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 ==

Revision as of 19:54, 25 February 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The mabila family of temperaments tempers out the mabila comma (monzo: [28 -3 -10⟩, ratio: 268435456/263671875) in the 5-limit. This gives a temperament structure superficially similar to mavila, with extremely sharp fourths/flat fifths, three of which make a major third. However, unlike mavila, 10 of these bad fifths reach a more in tune one, which is useful for creating resolutions when using a large enough gamut, such as the 9L 7s mos which has 3 good major and minor chords.

Mabila

Subgroup: 2.3.5

Comma list: 268435456/263671875

Mapping: [⟨1 -4 4], ⟨0 10 -3]]

mapping generators: ~2, ~375/256

Optimal tunings:

  • WE: ~2 = 1199.3545 ¢, ~375/256 = 669.9545 ¢
error map: ⟨-0.646 +0.173 +1.240]
  • CWE: ~2 = 1200.0000 ¢, ~375/256 = 670.2921 ¢
error map: ⟨-0.646 +0.173 +1.240]

Optimal ET sequence: 9, 25, 34, 77, 111, 145, 256c

Badness (Sintel): 5.45

Semabila

See also: No-threes subgroup temperaments § Mabilic

Semabila is so named because it is a semaphore temperament.

Subgroup: 2.3.5.7

Comma list: 49/48, 28672/28125

Mapping: [⟨1 -4 4 0], ⟨0 10 -3 5]]

Optimal tunings:

  • WE: ~2 = 1200.9854 ¢, ~112/75 = 670.8838 ¢
error map: ⟨+0.985 +2.941 +4.977 -14.407]
  • CWE: ~2 = 1200.0000 ¢, ~112/75 = 670.3712 ¢
error map: ⟨0.000 +1.757 +2.573 -16.970]

Optimal ET sequence: 9, 25, 34

Badness (Sintel): 3.38

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 56/55, 1350/1331

Mapping: [⟨1 -4 4 0 1], ⟨0 10 -3 5 8]]

Optimal tunings:

  • WE: ~2 = 1200.2248 ¢, ~22/15 = 670.3965 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 670.2804 ¢

Optimal ET sequence: 9, 25e, 34

Badness (Sintel): 2.03

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 56/55, 91/90, 847/845

Mapping: [⟨1 -4 4 0 1 -3], ⟨0 10 -3 5 8 12]]

Optimal tunings:

  • WE: ~2 = 1200.1265 ¢, ~22/15 = 670.3078 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 670.2429 ¢

Optimal ET sequence: 9, 25e, 34

Badness (Sintel): 1.54

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 49/48, 56/55, 91/90, 154/153, 375/374

Mapping: [⟨1 -4 4 0 1 -3 8], ⟨0 10 -3 5 8 12 -7]]

Optimal tunings:

  • WE: ~2 = 1199.8798 ¢, ~22/15 = 670.2382 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 670.3021 ¢

Optimal ET sequence: 9, 25e, 34

Badness (Sintel): 1.62

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187

Mapping: [⟨1 -4 4 0 1 -3 8 2], ⟨0 10 -3 5 8 12 -7 4]]

Optimal tunings:

  • WE: ~2 = 1200.4164 ¢, ~22/15 = 670.4966 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 670.2749 ¢

Optimal ET sequence: 9, 25e, 34

Badness (Sintel): 1.64

Amavil

Named by Petr Pařízek in 2011[1], amavil tempers out 225/224 and may be described as the 34d & 43 temperament.

Subgroup: 2.3.5.7

Comma list: 225/224, 17496/16807

Mapping: [⟨1 -4 4 -5], ⟨0 10 -3 14]]

Optimal tunings:

  • WE: ~2 = 1198.8499 ¢, ~35/24 = 669.3786 ¢
error map: ⟨-1.150 -3.569 +0.950 +8.224]
  • CWE: ~2 = 1200.0000 ¢, ~35/24 = 669.9710 ¢
error map: ⟨0.000 -2.245 +3.773 +10.768]

Optimal ET sequence: 9, 25d, 34d, 43, 77d

Badness (Sintel): 2.77

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 864/847

Mapping: [⟨1 -4 4 -5 -1], ⟨0 10 -3 14 8]]

Optimal tunings:

  • WE: ~2 = 1198.5522 ¢, ~22/15 = 669.2176 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 669.9619 ¢

Optimal ET sequence: 9, 25de, 34d, 43, 77de

Badness (Sintel): 1.41

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 99/98, 144/143, 176/175

Mapping: [⟨1 -4 4 -5 -1 -3], ⟨0 10 -3 14 8 12]]

Optimal tunings:

  • WE: ~2 = 1198.7386 ¢, ~22/15 = 669.3449 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 669.9903 ¢

