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Mabila family: Difference between revisions

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Source for *amavil*
Switch to Sintel's badness, WE & CWE tunings
Line 7: Line 7:
[[Comma list]]: 268435456/263671875
[[Comma list]]: 268435456/263671875


{{Mapping|legend=1| 1 6 1 | 0 -10 3 }}
{{Mapping|legend=1| 1 -4 4 | 0 10 -3 }}
: mapping generators: ~2, ~375/256


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~512/375 = 529.685{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.3545{{c}}, ~375/256 = 669.9545{{c}}
: [[error map]]: {{val| -0.646 +0.173 +1.240 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2921{{c}}
: error map: {{val| -0.646 +0.173 +1.240 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~375/256 = 670.315{{c}} -->


{{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }}
{{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }}


[[Badness]] (Smith): 0.232481
[[Badness]] (Sintel): 5.45


== Semabila ==
== Semabila ==
Line 24: Line 30:
[[Comma list]]: 49/48, 28672/28125
[[Comma list]]: 49/48, 28672/28125


{{Mapping|legend=1| 1 6 1 5 | 0 -10 3 -5 }}
{{Mapping|legend=1| 1 -4 4 0 | 0 10 -3 5 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~75/56 = 529.667{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.9854{{c}}, ~112/75 = 670.8838{{c}}
: [[error map]]: {{val| +0.985 +2.941 +4.977 -14.407 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~112/75 = 670.3712{{c}}
: error map: {{val| 0.000 +1.757 +2.573 -16.970 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~112/75 = 670.333{{c}} -->


{{Optimal ET sequence|legend=1| 9, 25, 34 }}
{{Optimal ET sequence|legend=1| 9, 25, 34 }}


[[Badness]] (Smith): 0.133638
[[Badness]] (Sintel): 3.38


=== 11-limit ===
=== 11-limit ===
Line 37: Line 48:
Comma list: 49/48, 56/55, 1350/1331
Comma list: 49/48, 56/55, 1350/1331


Mapping: {{mapping| 1 6 1 5 7 | 0 -10 3 -5 -8 }}
Mapping: {{mapping| 1 -4 4 0 1 | 0 10 -3 5 8 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.729{{c}}
Optimal tunings:
* WE: ~2 = 1200.2248{{c}}, ~22/15 = 670.3965{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2804{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.271{{c}} -->


{{Optimal ET sequence|legend=0| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness (Smith): 0.061501
Badness (Sintel): 2.03


=== 13-limit ===
=== 13-limit ===
Line 50: Line 64:
Comma list: 49/48, 56/55, 91/90, 847/845
Comma list: 49/48, 56/55, 91/90, 847/845


Mapping: {{mapping| 1 6 1 5 7 9 | 0 -10 3 -5 -8 -12 }}
Mapping: {{mapping| 1 -4 4 0 1 -3 | 0 10 -3 5 8 12 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.763{{c}}
Optimal tunings:
* WE: ~2 = 1200.1265{{c}}, ~22/15 = 670.3078{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2429{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.237{{c}} -->


{{Optimal ET sequence|legend=0| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness (Smith): 0.037270
Badness (Sintel): 1.54


=== 17-limit ===
=== 17-limit ===
Line 63: Line 80:
Comma list: 49/48, 56/55, 91/90, 154/153, 375/374
Comma list: 49/48, 56/55, 91/90, 154/153, 375/374


Mapping: {{mapping| 1 6 1 5 7 9 1 | 0 -10 3 -5 -8 -12 7 }}
Mapping: {{mapping| 1 -4 4 0 1 -3 8 | 0 10 -3 5 8 12 -7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.695{{c}}
Optimal tunings:
* WE: ~2 = 1199.8798{{c}}, ~22/15 = 670.2382{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.3021{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.305{{c}} -->


{{Optimal ET sequence|legend=0| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness (Smith): 0.031888
Badness (Sintel): 1.62


=== 19-limit ===
=== 19-limit ===
Line 76: Line 96:
Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187
Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187


Mapping: {{mapping| 1 6 1 5 7 9 1 6 | 0 -10 3 -5 -8 -12 7 -4 }}
Mapping: {{mapping| 1 -4 4 0 1 -3 8 2 | 0 10 -3 5 8 12 -7 4 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.736{{c}}
Optimal tunings:
* WE: ~2 = 1200.4164{{c}}, ~22/15 = 670.4966{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2749{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.264{{c}} -->


