Mabila family: Difference between revisions
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[[Badness]] (Sintel): 5.45 | [[Badness]] (Sintel): 5.45 | ||
== | == Amavil == | ||
{{ | Named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, amavil tempers out [[225/224]] and may be described as the {{nowrap| 34d & 43 }} temperament. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: | [[Comma list]]: 225/224, 17496/16807 | ||
{{Mapping|legend=1| 1 -4 4 | {{Mapping|legend=1| 1 -4 4 -5 | 0 10 -3 14 }} | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = | * [[WE]]: ~2 = 1198.8499{{c}}, ~35/24 = 669.3786{{c}} | ||
: [[error map]]: {{val| +0. | : [[error map]]: {{val| -1.150 -3.569 +0.950 +8.224 }} | ||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 669.9710{{c}} | ||
: error map: {{val| 0.000 + | : error map: {{val| 0.000 -2.245 +3.773 +10.768 }} | ||
{{Optimal ET sequence|legend=1| 9, | {{Optimal ET sequence|legend=1| 9, 25d, 34d, 43, 77d }} | ||
[[Badness]] (Sintel): | [[Badness]] (Sintel): 2.77 | ||
=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: | Comma list: 99/98, 176/175, 864/847 | ||
Mapping: {{mapping| 1 -4 4 | Mapping: {{mapping| 1 -4 4 -5 -1 | 0 10 -3 14 8 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = | * WE: ~2 = 1198.5522{{c}}, ~22/15 = 669.2176{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = | * CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9619{{c}} | ||
{{Optimal ET sequence|legend=0| 9, | {{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de }} | ||
Badness (Sintel): | Badness (Sintel): 1.41 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: | Comma list: 78/77, 99/98, 144/143, 176/175 | ||
Mapping: {{mapping| 1 -4 4 | Mapping: {{mapping| 1 -4 4 -5 -1 -3 | 0 10 -3 14 8 12 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = | * WE: ~2 = 1198.7386{{c}}, ~22/15 = 669.3449{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = | * CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9903{{c}} | ||
{{Optimal ET sequence|legend=0| 9, | {{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.07 | ||
=== 17-limit === | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
Comma list: | Comma list: 78/77, 99/98, 120/119, 144/143, 176/175 | ||
Mapping: {{mapping| 1 -4 4 | Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 | 0 10 -3 14 8 12 -7 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = | * WE: ~2 = 1198.7648{{c}}, ~22/15 = 669.3533{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670. | * CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.0080{{c}} | ||
{{Optimal ET sequence|legend=0| 9, | {{Optimal ET sequence|legend=0| 9, 25de, 34d, 43, 77de }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.13 | ||
=== 19-limit === | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
Comma list: | Comma list: 78/77, 96/95, 99/98, 120/119, 135/133, 144/143 | ||
Mapping: {{mapping| 1 -4 4 | Mapping: {{mapping| 1 -4 4 -5 -1 -3 8 -3 | 0 10 -3 14 8 12 -7 13 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = | * WE: ~2 = 1198.5939{{c}}, ~22/15 = 669.2282{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = | * CWE: ~2 = 1200.0000{{c}}, ~22/15 = 669.9712{{c}} | ||
{{Optimal ET sequence|legend=0| 9, 34dh, 43, 77deh }} | |||
Badness (Sintel): 1.09 | |||
== Semabila == | |||
{{See also| No-threes subgroup temperaments #Mabilic }} | |||
Semabila is so named because it is a semaphore temperament. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: | [[Comma list]]: 49/48, 28672/28125 | ||
{{Mapping|legend=1| 1 -4 4 | {{Mapping|legend=1| 1 -4 4 0 | 0 10 -3 5 }} | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = | * [[WE]]: ~2 = 1200.9854{{c}}, ~112/75 = 670.8838{{c}} | ||
: [[error map]]: {{val| | : [[error map]]: {{val| +0.985 +2.941 +4.977 -14.407 }} | ||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~112/75 = 670.3712{{c}} | ||
: error map: {{val| 0.000 | : error map: {{val| 0.000 +1.757 +2.573 -16.970 }} | ||
{{Optimal ET sequence|legend=1| 9, | {{Optimal ET sequence|legend=1| 9, 25, 34 }} | ||
[[Badness]] (Sintel): | [[Badness]] (Sintel): 3.38 | ||