Optimal ET sequence: 9, 25de, 34d, 43, 77de

Badness (Sintel): 1.07

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 78/77, 99/98, 120/119, 144/143, 176/175

Mapping: [⟨1 -4 4 -5 -1 -3 8], ⟨0 10 -3 14 8 12 -7]]

Optimal tunings:

  • WE: ~2 = 1198.7648 ¢, ~22/15 = 669.3533 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 670.0080 ¢

Optimal ET sequence: 9, 25de, 34d, 43, 77de

Badness (Sintel): 1.13

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 78/77, 96/95, 99/98, 120/119, 135/133, 144/143

Mapping: [⟨1 -4 4 -5 -1 -3 8 -3], ⟨0 10 -3 14 8 12 -7 13]]

Optimal tunings:

  • WE: ~2 = 1198.5939 ¢, ~22/15 = 669.2282 ¢
  • CWE: ~2 = 1200.0000 ¢, ~22/15 = 669.9712 ¢

Optimal ET sequence: 9, 34dh, 43, 77deh

Badness (Sintel): 1.09

Tuskaloosa

Subgroup: 2.3.5.7

Comma list: 19683/19600, 110592/109375

Mapping: [⟨1 -4 4 -24], ⟨0 10 -3 48]]

Optimal tunings:

  • WE: ~2 = 1199.4378 ¢, ~375/256 = 669.9137 ¢
error map: ⟨-0.562 -0.569 +1.696 +0.524]
  • CWE: ~2 = 1200.0000 ¢, ~375/256 = 670.2172 ¢
error map: ⟨0.000 +0.217 +3.035 +1.597]

Optimal ET sequence: 34d, 77, 111, 188, 299cd, 487ccd

Badness (Sintel): 3.67

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 1331/1323, 19683/19600

Mapping: [⟨1 -4 4 -24 -20], ⟨0 10 -3 48 42]]

Optimal tunings:

  • WE: ~2 = 1199.4934 ¢, ~165/112 = 669.9677 ¢
  • CWE: ~2 = 1200.0000 ¢, ~165/112 = 670.2405 ¢

Optimal ET sequence: 34d, 77, 111

Badness (Sintel): 2.04

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 351/350, 676/675, 1331/1323

Mapping: [⟨1 -4 4 -24 -20 -3], ⟨0 10 -3 48 42 12]]

Optimal tunings:

  • WE: ~2 = 1199.4539 ¢, ~96/65 = 669.9476 ¢
  • CWE: ~2 = 1200.0000 ¢, ~96/65 = 670.2425 ¢

Optimal ET sequence: 34d, 77, 111

Badness (Sintel): 1.30

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 176/175, 256/255, 351/350, 676/675, 715/714

Mapping: [⟨1 -4 4 -24 -20 -3 8], ⟨0 10 -3 48 42 12 -7]]

Optimal tunings:

  • WE: ~2 = 1199.3885 ¢, ~25/17 = 669.9167 ¢
  • CWE: ~2 = 1200.0000 ¢, ~25/17 = 670.2500 ¢

Optimal ET sequence: 34d, 77, 111

Badness (Sintel): 1.16

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 176/175, 256/255, 286/285, 351/350, 363/361, 476/475

Mapping: [⟨1 -4 4 -24 -20 -3 8 -22], ⟨0 10 -3 48 42 12 -7 47]]

Optimal tunings:

  • WE: ~2 = 1199.3711 ¢, ~25/17 = 669.8997 ¢
  • CWE: ~2 = 1200.0000 ¢, ~25/17 = 670.2422 ¢

Optimal ET sequence: 34dh, 77, 111

Badness (Sintel): 1.09

Muscogee

Subgroup: 2.3.5.7

Comma list: 126/125, 33756345/33554432

Mapping: [⟨1 -4 4 19], ⟨0 10 -3 -29]]

Optimal tunings:

  • WE: ~2 = 1199.9275 ¢, ~375/256 = 670.0525 ¢
error map: ⟨-0.073 -1.140 +3.239 -1.726]
  • CWE: ~2 = 1200.0000 ¢, ~375/256 = 670.0935 ¢
error map: ⟨0.000 -1.020 +3.406 -1.539]

Optimal ET sequence: 34, 43, 77

Badness (Sintel): 4.10

11-limit

Subgroup: 2.3.5.7.11

Comma list: 126/125, 176/175, 264627/262144

Mapping: [⟨1 -4 4 19 23], ⟨0 10 -3 -29 -35]]

Optimal tunings:

