 171 }}


Badness (Smith): 0.026974
Badness (Sintel): 1.11


=== 17-limit ===
=== 17-limit ===
Line 574: Line 684:
Mapping: {{mapping| 1 -3 -17 -8 -8 -13 9 | 0 14 59 33 35 51 -15 }}
Mapping: {{mapping| 1 -3 -17 -8 -8 -13 9 | 0 14 59 33 35 51 -15 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~64/51 = 392.985{{c}}
Optimal tunings:
* WE: ~2 = 1199.8396{{c}}, ~64/51 = 392.9322{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~64/51 = 392.9826{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~64/51 = 392.985{{c}} -->


{{Optimal ET sequence|legend=0| 58, 113, 171 }}
{{Optimal ET sequence|legend=0| 58, 113, 171 }}


Badness (Smith): 0.023205
Badness (Sintel): 1.18


== Quinmite ==
== Quinmite ==
Line 587: Line 700:
[[Comma list]]: 2401/2400, 1959552/1953125
[[Comma list]]: 2401/2400, 1959552/1953125


{{Mapping|legend=1| 1 27 24 20 | 0 -34 -29 -23 }}
{{Mapping|legend=1| 1 -7 -5 -3 | 0 34 29 23 }}
: mapping generators: ~2, ~42/25
: mapping generators: ~2, ~25/21


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~25/21 = 302.997{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9361{{c}}, ~25/21 = 302.9808{{c}}
: [[error map]]: {{val| -0.064 -0.162 +0.448 -0.077 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~25/21 = 302.9953{{c}}
: error map: {{val| 0.000 -0.116 +0.549 +0.065 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~25/21 = 302.997{{c}} -->


{{Optimal ET sequence|legend=1| 99, 202, 301, 400, 701, 1101c, 1802c, 2903cc }}
{{Optimal ET sequence|legend=1| 99, 202, 301, 400, 701, 1101c, 1802c }}


[[Badness]] (Smith): 0.037322
[[Badness]] (Sintel): 0.945


== Unthirds ==
== Unthirds ==
Line 605: Line 723:
[[Comma list]]: 2401/2400, 68359375/68024448
[[Comma list]]: 2401/2400, 68359375/68024448


{{Mapping|legend=1| 1 29 33 25 | 0 -42 -47 -34 }}
{{Mapping|legend=1| 1 -13 -14 -9 | 0 42 47 34 }}
: mapping generators: ~2, ~6125/3888
: mapping generators: ~2, ~3969/3125


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3969/3125 = 416.717{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0859{{c}}, ~3969/3125 = 416.7465{{c}}
: [[error map]]: {{val| +0.086 +0.281 -0.431 -0.218 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3969/3125 = 416.7184{{c}}
: error map: {{val| 0.000 +0.220 -0.547 -0.399 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3969/3125 = 416.717{{c}} -->


{{Optimal ET sequence|legend=1| 72, 167, 239, 311, 694, 1005c }}
{{Optimal ET sequence|legend=1| 72, 167, 239, 311, 694, 1005c }}


[[Badness]] (Smith): 0.075253
[[Badness]] (Sintel): 1.90


=== 11-limit ===
=== 11-limit ===
Line 619: Line 742:
Comma list: 2401/2400, 3025/3024, 4000/3993
Comma list: 2401/2400, 3025/3024, 4000/3993


Mapping: {{mapping| 1 29 33 25 25 | 0 -42 -47 -34 -33 }}
Mapping: {{mapping| 1 -13 -14 -9 -8 | 0 42 47 34 33 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~14/11 = 416.718{{c}}
Optimal tunings:
* WE: ~2 = 1200.0246{{c}}, ~14/11 = 416.7270{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/11 = 416.7190{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~14/11 = 416.718{{c}} -->


{{Optimal ET sequence|legend=0| 72, 167, 239, 311 }}
{{Optimal ET sequence|legend=0| 72, 167, 239, 311 }}


Badness (Smith): 0.022926
Badness (Sintel): 0.758


=== 13-limit ===
=== 13-limit ===
Line 632: Line 758:
Comma list: 625/624, 1575/1573, 2080/2079, 2401/2400
Comma list: 625/624, 1575/1573, 2080/2079, 2401/2400


Mapping: {{mapping| 1 29 33 25 25 99 | 0 -42 -47 -34 -33 -146 }}
Mapping: {{mapping| 1 -13 -14 -9 -8 -47 | 0 42 47 34 33 146 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~14/11 = 416.716{{c}}
Optimal tunings:
* WE: ~2 = 1200.0536{{c}}, ~14/11 = 416.7343{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/11 = 416.7164{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~14/11 = 416.716{{c}} -->


{{Optimal ET sequence|legend=0| 72, 239f, 311, 694, 1005c }}
{{Optimal ET sequence|legend=0| 72, 239f, 311, 694, 1005c }}


Badness (Smith): 0.020888
Badness (Sintel): 0.863


== Newt ==
== Newt ==
Line 650: Line 779:
: mapping generators: ~2, ~49/40
: mapping generators: ~2, ~49/40