=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: | Comma list: 49/48, 56/55, 1350/1331 | ||
Mapping: {{mapping| 1 -4 4 | Mapping: {{mapping| 1 -4 4 0 1 | 0 10 -3 5 8 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = | * WE: ~2 = 1200.2248{{c}}, ~22/15 = 670.3965{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = | * CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2804{{c}} | ||
{{Optimal ET sequence|legend=0| 9, | {{Optimal ET sequence|legend=0| 9, 25e, 34 }} | ||
Badness (Sintel): | Badness (Sintel): 2.03 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: | Comma list: 49/48, 56/55, 91/90, 847/845 | ||
Mapping: {{mapping| 1 -4 4 | Mapping: {{mapping| 1 -4 4 0 1 -3 | 0 10 -3 5 8 12 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = | * WE: ~2 = 1200.1265{{c}}, ~22/15 = 670.3078{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = | * CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2429{{c}} | ||
{{Optimal ET sequence|legend=0| 9, | {{Optimal ET sequence|legend=0| 9, 25e, 34 }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.54 | ||
=== 17-limit === | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
Comma list: | Comma list: 49/48, 56/55, 91/90, 154/153, 375/374 | ||
Mapping: {{mapping| 1 -4 4 | Mapping: {{mapping| 1 -4 4 0 1 -3 8 | 0 10 -3 5 8 12 -7 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = | * WE: ~2 = 1199.8798{{c}}, ~22/15 = 670.2382{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670. | * CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.3021{{c}} | ||
{{Optimal ET sequence|legend=0| 9, | {{Optimal ET sequence|legend=0| 9, 25e, 34 }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.62 | ||
=== 19-limit === | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
Comma list: | Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187 | ||
Mapping: {{mapping| 1 -4 4 | Mapping: {{mapping| 1 -4 4 0 1 -3 8 2 | 0 10 -3 5 8 12 -7 4 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = | * WE: ~2 = 1200.4164{{c}}, ~22/15 = 670.4966{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = | * CWE: ~2 = 1200.0000{{c}}, ~22/15 = 670.2749{{c}} | ||
{{Optimal ET sequence|legend=0| 9, | {{Optimal ET sequence|legend=0| 9, 25e, 34 }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.64 | ||
== Tuskaloosa == | == Tuskaloosa == | ||
| Line 334: | Line 334: | ||
Badness (Sintel): 1.44 | Badness (Sintel): 1.44 | ||
== | == Cohemimabila == | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: | [[Comma list]]: 3136/3125, 65536/64827 | ||
{{Mapping|legend=1| 1 - | {{Mapping|legend=1| 1 -4 4 7 | 0 20 -6 -15 }} | ||
: mapping generators: ~2, ~ | : mapping generators: ~2, ~128/105 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199. | * [[WE]]: ~2 = 1199.1476{{c}}, ~128/105 = 334.9440{{c}} | ||
: [[error map]]: {{val| -0. | : [[error map]]: {{val| -0.852 +0.335 +0.613 +1.047 }} | ||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 335.1779{{c}} | ||
: error map: {{val| 0.000 +1. | : error map: {{val| 0.000 +1.603 +2.619 +3.505 }} | ||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 25, 43, 68, 111, 179, 290cd, 469bccdd }} | ||
[[Badness]] (Sintel): | [[Badness]] (Sintel): 3.23 | ||
=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: | Comma list: 176/175, 1375/1372, 16384/16335 | ||
Mapping: {{mapping| 1 - | Mapping: {{mapping| 1 -4 4 7 11 | 0 20 -6 -15 -27 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1199. | * WE: ~2 = 1199.3670{{c}}, ~40/33 = 334.9711{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~40/33 = 335.1492{{c}} | ||
{{Optimal ET sequence|legend=0| | {{Optimal ET sequence|legend=0| 25, 43, 68, 111 }} | ||
Badness (Sintel): 2. | Badness (Sintel): 2.12 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: | Comma list: 176/175, 640/637, 676/675, 1375/1372 | ||
Mapping: {{mapping| 1 - | Mapping: {{mapping| 1 -4 4 7 11 -3 | 0 20 -6 -15 -27 24 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1199. | * WE: ~2 = 1199.3383{{c}}, ~40/33 = 334.9594{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~40/33 = 335.1431{{c}} | ||