  • WE: ~2 = 1200.0559 ¢, ~165/112 = 670.0760 ¢
  • CWE: ~2 = 1200.0000 ¢, ~165/112 = 670.0441 ¢

Optimal ET sequence: 34e, 43, 77, 120

Badness (Sintel): 2.56

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 176/175, 676/675, 1287/1280

Mapping: [⟨1 -4 4 19 23 -3], ⟨0 10 -3 -29 -35 12]]

Optimal tunings:

  • WE: ~2 = 1200.0428 ¢, ~96/65 = 670.0673 ¢
  • CWE: ~2 = 1200.0000 ¢, ~96/65 = 670.0431 ¢

Optimal ET sequence: 34e, 43, 77, 120

Badness (Sintel): 1.79

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 126/125, 176/175, 256/255, 273/272, 676/675

Mapping: [⟨1 -4 4 19 23 -3 8], ⟨0 10 -3 -29 -35 12 -7]]

Optimal tunings:

  • WE: ~2 = 1199.8666 ¢, ~25/17 = 669.9675 ¢
  • CWE: ~2 = 1200.0000 ¢, ~25/17 = 670.0429 ¢

Optimal ET sequence: 34e, 43, 77, 120g

Badness (Sintel): 1.59

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 126/125, 171/170, 176/175, 256/255, 273/272, 363/361

Mapping: [⟨1 -4 4 19 23 -3 8 21], ⟨0 10 -3 -29 -35 12 -7 -30]]

Optimal tunings:

  • WE: ~2 = 1199.8538 ¢, ~25/17 = 669.9631 ¢
  • CWE: ~2 = 1200.0000 ¢, ~25/17 = 670.0460 ¢

Optimal ET sequence: 34e, 43, 77, 120g

Badness (Sintel): 1.44

Hemimabila

Subgroup: 2.3.5.7

Comma list: 6144/6125, 117649/116640

Mapping: [⟨1 -14 7 -12], ⟨0 20 -6 19]]

mapping generators: ~2, ~12/7

Optimal tunings:

  • WE: ~2 = 1199.5170 ¢, ~12/7 = 934.7983 ¢
error map: ⟨-0.483 +0.773 +1.516 -1.862]
  • CWE: ~2 = 1200.0000 ¢, ~12/7 = 935.1643 ¢
error map: ⟨0.000 +1.330 +2.701 -0.705]

Optimal ET sequence: 9, …, 59, 68, 77, 145

Badness (Sintel): 2.81

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 67228/66825

Mapping: [⟨1 -14 7 -12 -2], ⟨0 20 -6 19 7]]

Optimal tunings:

  • WE: ~2 = 1199.9930 ¢, ~12/7 = 935.1459 ¢
  • CWE: ~2 = 1200.0000 ¢, ~12/7 = 935.1512 ¢

Optimal ET sequence: 9, 59, 68, 77, 145e

Badness (Sintel): 2.03

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 176/175, 196/195, 676/675

Mapping: [⟨1 -14 7 -12 -2 -15], ⟨0 20 -6 19 7 24]]

Optimal tunings:

  • WE: ~2 = 1199.9061 ¢, ~12/7 = 935.0656 ¢
  • CWE: ~2 = 1200.0000 ¢, ~12/7 = 935.1367 ¢

Optimal ET sequence: 9, 59f, 68, 77

Badness (Sintel): 1.43

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 121/120, 154/153, 176/175, 196/195, 676/675

Mapping: [⟨1 -14 7 -12 -2 -15 15], ⟨0 20 -6 19 7 24 -14]]

Optimal tunings:

  • WE: ~2 = 1199.7422 ¢, ~12/7 = 934.9596 ¢
  • CWE: ~2 = 1200.0000 ¢, ~12/7 = 935.1572 ¢

Optimal ET sequence: 9, 59f, 68, 77

Badness (Sintel): 1.42

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360

Mapping: [⟨1 -14 7 -12 -2 -15 15 -9], ⟨0 20 -6 19 7 24 -14 17]]

Optimal tunings:

  • WE: ~2 = 1199.7650 ¢, ~12/7 = 934.9782 ¢
  • CWE: ~2 = 1200.0000 ¢, ~12/7 = 935.1581 ¢

Optimal ET sequence: 9, 59f, 68, 77

Badness (Sintel): 1.22

Cohemimabila

Subgroup: 2.3.5.7

Comma list: 3136/3125, 65536/64827

Mapping: [⟨1 -4 4 7], ⟨0 20 -6 -15]]

mapping generators: ~2, ~128/105

Optimal tunings:

  • WE: ~2 = 1199.1476 ¢, ~128/105 = 334.9440 ¢
error map: ⟨-0.852 +0.335 +0.613 +1.047]
  • CWE: ~2 = 1200.0000 ¢, ~128/105 = 335.1779 ¢
error map: ⟨0.000 +1.603 +2.619 +3.505]