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/40 = 351.113{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9315{{c}}, ~49/40 = 351.0932{{c}}
: [[error map]]: {{val| -0.068 +0.163 +0.075 -0.188 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.1141{{c}}
: error map: {{val| 0.000 +0.273 +0.180 -0.022 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~49/40 = 351.113{{c}} -->


{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 2201 }}
{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 2201 }}


[[Badness]] (Smith): 0.041878
[[Badness]] (Sintel): 1.06


=== 11-limit ===
=== 11-limit ===
Line 663: Line 797:
Mapping: {{mapping| 1 1 19 11 -10 | 0 2 -57 -28 46 }}
Mapping: {{mapping| 1 1 19 11 -10 | 0 2 -57 -28 46 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/40 = 351.115{{c}}
Optimal tunings:
* WE: ~2 = 1199.9603{{c}}, ~49/40 = 351.1038{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1155{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~49/40 = 351.115{{c}} -->


{{Optimal ET sequence|legend=0| 41, 147ce, 188, 229, 270, 581, 851, 1121, 1972 }}
{{Optimal ET sequence|legend=0| 41, 188, 229, 270, 581, 851, 1121, 1972 }}


Badness (Smith): 0.019461
Badness (Sintel): 0.643


=== 13-limit ===
=== 13-limit ===
Line 676: Line 813:
Mapping: {{mapping| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}
Mapping: {{mapping| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/40 = 351.117{{c}}
Optimal tunings:
* WE: ~2 = 1199.9747{{c}}, ~49/40 = 351.1094{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1168{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~49/40 = 351.117{{c}} -->


{{Optimal ET sequence|legend=0| 41, 147cef, 188f, 229, 270, 581, 851, 2283b, 3134b }}
{{Optimal ET sequence|legend=0| 41, 229, 270, 581, 851, 2283b }}


Badness (Smith): 0.013830
Badness (Sintel): 0.571


=== 2.3.5.7.11.13.19 subgroup (neonewt) ===
=== 2.3.5.7.11.13.19 subgroup (neonewt) ===
Line 689: Line 829:
Mapping: {{mapping| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}
Mapping: {{mapping| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~49/40 = 351.117{{c}}
Optimal tunings:
* WE: ~2 = 1199.9782{{c}}, ~49/40 = 351.1102{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1166{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~49/40 = 351.117{{c}} -->
 
{{Optimal ET sequence|legend=0| 41, 229, 270, 581, 851 }}


{{Optimal ET sequence|legend=0| 41, 147cefh, 188f, 229, 270, 581, 851, 3134b, 3985b, 4836bb }}
Badness (Sintel): 0.438


== Septidiasemi ==
== Septidiasemi ==
Line 702: Line 847:
[[Comma list]]: 2401/2400, 2152828125/2147483648
[[Comma list]]: 2401/2400, 2152828125/2147483648


{{Mapping|legend=1| 1 25 -31 -8 | 0 -26 37 12 }}
{{Mapping|legend=1| 1 -1 6 4 | 0 26 -37 -12 }}
: mpping generators: ~2, ~28/15
: mpping generators: ~2, ~15/14


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~15/14 = 119.297{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1043{{c}}, ~15/14 = 119.3076{{c}}
: [[error map]]: {{val| +0.104 -0.061 -0.070 -0.100 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 119.2971{{c}}
: error map: {{val| 0.000 -0.230 -0.307 -0.391 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~15/14 = 119.297{{c}} -->


{{Optimal ET sequence|legend=1| 10, 151, 161, 171, 3581bcdd, 3752bcdd, 3923bcdd, 4094bcdd, 4265bccdd, 4436bccdd, 4607bccdd }}
{{Optimal ET sequence|legend=1| 10, 151, 161, 171, 3581bcdd, 3752bcdd, …, 5633bbccddd, 5804bbccddd }}


[[Badness]] (Smith): 0.044115
[[Badness]] (Sintel): 1.12


=== Sedia ===
=== Sedia ===
Line 718: Line 868:
Comma list: 243/242, 441/440, 939524096/935859375
Comma list: 243/242, 441/440, 939524096/935859375


Mapping: {{mapping| 1 25 -31 -8 62 | 0 -26 37 12 -65 }}
Mapping: {{mapping| 1 -1 6 4 -3 | 0 26 -37 -12 65 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 119.279{{c}}
Optimal tunings:
* WE: ~2 = 1199.9635{{c}}, ~15/14 = 119.2755{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 119.2791{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~15/14 = 119.279{{c}} -->


{{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332 }}
{{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332 }}


Badness (Smith): 0.090687
Badness (Sintel): 3.00


==== 13-limit ====
==== 13-limit ====
Line 731: Line 884:
Comma list: 243/242, 441/440, 2200/2197, 3584/3575
Comma list: 243/242, 441/440, 2200/2197, 3584/3575


Mapping: {{mapping| 1 25 -31 -8 62 1 | 0 -26 37 12 -65 3 }}
Mapping: {{mapping| 1 -1 6 4 -3 4 | 0 26 -37 -12 65 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 119.281{{c}}
Optimal tunings:
* WE: ~2 = 1199.8922{{c}}, ~15/14 = 119.2700{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 119.2804{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~15/14 = 119.281{{c}} -->


{{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332, 835eeff }}
{{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332 }}