{{Optimal ET sequence|legend=0| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 25e, 34 }}


Badness (Smith): 0.026981
Badness (Sintel): 1.64


== Amavil ==
== Amavil ==
Line 91: Line 114:
[[Comma list]]: 225/224, 17496/16807
[[Comma list]]: 225/224, 17496/16807


{{Mapping|legend=1| 1 6 1 9 | 0 -10 3 -14 }}
{{Mapping|legend=1| 1 -4 4 -5 | 0 10 -3 14 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~48/35 = 529.979{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.8499{{c}}, ~35/24 = 669.3786{{c}}
: [[error map]]: {{val| -1.150 -3.569 +0.950 +8.224 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 669.9710{{c}}
: error map: {{val| 0.000 -2.245 +3.773 +10.768 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~35/24 = 670.021{{c}} -->


{{Optimal ET sequence|legend=1| 9, 25d, 34d, 43, 77d, 120dd }}
{{Optimal ET sequence|legend=1| 9, 25d, 34d, 43, 77d }}


[[Badness]] (Smith): 0.109625
[[Badness]] (Sintel): 2.77


=== 11-limit ===
=== 11-limit ===
Line 104: Line 132:
Comma list: 99/98, 176/175, 864/847
Comma list: 99/98, 176/175, 864/847


Mapping: {{mapping| 1 6 1 9 7 | 0 -10 3 -14 -8 }}
Mapping: {{mapping| 1 -4 4 -5 -1 | 0 10 -3 14 8 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.974{{c}}
Optimal tunings:
* WE: ~2 = 1198.5522{{c}}, ~22/15 = 669.2176{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9619{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.026{{c}} -->


{{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de, 120dde }}
{{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de }}


Badness (Smith): 0.042649
Badness (Sintel): 1.41


=== 13-limit ===
=== 13-limit ===
Line 117: Line 148:
Comma list: 78/77, 99/98, 144/143, 176/175
Comma list: 78/77, 99/98, 144/143, 176/175


Mapping: {{mapping| 1 6 1 9 7 9 | 0 -10 3 -14 -8 -12 }}
Mapping: {{mapping| 1 -4 4 -5 -1 -3 | 0 10 -3 14 8 12 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.951{{c}}
Optimal tunings:
* WE: ~2 = 1198.7386{{c}}, ~22/15 = 669.3449{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9903{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.049{{c}} -->


{{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de, 120dde }}
{{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de }}


Badness (Smith): 0.025791
Badness (Sintel): 1.07


=== 17-limit ===
=== 17-limit ===
Line 130: Line 164:
Comma list: 78/77, 99/98, 120/119, 144/143, 176/175
Comma list: 78/77, 99/98, 120/119, 144/143, 176/175


Mapping: {{mapping| 1 6 1 9 7 9 1 | 0 -10 3 -14 -8 -12 7 }}
Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 | 0 10 -3 14 8 12 -7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.957{{c}}
Optimal tunings:
* WE: ~2 = 1198.7648{{c}}, ~22/15 = 669.3533{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.0080{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.043{{c}} -->


{{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de, 120ddeg }}
{{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de }}


Badness (Smith): 0.022092
Badness (Sintel): 1.13


=== 19-limit ===
=== 19-limit ===
Line 143: Line 180:
Comma list: 78/77, 96/95, 99/98, 120/119, 135/133, 144/143
Comma list: 78/77, 96/95, 99/98, 120/119, 135/133, 144/143


Mapping: {{mapping| 1 6 1 9 7 9 1 10 | 0 -10 3 -14 -8 -12 7 -13 }}
Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 -3 | 0 10 -3 14 8 12 -7 13 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 529.987{{c}}
Optimal tunings:
* WE: ~2 = 1198.5939{{c}}, ~22/15 = 669.2282{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9712{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~22/15 = 670.013{{c}} -->


{{Optimal ET sequence|legend=0| 9, 25deh, 34dh, 43, 77deh, 120ddeghh }}
{{Optimal ET sequence|legend=0| 9, 34dh, 43, 77deh }}


Badness (Smith): 0.017955
Badness (Sintel): 1.09


== Tuskaloosa ==
== Tuskaloosa ==
Line 156: Line 196:
[[Comma list]]: 19683/19600, 110592/109375
[[Comma list]]: 19683/19600, 110592/109375