Optimal ET sequence: 25, 43, 68, 111, 179, 290cd, 469bccdd

Badness (Sintel): 3.23

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 1375/1372, 16384/16335

Mapping: [⟨1 -4 4 7 11], ⟨0 20 -6 -15 -27]]

Optimal tunings:

  • WE: ~2 = 1199.3670 ¢, ~40/33 = 334.9711 ¢
  • CWE: ~2 = 1200.0000 ¢, ~40/33 = 335.1492 ¢

Optimal ET sequence: 25, 43, 68, 111

Badness (Sintel): 2.12

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 640/637, 676/675, 1375/1372

Mapping: [⟨1 -4 4 7 11 -3], ⟨0 20 -6 -15 -27 24]]

Optimal tunings:

  • WE: ~2 = 1199.3383 ¢, ~40/33 = 334.9594 ¢
  • CWE: ~2 = 1200.0000 ¢, ~40/33 = 335.1431 ¢

Optimal ET sequence: 25, 43, 68, 111

Badness (Sintel): 1.47

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 176/175, 256/255, 442/441, 640/637, 715/714

Mapping: [⟨1 -4 4 7 11 -3 8], ⟨0 20 -6 -15 -27 24 -14]]

Optimal tunings:

  • WE: ~2 = 1199.3269 ¢, ~17/14 = 334.9571 ¢
  • CWE: ~2 = 1200.0000 ¢, ~17/14 = 335.1451 ¢

Optimal ET sequence: 25, 43, 68, 111

Badness (Sintel): 1.16

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 176/175, 256/255, 286/285, 363/361, 442/441, 476/475

Mapping: [⟨1 -4 4 7 11 -3 8 9], ⟨0 20 -6 -15 -27 24 -14 -17]]

Optimal tunings:

  • WE: ~2 = 1199.2658 ¢, ~17/14 = 334.9455 ¢
  • CWE: ~2 = 1200.0000 ¢, ~17/14 = 335.1516 ¢

Optimal ET sequence: 25, 43, 68, 111

Badness (Sintel): 1.06

Trimabila

Subgroup: 2.3.5.7

Comma list: 1728/1715, 268435456/263671875

Mapping: [⟨3 -2 9 1], ⟨0 10 -3 11]]

mapping generators: ~1125/896, ~7/6

Optimal tunings:

  • WE: ~1125/896 = 399.7349 ¢, ~7/6 = 270.0900 ¢
error map: ⟨-0.795 -0.525 +1.030 +1.899]
  • CWE: ~1125/896 = 400.0000 ¢, ~7/6 = 270.2343 ¢
error map: ⟨0.000 +0.388 +2.983 +3.752]

Optimal ET sequence: 9, …, 102d, 111

Badness (Sintel): 6.76

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 540/539, 805255/802816

Mapping: [⟨3 -2 9 1 7], ⟨0 10 -3 11 5]]

Optimal tunings:

  • WE: ~495/392 = 399.7963 ¢, ~7/6 = 270.1183 ¢
  • CWE: ~495/392 = 400.0000 ¢, ~7/6 = 270.2301 ¢

Optimal ET sequence: 9, …, 102d, 111

Badness (Sintel): 2.71

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 540/539, 676/675, 1573/1568

Mapping: [⟨3 -2 9 1 7 3], ⟨0 10 -3 11 5 12]]

Optimal tunings:

  • WE: ~495/392 = 399.7935 ¢, ~7/6 = 270.1144 ¢
  • CWE: ~495/392 = 400.0000 ¢, ~7/6 = 270.2258 ¢

Optimal ET sequence: 9, …, 102df, 111

Badness (Sintel): 1.66

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 176/175, 256/255, 540/539, 676/675, 715/714

Mapping: [⟨3 -2 9 1 7 3 17], ⟨0 10 -3 11 5 12 -7]]

Optimal tunings:

  • WE: ~495/392 = 399.7781 ¢, ~7/6 = 270.1159 ¢
  • CWE: ~495/392 = 400.0000 ¢, ~7/6 = 270.2476 ¢

Optimal ET sequence: 9, 102df, 111

Badness (Sintel): 1.56

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 176/175, 256/255, 286/285, 363/361, 476/475, 540/539

Mapping: [⟨3 -2 9 1 7 3 17 6], ⟨0 10 -3 11 5 12 -7 10]]

Optimal tunings:

  • WE: ~208/165 = 399.7588 ¢, ~7/6 = 270.0969 ¢
  • CWE: ~208/165 = 400.0000 ¢, ~7/6 = 270.2391 ¢

Optimal ET sequence: 9, 102dfh, 111

Badness (Sintel): 1.39

References

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
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