Badness (Smith): 0.045773
Badness (Sintel): 1.89


==== 17-limit ====
==== 17-limit ====
Line 744: Line 900:
Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575
Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575


Mapping: {{mapping| 1 25 -31 -8 62 1 23 | 0 -26 37 12 -65 3 -21 }}
Mapping: {{mapping| 1 -1 6 4 -3 4 2 | 0 26 -37 -12 65 -3 21 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 119.281{{c}}
Optimal tunings:
* WE: ~2 = 1199.9088{{c}}, ~15/14 = 119.2719{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 119.2808{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~15/14 = 119.281{{c}} -->


{{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332, 503ef, 835eeff }}
{{Optimal ET sequence|legend=0| 10, 151, 161, 171, 332, 503ef }}


Badness (Smith): 0.027322
Badness (Sintel): 1.39


== Maviloid ==
== Maviloid ==
Line 759: Line 918:
[[Comma list]]: 2401/2400, 1224440064/1220703125
[[Comma list]]: 2401/2400, 1224440064/1220703125


{{Mapping|legend=1| 1 31 34 26 | 0 -52 -56 -41 }}
{{Mapping|legend=1| 1 -21 -22 -15 | 0 52 56 41 }}
: mapping generators: ~2, ~1296/875
: mapping generators: ~2, ~875/648


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~1296/875 = 678.810{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9863{{c}}, ~875/648 = 521.1837{{c}}
: [[error map]]: {{val| -0.014 -0.115 +0.274 -0.089 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~875/648 = 521.1894{{c}}
: error map: {{val| 0.000 -0.106 +0.293 -0.060 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~875/648 = 521.190{{c}} -->


{{Optimal ET sequence|legend=1| 76, 99, 274, 373, 472, 571, 1043, 1614 }}
{{Optimal ET sequence|legend=1| 76, 99, 274, 373, 472, 571, 1043, 1614 }}


[[Badness]] (Smith): 0.057632
[[Badness]] (Sintel): 1.46


== Subneutral ==
== Subneutral ==
Line 775: Line 939:
[[Comma list]]: 2401/2400, 274877906944/274658203125
[[Comma list]]: 2401/2400, 274877906944/274658203125


{{Mapping|legend=1| 1 19 0 6 | 0 -60 8 -11 }}
{{Mapping|legend=1| 1 -41 8 -5 | 0 60 -8 11 }}
: mapping generators: ~2, ~57344/46875
: mapping generators: ~2, ~46875/28672


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~57344/46875 = 348.301{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9998{{c}}, ~46875/28672 = 851.6994 (~57344/46875 = 348.3005{{c}})
: [[error map]]: {{val| -0.000 +0.013 +0.090 -0.132 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~46875/28672 = 851.6995{{c}} (~57344/46875 = 348.3005{{c}})
: error map: {{val| 0.000 +0.014 +0.090 -0.132 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~57344/46875 = 348.301{{c}} -->


{{Optimal ET sequence|legend=1| 31, …, 348, 379, 410, 441, 1354, 1795, 2236 }}
{{Optimal ET sequence|legend=1| 31, …, 348, 379, 410, 441, 1354, 1795, 2236 }}


[[Badness]] (Smith): 0.045792
[[Badness]] (Sintel): 1.16


== Osiris ==
== Osiris ==
Line 791: Line 960:
[[Comma list]]: 2401/2400, 31381059609/31360000000
[[Comma list]]: 2401/2400, 31381059609/31360000000


{{Mapping|legend=1| 1 13 33 21 | 0 -32 -86 -51 }}
{{Mapping|legend=1| 1 13 33 21 | 0 32 86 51 }}
: mapping generators: ~2, ~2800/2187
: mapping generators: ~2, ~2187/1400


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~2800/2187 = 428.066{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0285{{c}}, ~2187/1400 = 771.9522{{c}}
: [[error map]]: {{val| +0.028 -0.025 +0.068 -0.117 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~2187/1400 = 771.9343{{c}}
: error map: {{val| 0.000 -0.056 +0.039 -0.175 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~2187/1400 = 771.934{{c}} -->


{{Optimal ET sequence|legend=1| 157, 171, 1012, 1183, 1354, 1525, 1696 }}
{{Optimal ET sequence|legend=1| 157, 171, 1012, 1183, 1354, 1525, 1696 }}


[[Badness]] (Smith): 0.028307
[[Badness]] (Sintel): 0.716


== Gorgik ==
== Gorgik ==
Line 805: Line 979:
[[Comma list]]: 2401/2400, 28672/28125
[[Comma list]]: 2401/2400, 28672/28125


{{Mapping|legend=1| 1 5 1 3 | 0 -18 7 -1 }}
{{Mapping|legend=1| 1 -13 8 2 | 0 18 -7 1 }}
: mapping generators: ~2, ~8/7
: mapping generators: ~2, ~7/4


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~8/7 = 227.512{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.5503{{c}}, ~7/4 = 971.3132{{c}} (~8/7 = 227.2371{{c}})
: [[error map]]: {{val| -1.450 +0.528 +2.896 -0.412 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 972.4675{{c}} (~8/7 = 227.5325{{c}})
: error map: {{val| 0.000 +2.460 +6.414 +3.642 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 227.512{{c}} -->