{{Mapping|legend=1| 1 6 1 24 | 0 -10 3 -48 }}
{{Mapping|legend=1| 1 -4 4 -24 | 0 10 -3 48 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~512/375 = 529.772{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.4378{{c}}, ~375/256 = 669.9137{{c}}
: [[error map]]: {{val| -0.562 -0.569 +1.696 +0.524 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.2172{{c}}
: error map: {{val| 0.000 +0.217 +3.035 +1.597 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~375/256 = 670.228{{c}} -->


{{Optimal ET sequence|legend=1| 34d, 77, 111, 188, 299cd }}
{{Optimal ET sequence|legend=1| 34d, 77, 111, 188, 299cd, 487ccd }}


[[Badness]] (Smith): 0.145058
[[Badness]] (Sintel): 3.67


=== 11-limit ===
=== 11-limit ===
Line 169: Line 214:
Comma list: 176/175, 1331/1323, 19683/19600
Comma list: 176/175, 1331/1323, 19683/19600


Mapping: {{mapping| 1 6 1 24 22 | 0 -10 3 -48 -42 }}
Mapping: {{mapping| 1 -4 4 -24 -20 | 0 10 -3 48 42 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~224/165 = 529.749{{c}}
Optimal tunings:
* WE: ~2 = 1199.4934{{c}}, ~165/112 = 669.9677{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~165/112 = 670.2405{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~165/112 = 670.251{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 77, 111, 299cd, 410ccd, 521ccdd }}
{{Optimal ET sequence|legend=0| 34d, 77, 111 }}


Badness (Smith): 0.061773
Badness (Sintel): 2.04


=== 13-limit ===
=== 13-limit ===
Line 182: Line 230:
Comma list: 176/175, 351/350, 676/675, 1331/1323
Comma list: 176/175, 351/350, 676/675, 1331/1323


Mapping: {{mapping| 1 6 1 24 22 9 | 0 -10 3 -48 -42 -12 }}
Mapping: {{mapping| 1 -4 4 -24 -20 -3 | 0 10 -3 48 42 12 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~65/48 = 529.747{{c}}
Optimal tunings:
* WE: ~2 = 1199.4539{{c}}, ~96/65 = 669.9476{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~96/65 = 670.2425{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~96/65 = 670.253{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 77, 111, 410ccdf, 521ccddff }}
{{Optimal ET sequence|legend=0| 34d, 77, 111 }}


Badness (Smith): 0.031480
Badness (Sintel): 1.30


=== 17-limit ===
=== 17-limit ===
Line 195: Line 246:
Comma list: 176/175, 256/255, 351/350, 676/675, 715/714
Comma list: 176/175, 256/255, 351/350, 676/675, 715/714


Mapping: {{mapping| 1 6 1 24 22 9 1 | 0 -10 3 -48 -42 -12 7 }}
Mapping: {{mapping| 1 -4 4 -24 -20 -3 8 | 0 10 -3 48 42 12 -7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~34/25 = 529.742{{c}}
Optimal tunings:
* WE: ~2 = 1199.3885{{c}}, ~25/17 = 669.9167{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.2500{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~25/17 = 670.258{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 77, 111 }}
{{Optimal ET sequence|legend=0| 34d, 77, 111 }}


Badness (Smith): 0.022765
Badness (Sintel): 1.16


=== 19-limit ===
=== 19-limit ===
Line 208: Line 262:
Comma list: 176/175, 256/255, 286/285, 351/350, 363/361, 476/475
Comma list: 176/175, 256/255, 286/285, 351/350, 363/361, 476/475


Mapping: {{mapping| 1 6 1 24 22 9 1 25 | 0 -10 3 -48 -42 -12 7 -47 }}
Mapping: {{mapping| 1 -4 4 -24 -20 -3 8 -22 | 0 10 -3 48 42 12 -7 47 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~19/14 = 529.749{{c}}
Optimal tunings:
* WE: ~2 = 1199.3711{{c}}, ~25/17 = 669.8997{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.2422{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~25/17 = 670.251{{c}} -->


{{Optimal ET sequence|legend=0| 34dh, 77, 111 }}
{{Optimal ET sequence|legend=0| 34dh, 77, 111 }}


Badness (Smith): 0.017924
Badness (Sintel): 1.09


== Muscogee ==
== Muscogee ==
Line 221: Line 278:
[[Comma list]]: 126/125, 33756345/33554432
[[Comma list]]: 126/125, 33756345/33554432