{{Optimal ET sequence|legend=0| | {{Optimal ET sequence|legend=0| 25, 43, 68, 111 }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.47 | ||
=== 17-limit === | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
Comma list: | Comma list: 176/175, 256/255, 442/441, 640/637, 715/714 | ||
Mapping: {{mapping| 1 - | Mapping: {{mapping| 1 -4 4 7 11 -3 8 | 0 20 -6 -15 -27 24 -14 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1199. | * WE: ~2 = 1199.3269{{c}}, ~17/14 = 334.9571{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~17/14 = 335.1451{{c}} | ||
{{Optimal ET sequence|legend=0| | {{Optimal ET sequence|legend=0| 25, 43, 68, 111 }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.16 | ||
=== 19-limit === | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
Comma list: | Comma list: 176/175, 256/255, 286/285, 363/361, 442/441, 476/475 | ||
Mapping: {{mapping| 1 - | Mapping: {{mapping| 1 -4 4 7 11 -3 8 9 | 0 20 -6 -15 -27 24 -14 -17 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1199. | * WE: ~2 = 1199.2658{{c}}, ~17/14 = 334.9455{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~17/14 = 335.1516{{c}} | ||
{{Optimal ET sequence|legend=0| | {{Optimal ET sequence|legend=0| 25, 43, 68, 111 }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.06 | ||
== | == Hemimabila == | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: | [[Comma list]]: 6144/6125, 117649/116640 | ||
{{Mapping|legend=1| 1 - | {{Mapping|legend=1| 1 -14 7 -12 | 0 20 -6 19 }} | ||
: mapping generators: ~2, ~ | : mapping generators: ~2, ~12/7 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199. | * [[WE]]: ~2 = 1199.5170{{c}}, ~12/7 = 934.7983{{c}} | ||
: [[error map]]: {{val| -0. | : [[error map]]: {{val| -0.483 +0.773 +1.516 -1.862 }} | ||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~12/7 = 935.1643{{c}} | ||
: error map: {{val| 0.000 +1. | : error map: {{val| 0.000 +1.330 +2.701 -0.705 }} | ||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 9, …, 59, 68, 77, 145 }} | ||
[[Badness]] (Sintel): | [[Badness]] (Sintel): 2.81 | ||
=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 176/175, | Comma list: 121/120, 176/175, 67228/66825 | ||
Mapping: {{mapping| 1 - | Mapping: {{mapping| 1 -14 7 -12 -2 | 0 20 -6 19 7 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1199. | * WE: ~2 = 1199.9930{{c}}, ~12/7 = 935.1459{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1512{{c}} | ||
{{Optimal ET sequence|legend=0| | {{Optimal ET sequence|legend=0| 9, 59, 68, 77, 145e }} | ||
Badness (Sintel): 2. | Badness (Sintel): 2.03 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 176/175, | Comma list: 121/120, 176/175, 196/195, 676/675 | ||
Mapping: {{mapping| 1 - | Mapping: {{mapping| 1 -14 7 -12 -2 -15 | 0 20 -6 19 7 24 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1199. | * WE: ~2 = 1199.9061{{c}}, ~12/7 = 935.0656{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1367{{c}} | ||
{{Optimal ET sequence|legend=0| | {{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.43 | ||
=== 17-limit === | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
Comma list: | Comma list: 121/120, 154/153, 176/175, 196/195, 676/675 | ||
Mapping: {{mapping| 1 - | Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 | 0 20 -6 19 7 24 -14 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1199. | * WE: ~2 = 1199.7422{{c}}, ~12/7 = 934.9596{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1572{{c}} | ||
{{Optimal ET sequence|legend=0| | {{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.42 | ||
=== 19-limit === | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
Comma list: | Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360 | ||
Mapping: {{mapping| 1 - | Mapping: {{mapping| 1 -14 7 -12 -2 -15 15 -9 | 0 20 -6 19 7 24 -14 17 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1199. | * WE: ~2 = 1199.7650{{c}}, ~12/7 = 934.9782{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~12/7 = 935.1581{{c}} | ||
{{Optimal ET sequence|legend=0| | {{Optimal ET sequence|legend=0| 9, 59f, 68, 77 }} | ||
Badness (Sintel): 1. | Badness (Sintel): 1.22 | ||
== Trimabila == | == Trimabila == | ||