{{Optimal ET sequence|legend=1| 21, 37, 58, 153bc, 211bccd, 269bccd }}
{{Optimal ET sequence|legend=1| 21, 37, 58, 153bc, 211bccd, 269bccd }}


[[Badness]] (Smith): 0.158384
[[Badness]] (Sintel): 4.01


=== 11-limit ===
=== 11-limit ===
Line 819: Line 998:
Comma list: 176/175, 2401/2400, 2560/2541
Comma list: 176/175, 2401/2400, 2560/2541


Mapping: {{mapping| 1 5 1 3 1 | 0 -18 7 -1 13 }}
Mapping: {{mapping| 1 -13 8 2 14 | 0 18 -7 1 -13 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~8/7 = 227.500{{c}}
Optimal tunings:
* WE: ~2 = 1198.4615{{c}}, ~7/4 = 971.2535{{c}} (~8/7 = 227.2079{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 972.4918{{c}} (~8/7 = 227.5082{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~8/7 = 227.500{{c}} -->


{{Optimal ET sequence|legend=0| 21, 37, 58, 153bce, 211bccdee, 269bccdee }}
{{Optimal ET sequence|legend=0| 21, 37, 58, 153bce, 211bccdee, 269bccdee }}


Badness (Smith): 0.059260
Badness (Sintel): 1.96


=== 13-limit ===
=== 13-limit ===
Line 832: Line 1,014:
Comma list: 176/175, 196/195, 364/363, 512/507
Comma list: 176/175, 196/195, 364/363, 512/507


Mapping: {{mapping| 1 5 1 3 1 2 | 0 -18 7 -1 13 9 }}
Mapping: {{mapping| 1 -13 8 2 14 11 | 0 18 -7 1 -13 -9 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~8/7 = 227.493{{c}}
Optimal tunings:
* WE: ~2 = 1198.4012{{c}}, ~7/4 = 971.2110{{c}} (~8/7 = 227.1903{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 972.5030{{c}} (~8/7 = 227.4970{{c}})
<!-- * POTE: ~2 = 1200.000{{c}}, ~8/7 = 227.493{{c}} -->


{{Optimal ET sequence|legend=0| 21, 37, 58, 153bcef, 211bccdeeff }}
{{Optimal ET sequence|legend=0| 21, 37, 58, 153bcef, 211bccdeeff }}


Badness (Smith): 0.032205
Badness (Sintel): 1.33


== Fibo ==
== Fibo ==
Line 845: Line 1,030:
[[Comma list]]: 2401/2400, 341796875/339738624
[[Comma list]]: 2401/2400, 341796875/339738624


{{Mapping|legend=1| 1 19 8 10 | 0 -46 -15 -19 }}
{{Mapping|legend=1| 1 -27 -7 -9 | 0 46 15 19 }}
: mapping generators: ~2, ~125/96
: mapping generators: ~2, ~192/125


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~125/96 = 454.310{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.2050{{c}}, ~192/125 = 745.8170{{c}}
: [[error map]]: {{val| +0.205 +0.094 -0.493 -0.147 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~192/125 = 745.6927{{c}}
: error map: {{val| 0.000 -0.092 -0.924 -0.665 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~192/125 = 745.690{{c}} -->


{{Optimal ET sequence|legend=1| 37, 66b, 103, 140, 243, 383, 1009cd, 1392ccd }}
{{Optimal ET sequence|legend=1| 37, 66b, 103, 140, 243, 383, 1009cd, 1392ccd }}


Badness (Smith): 0.100511
Badness (Sintel): 2.54


=== 11-limit ===
=== 11-limit ===
Line 859: Line 1,049:
Comma list: 385/384, 1375/1372, 43923/43750
Comma list: 385/384, 1375/1372, 43923/43750


Mapping: {{mapping| 1 19 8 10 8 | 0 -46 -15 -19 -12 }}
Mapping: {{mapping| 1 -27 -7 -9 -4 | 0 46 15 19 12 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~100/77 = 454.318{{c}}
Optimal tunings:
* WE: ~2 = 1200.4064{{c}}, ~77/50 = 745.9349{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/50 = 745.6876{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~77/50 = 745.682{{c}} -->


{{Optimal ET sequence|legend=0| 37, 66b, 103, 140, 243e }}
{{Optimal ET sequence|legend=0| 37, 66b, 103, 140, 243e }}


Badness (Smith): 0.056514
Badness (Sintel): 1.87


=== 13-limit ===
=== 13-limit ===
Line 872: Line 1,065:
Comma list: 385/384, 625/624, 847/845, 1375/1372
Comma list: 385/384, 625/624, 847/845, 1375/1372


Mapping: {{mapping| 1 19 8 10 8 9 | 0 -46 -15 -19 -12 -14 }}
Mapping: {{mapping| 1 -27 -7 -9 -4 -5 | 0 46 15 19 12 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/10 = 454.316{{c}}
Optimal tunings:
* WE: ~2 = 1200.3728{{c}}, ~20/13 = 745.9152{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 745.6879{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~20/13 = 745.684{{c}} -->


{{Optimal ET sequence|legend=0| 37, 66b, 103, 140, 243e }}
{{Optimal ET sequence|legend=0| 37, 66b, 103, 140, 243e }}