{{Mapping|legend=1| 1 6 1 -10 | 0 -10 3 29 }}
{{Mapping|legend=1| 1 -4 4 19 | 0 10 -3 -29 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~512/375 = 529.907{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9275{{c}}, ~375/256 = 670.0525{{c}}
: [[error map]]: {{val| -0.073 -1.140 +3.239 -1.726 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~375/256 = 670.0935{{c}}
: error map: {{val| 0.000 -1.020 +3.406 -1.539 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~375/256 = 670.093{{c}} -->


{{Optimal ET sequence|legend=1| 34, 43, 77, 274c, 351cc, 428ccd }}
{{Optimal ET sequence|legend=1| 34, 43, 77 }}


[[Badness]] (Smith): 0.162021
[[Badness]] (Sintel): 4.10


=== 11-limit ===
=== 11-limit ===
Line 234: Line 296:
Comma list: 126/125, 176/175, 264627/262144
Comma list: 126/125, 176/175, 264627/262144


Mapping: {{mapping| 1 6 1 -10 -12 | 0 -10 3 29 35 }}
Mapping: {{mapping| 1 -4 4 19 23 | 0 10 -3 -29 -35 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~224/165 = 529.955{{c}}
Optimal tunings:
* WE: ~2 = 1200.0559{{c}}, ~165/112 = 670.0760{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~165/112 = 670.0441{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~165/112 = 670.045{{c}} -->


{{Optimal ET sequence|legend=0| 34e, 43, 77, 120, 197ce }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120 }}


Badness (Smith): 0.077552
Badness (Sintel): 2.56


=== 13-limit ===
=== 13-limit ===
Line 247: Line 312:
Comma list: 126/125, 176/175, 676/675, 1287/1280
Comma list: 126/125, 176/175, 676/675, 1287/1280


Mapping: {{mapping| 1 6 1 -10 -12 9 | 0 -10 3 29 35 -12 }}
Mapping: {{mapping| 1 -4 4 19 23 -3 | 0 10 -3 -29 -35 12 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~65/48 = 529.957{{c}}
Optimal tunings:
* WE: ~2 = 1200.0428{{c}}, ~96/65 = 670.0673{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~96/65 = 670.0431{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~96/65 = 670.043{{c}} -->


{{Optimal ET sequence|legend=0| 34e, 43, 77, 120, 197ce }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120 }}


Badness (Smith): 0.043352
Badness (Sintel): 1.79


=== 17-limit ===
=== 17-limit ===
Line 260: Line 328:
Comma list: 126/125, 176/175, 256/255, 273/272, 676/675
Comma list: 126/125, 176/175, 256/255, 273/272, 676/675


Mapping: {{mapping| 1 6 1 -10 -12 9 1 | 0 -10 3 29 35 -12 7 }}
Mapping: {{mapping| 1 -4 4 19 23 -3 8 | 0 10 -3 -29 -35 12 -7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~34/25 = 529.958{{c}}
Optimal tunings:
* WE: ~2 = 1199.8666{{c}}, ~25/17 = 669.9675{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.0429{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~25/17 = 670.042{{c}} -->


{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g, 197ceg }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g }}


Badness (Smith): 0.031217
Badness (Sintel): 1.59


=== 19-limit ===
=== 19-limit ===
Line 273: Line 344:
Comma list: 126/125, 171/170, 176/175, 256/255, 273/272, 363/361
Comma list: 126/125, 171/170, 176/175, 256/255, 273/272, 363/361


Mapping: {{mapping| 1 6 1 -10 -12 9 1 -9 | 0 -10 3 29 35 -12 7 30 }}
Mapping: {{mapping| 1 -4 4 19 23 -3 8 21 | 0 10 -3 -29 -35 12 -7 -30 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~19/14 = 529.955{{c}}
Optimal tunings:
* WE: ~2 = 1199.8538{{c}}, ~25/17 = 669.9631{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/17 = 670.0460{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~25/17 = 529.955{{c}} -->


{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g, 197ceg }}
{{Optimal ET sequence|legend=0| 34e, 43, 77, 120g }}


Badness (Smith): 0.023670
Badness (Sintel): 1.44


== Hemimabila ==
== Hemimabila ==
Line 286: Line 360:
[[Comma list]]: 6144/6125, 117649/116640
[[Comma list]]: 6144/6125, 117649/116640