Badness (Smith): 0.027429
Badness (Sintel): 1.13


== Mintone ==
== Mintone ==
Line 887: Line 1,083:
[[Comma list]]: 2401/2400, 177147/175000
[[Comma list]]: 2401/2400, 177147/175000


{{Mapping|legend=1| 1 5 9 7 | 0 -22 -43 -27 }}
{{Mapping|legend=1| 1 -17 -34 -20 | 0 22 43 27 }}
: mapping generators: ~2, ~10/9
: mapping generators: ~2, ~9/5


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~10/9 = 186.343{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1458{{c}}, ~9/5 = 1013.7798{{c}}
: [[error map]]: {{val| +0.146 -1.277 +1.263 +0.314 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1013.6611{{c}}
: error map: {{val| 0.000 -1.410 +1.116 +0.025 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~9/5 = 1013.657{{c}} -->


{{Optimal ET sequence|legend=1| 45, 58, 103, 161, 586b, 747bc, 908bbc }}
{{Optimal ET sequence|legend=1| 45, 58, 103, 161 }}


[[Badness]] (Smith): 0.125672
[[Badness]] (Sintel): 3.18


=== 11-limit ===
=== 11-limit ===
Line 901: Line 1,102:
Comma list: 243/242, 441/440, 43923/43750
Comma list: 243/242, 441/440, 43923/43750


Mapping: {{mapping| 1 5 9 7 12 | 0 -22 -43 -27 -55 }}
Mapping: {{mapping| 1 -17 -34 -20 -43 | 0 22 43 27 55 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 186.345{{c}}
Optimal tunings:
* WE: ~2 = 1200.1491{{c}}, ~9/5 = 1013.7809{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1013.6593{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~9/5 = 1013.655{{c}} -->


{{Optimal ET sequence|legend=0| 58, 103, 161, 425b, 586b, 747bc }}
{{Optimal ET sequence|legend=0| 45e, 58, 103, 161, 425b }}


Badness (Smith): 0.039962
Badness (Sintel): 1.32


=== 13-limit ===
=== 13-limit ===
Line 914: Line 1,118:
Comma list: 243/242, 351/350, 441/440, 847/845
Comma list: 243/242, 351/350, 441/440, 847/845


Mapping: {{mapping| 1 5 9 7 12 11 | 0 -22 -43 -27 -55 -47 }}
Mapping: {{mapping| 1 -17 -34 -20 -43 -36 | 0 22 43 27 55 47 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 186.347{{c}}
Optimal tunings:
* WE: ~2 = 1200.0928{{c}}, ~9/5 = 1013.7311{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1013.6556{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~9/5 = 1013.653{{c}} -->


{{Optimal ET sequence|legend=0| 58, 103, 161, 425b, 586bf }}
{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161 }}


Badness (Smith): 0.021849
Badness (Sintel): 0.903


=== 17-limit ===
=== 17-limit ===
Line 927: Line 1,134:
Comma list: 243/242, 351/350, 441/440, 561/560, 847/845
Comma list: 243/242, 351/350, 441/440, 561/560, 847/845


Mapping: {{mapping| 1 5 9 7 12 11 3 | 0 -22 -43 -27 -55 -47 7 }}
Mapping: {{mapping| 1 -17 -34 -20 -43 -36 10 | 0 22 43 27 55 47 -7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 186.348{{c}}
Optimal tunings:
* WE: ~2 = 1200.1085{{c}}, ~9/5 = 1013.7433{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1013.6537{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~9/5 = 1013.652{{c}} -->


{{Optimal ET sequence|legend=0| 58, 103, 161, 425b, 586bf }}
{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161 }}


Badness (Smith): 0.020295
Badness (Sintel): 1.03


== Catafourth ==
== Catafourth ==
Line 942: Line 1,152:
[[Comma list]]: 2401/2400, 78732/78125
[[Comma list]]: 2401/2400, 78732/78125


{{Mapping|legend=1| 1 13 17 13 | 0 -28 -36 -25 }}
{{Mapping|legend=1| 1 -15 -19 -12 | 0 28 36 25 }}
: mapping generators: ~2, ~250/189
: mapping generators: ~2, ~189/125


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~250/189 = 489.235{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9278{{c}}, ~189/125 = 710.7220{{c}}
: [[error map]]: {{val| -0.072 -0.656 +1.050 +0.091 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~189/125 = 710.7626{{c}}
: error map: {{val| 0.000 -0.603 +1.139 +0.238 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~189/125 = 710.765{{c}} -->


{{Optimal ET sequence|legend=1| 27, 76, 103, 130 }}
{{Optimal ET sequence|legend=1| 27, 76, 103, 130 }}


Badness (Smith): 0.079579
[[Badness]] (Sintel): 2.01


=== 11-limit ===
=== 11-limit ===
Line 956: Line 1,171:
Comma list: 243/242, 441/440, 78408/78125
Comma list: 243/242, 441/440, 78408/78125


Mapping: {{mapping| 1 13 17 13 32 | 0 -28 -36 -25 -70 }}
Mapping: {{mapping| 1 -15 -19 -12 -38 | 0 28 36 25 70 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~250/189 = 489.252{{c}}
Optimal tunings:
* WE: ~2 = 1200.0219{{c}}, ~189/125 = 710.7610{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~189/125 = 710.7487{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~189/125 = 710.748{{c}} -->


{{Optimal ET sequence|legend=0| 103, 130, 233, 363, 493e, 856be }}
{{Optimal ET sequence|legend=0| 27e, 76e, 103, 130, 233, 363, 493e }}


Badness (Smith): 0.036785
Badness (Sintel): 1.22


=== 13-limit ===
=== 13-limit ===
Line 969: Line 1,187:
Comma list: 243/242, 351/350, 441/440, 10985/10976
Comma list: 243/242, 351/350, 441/440, 10985/10976


Mapping: {{mapping| 1 13 17 13 32 9 | 0 -28 -36 -25 -70 -13 }}
Mapping: {{mapping| 1 -15 -19 -12 -38 -4 | 0 28 36 25 70 13 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~65/49 = 489.256{{c}}
Optimal tunings:
* WE: ~2 = 1200.1023{{c}}, ~98/65 = 710.8043{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~98/65 = 710.7459{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~98/65 = 710.744{{c}} -->


{{Optimal ET sequence|legend=0| 103, 130, 233, 363 }}
{{Optimal ET sequence|legend=0| 27e, 76e, 103, 130, 233, 363 }}


Badness (Smith): 0.021694
Badness (Sintel): 0.896


== Cotritone ==
== Cotritone ==
Line 982: Line 1,203:
[[Comma list]]: 2401/2400, 390625/387072
[[Comma list]]: 2401/2400, 390625/387072


{{Mapping|legend=1| 1 17 9 10 | 0 -30 -13 -14 }}
{{Mapping|legend=1| 1 -13 -4 -4 | 0 30 13 14 }}
: mappping generators: ~2, ~10/7
: mappping generators: ~2, ~7/5


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 583.385{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9278{{c}}, ~7/5 = 583.5994{{c}}
: [[error map]]: {{val| +0.441 +0.289 -1.287 -0.200 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/5 = 583.3956{{c}}
: error map: {{val| 0.000 -0.086 -2.170 -1.287 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~7/5 = 583.385{{c}} -->


{{Optimal ET sequence|legend=1| 35, 37, 72, 109, 181, 253 }}
{{Optimal ET sequence|legend=1| 35, 37, 72, 181, 253, 325c }}


[[Badness]] (Smith): 0.098322
[[Badness]] (Sintel): 2.49


=== 11-limit ===
=== 11-limit ===
Line 996: Line 1,222:
Comma list: 385/384, 1375/1372, 4000/3993
Comma list: 385/384, 1375/1372, 4000/3993


Mapping: {{mapping| 1 17 9 10 5 | 0 -30 -13 -14 -3 }}
Mapping: {{mapping| 1 -13 -4 -4 2 | 0 30 13 14 3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 583.387{{c}}
Optimal tunings:
* WE: ~2 = 1200.4058{{c}}, ~7/5 = 583.5845{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/5 = 583.3950{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~7/5 = 583.387{{c}} -->


{{Optimal ET sequence|legend=0| 35, 37, 72, 109, 181, 253 }}
{{Optimal ET sequence|legend=0| 35, 37, 72, 181, 253, 325c }}


Badness (Smith): 0.032225
Badness (Sintel): 1.07


=== 13-limit ===
=== 13-limit ===
Line 1,009: Line 1,238:
Comma list: 169/168, 364/363, 385/384, 625/624
Comma list: 169/168, 364/363, 385/384, 625/624


Mapping: {{mapping| 1 17 9 10 5 15 | 0 -30 -13 -14 -3 -22 }}
Mapping: {{mapping| 1 -13 -4 -4 2 -7 | 0 30 13 14 3 22 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 583.387{{c}}
Optimal tunings:
* WE: ~2 = 1200.6111{{c}}, ~7/5 = 583.6837{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/5 = 583.3987{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~7/5 = 583.387{{c}} -->


{{Optimal ET sequence|legend=0| 37, 72, 109, 181f }}
{{Optimal ET sequence|legend=0| 35f, 37, 72, 181f, 253ff }}


Badness (Smith): 0.028683
Badness (Sintel): 1.19


== Quasimoha ==
== Quasimoha ==
Line 1,027: Line 1,259:
: mapping generators: ~2, ~49/40
: mapping generators: ~2, ~49/40


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/40 = 348.603{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.5059{{c}}, ~49/40 = 348.0409{{c}}
: [[error map]]: {{val| +1.506 -2.367 -0.702 +0.759 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 348.5582{{c}}
: error map: {{val| 0.000 -4.839 -3.152 -2.966 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~49/40 = 348.603{{c}} -->


{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}
{{Optimal ET sequence|legend=1| 24c, 31, 117c, 148bc, 179bcd }}


[[Badness]] (Smith): 0.110820
[[Badness]] (Sintel): 2.80


=== 11-limit ===
=== 11-limit ===
Line 1,040: Line 1,277:
Mapping: {{mapping| 1 1 9 6 2 | 0 2 -23 -11 5 }}
Mapping: {{mapping| 1 1 9 6 2 | 0 2 -23 -11 5 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 348.639{{c}}
Optimal tunings:
* WE: ~2 = 1201.7630{{c}}, ~11/9 = 349.1510{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 348.6050{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/9 = 348.639{{c}} -->