{{Mapping|legend=1| 1 6 1 7 | 0 -20 6 -19 }}
{{Mapping|legend=1| 1 -14 7 -12 | 0 20 -6 19 }}
: mapping generators: ~2, ~12/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/6 = 264.825{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5170{{c}}, ~12/7 = 934.7983{{c}}
: [[error map]]: {{val| -0.483 +0.773 +1.516 -1.862 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~12/7 = 935.1643{{c}}
: error map: {{val| 0.000 +1.330 +2.701 -0.705 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 935.175{{c}} -->


{{Optimal ET sequence|legend=1| 9, 59, 68, 77, 145 }}
{{Optimal ET sequence|legend=1| 9, …, 59, 68, 77, 145 }}


[[Badness]] (Smith): 0.111130
[[Badness]] (Sintel): 2.81


=== 11-limit ===
=== 11-limit ===
Line 299: Line 379:
Comma list: 121/120, 176/175, 67228/66825
Comma list: 121/120, 176/175, 67228/66825


Mapping: {{mapping| 1 6 1 7 5 | 0 -20 6 -19 -7 }}
Mapping: {{mapping| 1 -14 7 -12 -2 | 0 20 -6 19 7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 264.849{{c}}
Optimal tunings:
* WE: ~2 = 1199.9930{{c}}, ~12/7 = 935.1459{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1512{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~12/7 = 935.151{{c}} -->


{{Optimal ET sequence|legend=0| 9, 59, 68, 77, 145e }}
{{Optimal ET sequence|legend=0| 9, 59, 68, 77, 145e }}


Badness (Smith): 0.061426
Badness (Sintel): 2.03


=== 13-limit ===
=== 13-limit ===
Line 312: Line 395:
Comma list: 121/120, 176/175, 196/195, 676/675
Comma list: 121/120, 176/175, 196/195, 676/675


Mapping: {{mapping| 1 6 1 7 5 9 | 0 -20 6 -19 -7 -24 }}
Mapping: {{mapping| 1 -14 7 -12 -2 -15 | 0 20 -6 19 7 24 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 264.861{{c}}
Optimal tunings:
* WE: ~2 = 1199.9061{{c}}, ~12/7 = 935.0656{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1367{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~12/7 = 935.139{{c}} -->


{{Optimal ET sequence|legend=0| 9, 59f, 68, 77, 145e, 222cef }}
{{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }}


Badness (Smith): 0.034531
Badness (Sintel): 1.43


=== 17-limit ===
=== 17-limit ===
Line 325: Line 411:
Comma list: 121/120, 154/153, 176/175, 196/195, 676/675
Comma list: 121/120, 154/153, 176/175, 196/195, 676/675


Mapping: {{mapping| 1 6 1 7 5 9 1 | 0 -20 6 -19 -7 -24 14 }}
Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 | 0 20 -6 19 7 24 -14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 264.839{{c}}
Optimal tunings:
* WE: ~2 = 1199.7422{{c}}, ~12/7 = 934.9596{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1572{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~12/7 = 935.161{{c}} -->


{{Optimal ET sequence|legend=0| 9, 59f, 68, 77, 145e }}
{{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }}


Badness (Smith): 0.027851
Badness (Sintel): 1.42


=== 19-limit ===
=== 19-limit ===
Line 338: Line 427:
Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360
Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360


Mapping: {{mapping| 1 6 1 7 5 9 1 8 | 0 -20 6 -19 -7 -24 14 -17 }}
Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 -9 | 0 20 -6 19 7 24 -14 17 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 264.839{{c}}
Optimal tunings:
* WE: ~2 = 1199.7650{{c}}, ~12/7 = 934.9782{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1581{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~7/6 = 264.839{{c}} -->


{{Optimal ET sequence|legend=0| 9, 59f, 68, 77, 145e }}
{{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }}


Badness (Smith): 0.020053
Badness (Sintel): 1.22


== Cohemimabila ==
== Cohemimabila ==
Line 352: Line 444:


{{Mapping|legend=1| 1 -4 4 7 | 0 20 -6 -15 }}
{{Mapping|legend=1| 1 -4 4 7 | 0 20 -6 -15 }}
: mapping generators: ~2, ~128/105


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~128/105 = 335.182{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.1476{{c}}, ~128/105 = 334.9440{{c}}
: [[error map]]: {{val| -0.852 +0.335 +0.613 +1.047 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 335.1779{{c}}
: error map: {{val| 0.000 +1.603 +2.619 +3.505 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~128/105 = 335.182{{c}} -->