{{Optimal ET sequence|legend=0| 31, 86ce, 117ce, 148bce }}
{{Optimal ET sequence|legend=0| 24c, 31, 86ce, 117ce, 148bce }}


Badness (Smith): 0.046181
Badness (Sintel): 1.53


== Lockerbie ==
== Lockerbie ==
Line 1,063: Line 1,303:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000{{c}}, ~3828125/2985984 = 431.1071{{c}}
* [[WE]]: ~2 = 1199.9950{{c}}, ~3828125/2985984 = 431.1055{{c}}
: [[error map]]: {{val| 0.0000 -0.0270 +0.1502 -0.1120 }}
: [[error map]]: {{val| -0.005 -0.024 +0.146 -0.120 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3828125/2985984 = 431.1072{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3828125/2985984 = 431.1072{{c}}
: error map: {{val| 0.0000 -0.0205 +0.1547 -0.1081 }}
: error map: {{val| 0.0000 -0.020 +0.155 -0.108 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3828125/2985984 = 431.1071{{c}}
: [[error map]]: {{val| 0.000 -0.027 +0.150 -0.112 }} -->


{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913 }}
{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913, 1183 }}


[[Badness]] (Smith): 0.0597
[[Badness]] (Sintel): 1.51


=== 11-limit ===
=== 11-limit ===
Line 1,080: Line 1,322:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1082{{c}}
* WE: ~2 = 1200.0199{{c}}, ~77/60 = 431.1147{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1078{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1078{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1082{{c}} -->


{{Optimal ET sequence|legend=0| 103, 167, 270, 643, 913, 1183e }}
{{Optimal ET sequence|legend=0| 103, 167, 270, 643, 913, 1183e }}


Badness (Smith): 0.0262
Badness (Sintel): 0.865


=== 13-limit ===
=== 13-limit ===
Line 1,095: Line 1,338:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1085{{c}}
* WE: ~2 = 1200.0707{{c}}, ~77/60 = 431.1316{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1069{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1069{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1085{{c}} -->


{{Optimal ET sequence|legend=0| 103, 167, 270, 643, 913f }}
{{Optimal ET sequence|legend=0| 103, 167, 270, 643, 913f }}


Badness (Smith): 0.0160
Badness (Sintel): 0.662


=== 17-limit ===
=== 17-limit ===
Line 1,110: Line 1,354:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~77/60 = 431.107{{c}}
* WE: ~2 = 1199.9639{{c}}, ~77/60 = 431.0957{{c}}
* CWE: ~2 = 1200.000{{c}}, ~77/60 = 431.108{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/60 = 431.1083{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~77/60 = 431.107{{c}} -->


{{Optimal ET sequence|legend=0| 103, 167, 270 }}
{{Optimal ET sequence|legend=0| 103, 167, 270 }}


Badness (Smith): 0.0210
Badness (Sintel): 1.07


=== 2.3.5.7.11.13.17.41 subgroup ===
=== 2.3.5.7.11.13.17.41 subgroup ===
Line 1,125: Line 1,370:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~41/32 = 431.107{{c}}
* WE: ~2 = 1199.8693{{c}}, ~41/32 = 431.0650{{c}}
* CWE: ~2 = 1200.000{{c}}, ~41/32 = 431.111{{c}}
* CWE: ~2 = 1200.000{{c}}, ~41/32 = 431.1109{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~41/32 = 431.107{{c}} -->


{{Optimal ET sequence|legend=0| 103, 167, 270 }}
{{Optimal ET sequence|legend=0| 103, 167, 270 }}
Badness (Sintel): 1.25


== Hemigoldis ==
== Hemigoldis ==
Line 1,139: Line 1,387:
[[Comma list]]: 2401/2400, 549755813888/533935546875
[[Comma list]]: 2401/2400, 549755813888/533935546875


{{Mapping|legend=1| 1 21 -9 2 | 0 -24 14 1 }}
{{Mapping|legend=1| 1 21 -9 2 | 0 24 -14 -1 }}
: mapping generators: ~2, ~7/4
: mapping generators: ~2, ~8/7


[[Optimal tuning]] ([[CWE]]): ~2 = 1200.000{{c}}, ~7/4 = 970.690{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.2264{{c}}, ~8/7 = 229.1679{{c}}
: [[error map]]: {{val| -0.774 +0.394 +1.468 -0.314 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 229.3103{{c}}
: error map: {{val| 0.000 +1.491 +3.343 +1.864 }}


{{Optimal ET sequence|legend=1| 21, 47b, 68, 157, 382bccd, 529bccd }}
{{Optimal ET sequence|legend=1| 21, 47b, 68, 157, 382bccd, 529bccd }}
Line 1,155: Line 1,407:
[[Comma list]]: 2401/2400, {{monzo| 93 -32 -17 -1 }}
[[Comma list]]: 2401/2400, {{monzo| 93 -32 -17 -1 }}


{{Mapping|legend=1| 1 43 -74 -25 | 0 -70 129 47 }}
{{Mapping|legend=1| 1 -27 55 22 | 0 70 -129 -47 }}
: mapping generators: ~2, ~675/448
: mapping generators: ~2, ~896/675


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~675/448 = 709.9719{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0051{{c}}, ~896/675 = 490.0303{{c}}
: [[error map]]: {{val| +0.005 +0.025 +0.063 -0.136 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~896/675 = 490.0282{{c}}
: error map: {{val| 0.000 +0.017 +0.052 -0.150 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~896/675 = 490.0281{{c}} -->


{{Optimal ET sequence|legend=1| 120, 191, 311, 742, 1053, 2848, 3901 }}
{{Optimal ET sequence|legend=1| 120, 191, 311, 742, 1053, 2848, 3901 }}


[[Badness]] (Smith): 0.202249
[[Badness]] (Sintel): 5.12


=== 11-limit ===
=== 11-limit ===
Line 1,169: Line 1,426:
Comma list: 2401/2400, 820125/819896, 2097152/2096325
Comma list: 2401/2400, 820125/819896, 2097152/2096325


Mapping: {{mapping| 1 43 -74 -25 36 | 0 -70 129 47 -55 }}
Mapping: {{mapping| 1 -27 55 22 -19 | 0 70 -129 -47 55 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~675/448 = 709.9720{{c}}
Optimal tunings:
* WE: ~2 = 1199.9901{{c}}, ~896/675 = 490.0239{{c}}
* CWE: ~2 = 1200.000{{c}}, ~896/675 = 490.0279{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~896/675 = 490.0280{{c}} -->


{{Optimal ET sequence|legend=0| 120, 191, 311, 742, 1053, 1795 }}
{{Optimal ET sequence|legend=0| 120, 191, 311, 742, 1053, 1795 }}


Badness (Smith): 0.052308
Badness (Sintel): 1.73


=== 13-limit ===
=== 13-limit ===
Line 1,182: Line 1,442:
Comma list: 2401/2400, 4096/4095, 6656/6655, 24192/24167
Comma list: 2401/2400, 4096/4095, 6656/6655, 24192/24167


Mapping: {{mapping| 1 43 -74 -25 36 25 | 0 -70 129 47 -55 -36 }}
Mapping: {{mapping| 1 -27 55 22 -19 -11 | 0 70 -129 -47 55 36 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~98/65 = 709.9723{{c}}
Optimal tunings:
* WE: ~2 = 1199.9701{{c}}, ~65/49 = 490.0155{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~65/49 = 490.0277{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~65/49 = 490.0277{{c}} -->


{{Optimal ET sequence|legend=0| 120, 191, 311, 742, 1053, 1795f }}
{{Optimal ET sequence|legend=0| 120, 191, 311, 742, 1053, 1795f }}


Badness (Smith): 0.032503
Badness (Sintel): 1.34


=== 17-limit ===
=== 17-limit ===
Line 1,195: Line 1,458:
Comma list: 2401/2400, 2601/2600, 4096/4095, 6656/6655, 8624/8619
Comma list: 2401/2400, 2601/2600, 4096/4095, 6656/6655, 8624/8619


Mapping: {{mapping| 1 43 -74 -25 36 25 -103 | 0 -70 129 47 -55 -36 181 }}
Mapping: {{mapping| 1 -27 55 22 -19 -11 78 | 0 70 -129 -47 55 36 -181 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~98/65 = 709.9722{{c}}
Optimal tunings:
* WE: ~2 = 1199.9726{{c}}, ~65/49 = 490.0164{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~65/49 = 490.0276{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~65/49 = 490.0278{{c}} -->


{{Optimal ET sequence|legend=0| 120g, 191g, 311, 431, 742, 1795f }}
{{Optimal ET sequence|legend=0| 120g, 191g, 311, 431, 742, 1795f }}


Badness (Smith): 0.020995
Badness (Sintel): 1.07


=== 19-limit ===
=== 19-limit ===
Line 1,208: Line 1,474:
Comma list: 2401/2400, 2601/2600, 2926/2925, 3136/3135, 3213/3211, 5985/5984
Comma list: 2401/2400, 2601/2600, 2926/2925, 3136/3135, 3213/3211, 5985/5984


Mapping: {{mapping| 1 43 -74 -25 36 25 -103 -49 | 0 -70 129 47 -55 -36 181 90 }}
Mapping: {{mapping| 1 -27 55 22 -19 -11 78 41 | 0 70 -129 -47 55 36 -181 -90 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~98/65 = 709.9722{{c}}
Optimal tunings:
* WE: ~2 = 1199.9756{{c}}, ~65/49 = 490.0176{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~65/49 = 490.0276{{c}}
<!-- * CTE:~2 = 1200.0000{{c}}, ~98/65 = 709.9722{{c}} -->


{{Optimal ET sequence|legend=0| 120g, 191g, 311, 431, 742, 1795f }}
{{Optimal ET sequence|legend=0| 120g, 191g, 311, 431, 742, 1795f }}


Badness (Smith): 0.013771
Badness (Sintel): 0.838


== References ==
== References ==
Retrieved from "https://en.xen.wiki/w/Breedsmic_temperaments"