{{Optimal ET sequence|legend=1| 25, 43, 68, 111, 179, 290cd, 469bccdd }}
{{Optimal ET sequence|legend=1| 25, 43, 68, 111, 179, 290cd, 469bccdd }}


[[Badness]] (Smith): 0.127451
[[Badness]] (Sintel): 3.23


=== 11-limit ===
=== 11-limit ===
Line 366: Line 464:
Mapping: {{mapping| 1 -4 4 7 11 | 0 20 -6 -15 -27 }}
Mapping: {{mapping| 1 -4 4 7 11 | 0 20 -6 -15 -27 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~40/33 = 335.148{{c}}
Optimal tunings:
* WE: ~2 = 1199.3670{{c}}, ~40/33 = 334.9711{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/33 = 335.1492{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~40/33 = 335.148{{c}} -->


{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness (Smith): 0.064164
Badness (Sintel): 2.12


=== 13-limit ===
=== 13-limit ===
Line 379: Line 480:
Mapping: {{mapping| 1 -4 4 7 11 -3 | 0 20 -6 -15 -27 24 }}
Mapping: {{mapping| 1 -4 4 7 11 -3 | 0 20 -6 -15 -27 24 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~40/33 = 335.144{{c}}
Optimal tunings:
* WE: ~2 = 1199.3383{{c}}, ~40/33 = 334.9594{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/33 = 335.1431{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~40/33 = 335.144{{c}} -->


{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness (Smith): 0.035463
Badness (Sintel): 1.47


=== 17-limit ===
=== 17-limit ===
Line 392: Line 496:
Mapping: {{mapping| 1 -4 4 7 11 -3 8 | 0 20 -6 -15 -27 24 -14 }}
Mapping: {{mapping| 1 -4 4 7 11 -3 8 | 0 20 -6 -15 -27 24 -14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/14 = 335.145{{c}}
Optimal tunings:
* WE: ~2 = 1199.3269{{c}}, ~17/14 = 334.9571{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/14 = 335.1451{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~17/14 = 335.145{{c}} -->


{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness (Smith): 0.022728
Badness (Sintel): 1.16


=== 19-limit ===
=== 19-limit ===
Line 405: Line 512:
Mapping: {{mapping| 1 -4 4 7 11 -3 8 9 | 0 20 -6 -15 -27 24 -14 -17 }}
Mapping: {{mapping| 1 -4 4 7 11 -3 8 9 | 0 20 -6 -15 -27 24 -14 -17 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/14 = 335.151{{c}}
Optimal tunings:
* WE: ~2 = 1199.2658{{c}}, ~17/14 = 334.9455{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/14 = 335.1516{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~17/14 = 335.151{{c}} -->


{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}
{{Optimal ET sequence|legend=0| 25, 43, 68, 111 }}


Badness (Smith): 0.017450
Badness (Sintel): 1.06


== Trimabila ==
== Trimabila ==
Line 416: Line 526:
[[Comma list]]: 1728/1715, 268435456/263671875
[[Comma list]]: 1728/1715, 268435456/263671875


{{Mapping|legend=1| 3 8 6 12 | 0 -10 3 -11 }}
{{Mapping|legend=1| 3 -2 9 1 | 0 10 -3 11 }}
: mapping generators: ~1125/896, ~7/6


[[Optimal tuning]] ([[POTE]]): ~1125/896 = 400.000{{c}}, ~7/6 = 270.269{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~1125/896 = 399.7349{{c}}, ~7/6 = 270.0900{{c}}
: [[error map]]: {{val| -0.795 -0.525 +1.030 +1.899 }}
* [[CWE]]: ~1125/896 = 400.0000{{c}}, ~7/6 = 270.2343{{c}}
: error map: {{val| 0.000 +0.388 +2.983 +3.752 }}
<!-- * [[POTE]]: ~1125/896 = 400.000{{c}}, ~7/6 = 270.269{{c}} -->


{{Optimal ET sequence|legend=1| 9, 102d, 111 }}
{{Optimal ET sequence|legend=1| 9, …, 102d, 111 }}


[[Badness]] (Smith): 0.267168
[[Badness]] (Sintel): 6.76


=== 11-limit ===
=== 11-limit ===
Line 429: Line 545:
Comma list: 176/175, 540/539, 805255/802816
Comma list: 176/175, 540/539, 805255/802816


Mapping: {{mapping| 3 8 6 12 12 | 0 -10 3 -11 -5 }}
Mapping: {{mapping| 3 -2 9 1 7 | 0 10 -3 11 5 }}


Optimal tuning (POTE): ~495/392 = 400.000{{c}}, ~7/6 = 270.256{{c}}
Optimal tunings:
* WE: ~495/392 = 399.7963{{c}}, ~7/6 = 270.1183{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2301{{c}}
<!-- * POTE: ~495/392 = 400.000{{c}}, ~7/6 = 270.256{{c}} -->


{{Optimal ET sequence|legend=0| 9, 102d, 111 }}
{{Optimal ET sequence|legend=0| 9, …, 102d, 111 }}


Badness (Smith): 0.081946
Badness (Sintel): 2.71


=== 13-limit ===
=== 13-limit ===
Line 442: Line 561:
Comma list: 176/175, 540/539, 676/675, 1573/1568
Comma list: 176/175, 540/539, 676/675, 1573/1568


Mapping: {{mapping| 3 8 6 12 12 15 | 0 -10 3 -11 -5 -12 }}
Mapping: {{mapping| 3 -2 9 1 7 3 | 0 10 -3 11 5 12 }}


Optimal tuning (POTE): ~495/392 = 400.000{{c}}, ~7/6 = 270.254{{c}} (or ~14/13 = 129.746{{c}})
Optimal tunings:
* WE: ~495/392 = 399.7935{{c}}, ~7/6 = 270.1144{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2258{{c}}
<!-- * POTE: ~495/392 = 400.000{{c}}, ~7/6 = 270.254{{c}} (or ~14/13 = 129.746{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 102df, 111 }}
{{Optimal ET sequence|legend=0| 9, …, 102df, 111 }}


Badness (Smith): 0.040102
Badness (Sintel): 1.66


=== 17-limit ===
=== 17-limit ===
Line 455: Line 577:
Comma list: 176/175, 256/255, 540/539, 676/675, 715/714
Comma list: 176/175, 256/255, 540/539, 676/675, 715/714


Mapping: {{mapping| 3 8 6 12 12 15 10 | 0 -10 3 -11 -5 -12 7 }}
Mapping: {{mapping| 3 -2 9 1 7 3 17 | 0 10 -3 11 5 12 -7 }}


Optimal tuning (POTE): ~495/392 = 400.000{{c}}, ~7/6 = 270.266{{c}} (or ~14/13 = 129.734{{c}})
Optimal tunings:
* WE: ~495/392 = 399.7781{{c}}, ~7/6 = 270.1159{{c}}
* CWE: ~495/392 = 400.0000{{c}}, ~7/6 = 270.2476{{c}}
<!-- * POTE: ~495/392 = 400.000{{c}}, ~7/6 = 270.266{{c}} (or ~14/13 = 129.734{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 102df, 111 }}
{{Optimal ET sequence|legend=0| 9, 102df, 111 }}


Badness (Smith): 0.030657
Badness (Sintel): 1.56


=== 19-limit ===
=== 19-limit ===
Line 468: Line 593:
Comma list: 176/175, 256/255, 286/285, 363/361, 476/475, 540/539
Comma list: 176/175, 256/255, 286/285, 363/361, 476/475, 540/539


Mapping: {{mapping| 3 8 6 12 12 15 10 16 | 0 -10 3 -11 -5 -12 7 -10 }}
Mapping: {{mapping| 3 -2 9 1 7 3 17 6 | 0 10 -3 11 5 12 -7 10 }}


Optimal tuning (POTE): ~208/165 = 400.000{{c}}, ~7/6 = 270.260{{c}} (or ~14/13 = 129.740{{c}})
Optimal tunings:
* WE: ~208/165 = 399.7588{{c}}, ~7/6 = 270.0969{{c}}
* CWE: ~208/165 = 400.0000{{c}}, ~7/6 = 270.2391{{c}}
<!-- * POTE: ~208/165 = 400.000{{c}}, ~7/6 = 270.260{{c}} (or ~14/13 = 129.740{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 102dfh, 111 }}
{{Optimal ET sequence|legend=0| 9, 102dfh, 111 }}


Badness (Smith): 0.022851
Badness (Sintel): 1.39


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