Sensamagic family: Difference between revisions
m Units & misc. cleanup |
Switch to Sintel's badness, WE & CWE tunings, per community consensus |
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| Line 12: | Line 12: | ||
{{Mapping|legend=1| 1 0 0 0 | 0 1 1 2 | 0 0 2 -1 }} | {{Mapping|legend=1| 1 0 0 0 | 0 1 1 2 | 0 0 2 -1 }} | ||
: mapping generators: ~2, ~3, ~9/7 | : mapping generators: ~2, ~3, ~9/7 | ||
| Line 21: | Line 20: | ||
: Angle (3/2, 9/7) = 86.5288° | : Angle (3/2, 9/7) = 86.5288° | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199.9983{{c}}, ~3/2 = 703.7414{{c}}, ~9/7 = 440.9014{{c}} | |||
: [[error map]]: {{val| -0.002 +1.785 -0.771 -2.248 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7411{{c}}, ~9/7 = 440.9017{{c}} | |||
: error map: {{val| 0.000 +1.786 -0.769 -2.245 }} | |||
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7424{{c}}, ~9/7 = 440.9020{{c}} --> | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
| Line 33: | Line 37: | ||
{{Optimal ET sequence|legend=1| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }} | {{Optimal ET sequence|legend=1| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 0.570 | ||
[[Projection pair]]: 5 243/49 to 2.3.7 | [[Projection pair]]: 5 243/49 to 2.3.7 | ||
| Line 58: | Line 62: | ||
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 2 -2 | 0 0 2 -1 -1 }} | {{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 2 -2 | 0 0 2 -1 -1 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199.9667{{c}}, ~3/2 = 703.7809{{c}}, ~9/7 = 440.9056{{c}} | |||
: [[error map]]: {{val| -0.033 +1.793 -0.755 -2.236 +0.048 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7948{{c}}, ~9/7 = 440.9180{{c}} | |||
: error map: {{val| 0.000 +1.840 -0.683 -2.1554 +0.175 }} | |||
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.8004{{c}}, ~9/7 = 440.9178{{c}} --> | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 21/13 6/13 -1/13 1/13 -3/13 }}, {{monzo| 35/13 10/13 7/13 -7/13 -5/13 }}, {{monzo| 35/13 10/13 -6/13 6/13 -5/13 }}, {{monzo| 42/13 -14/13 -2/13 2/13 7/13 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 21/13 6/13 -1/13 1/13 -3/13 }}, {{monzo| 35/13 10/13 7/13 -7/13 -5/13 }}, {{monzo| 35/13 10/13 -6/13 6/13 -5/13 }}, {{monzo| 42/13 -14/13 -2/13 2/13 7/13 }}] | ||
: [[ | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/9 | ||
{{Optimal ET sequence|legend=1| 17, 19, 22, 41, 68, 87, 196, 283 | {{Optimal ET sequence|legend=1| 17, 19, 22, 41, 68, 87, 196, 283 }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 0.868 | ||
[[Projection pair]]s: 5 243/49 11 896/81 to 2.3.7 | [[Projection pair]]s: 5 243/49 11 896/81 to 2.3.7 | ||
| Line 78: | Line 87: | ||
Mapping: {{mapping| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }} | Mapping: {{mapping| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }} | ||
{{ | Optimal tunings: | ||
* WE: ~2 = 1199.9905{{c}}, ~3/2 = 703.7325{{c}}, ~9/7 = 440.9149{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.7381{{c}}, ~9/7 = 440.9184{{c}} | |||
Badness ( | {{Optimal ET sequence|legend=0| 17, 19f, 22, 41, 46, 63, 87, 237, 283 }} | ||
Badness (Sintel): 1.12 | |||
== Sensawer == | == Sensawer == | ||
| Line 89: | Line 102: | ||
{{Mapping|legend=1| 1 0 0 0 -3 | 0 1 1 2 5 | 0 0 2 -1 -4 }} | {{Mapping|legend=1| 1 0 0 0 -3 | 0 1 1 2 5 | 0 0 2 -1 -4 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.1654{{c}}, ~3/2 = 703.2870{{c}}, ~9/7 = 441.1967{{c}} | |||
: [[error map]]: {{val| -0.033 +1.793 -0.755 -2.236 +0.048 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.2917{{c}}, ~9/7 = 441.1849{{c}} | |||
: error map: {{val| 0.000 +1.840 -0.683 -2.1554 +0.175 }} | |||
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.1900{{c}}, ~9/7 = 441.1359{{c}} --> | |||
{{Optimal ET sequence|legend=1| 14c, 19e, 27e, 41, 60e, 87 | {{Optimal ET sequence|legend=1| 14c, 19e, 27e, 41, 60e, 87 }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 0.957 | ||
=== 13-limit === | === 13-limit === | ||
| Line 101: | Line 119: | ||
Mapping: {{mapping| 1 0 0 0 -3 2 | 0 1 1 2 5 2 | 0 0 2 -1 -4 -4 }} | Mapping: {{mapping| 1 0 0 0 -3 2 | 0 1 1 2 5 2 | 0 0 2 -1 -4 -4 }} | ||
Optimal tunings: | |||
* WE: ~2 = 1199.9800{{c}}, ~3/2 = 703.4468{{c}}, ~9/7 = 441.3705{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.4494{{c}}, ~9/7 = 441.3758{{c}} | |||
{{Optimal ET sequence|legend=0| 14c, 19e, 27e, 41, 46, 60e, 68e, 87, 522bd }} | {{Optimal ET sequence|legend=0| 14c, 19e, 27e, 41, 46, 60e, 68e, 87, 522bd }} | ||
Badness ( | Badness (Sintel): 0.868 | ||
== Octarod == | == Octarod == | ||
| Line 113: | Line 135: | ||
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 2 0 | 0 0 2 -1 4 }} | {{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 2 0 | 0 0 2 -1 4 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199.2854{{c}}, ~3/2 = 704.6266{{c}}, ~9/7 = 439.2433{{c}} | |||
: [[error map]]: {{val| -0.715 +1.957 -3.915 -0.245 +4.226 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5246{{c}}, ~9/7 = 439.2798{{c}} | |||
: error map: {{val| 0.000 +2.570 -3.230 +0.944 +5.801 }} | |||
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.0464{{c}}, ~9/7 = 439.5050{{c}} --> | |||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 14c, 19, 22, 27e, 41, 90e, 131e }} * | ||
[[Badness]] ( | <nowiki/>[[optimal patent val]]: [[104edo|104]] | ||
[[Badness]] (Sintel): 0.698 | |||
Scales: [[octarod1]], [[octarod2]], [[octarod3]], [[octarod4]], [[octarod5]] | Scales: [[octarod1]], [[octarod2]], [[octarod3]], [[octarod4]], [[octarod5]] | ||
| Line 128: | Line 157: | ||
{{Mapping|legend=1| 1 0 0 0 -4 | 0 1 1 2 4 | 0 0 2 -1 3 }} | {{Mapping|legend=1| 1 0 0 0 -4 | 0 1 1 2 4 | 0 0 2 -1 3 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1198.9114{{c}}, ~3/2 = 705.7294{{c}}, ~9/7 = 441.7137{{c}} | |||
: [[error map]]: {{val| -1.089 +2.686 +1.754 -1.258 -3.259 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.8402{{c}}, ~9/7 = 442.1064{{c}} | |||
: error map: {{val| 0.000 +3.885 +3.739 +0.748 -1.638 }} | |||
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 706.3702{{c}}, ~9/7 = 442.1147{{c}} --> | |||
{{Optimal ET sequence|legend=1| 22, 46, 68, 95, 141bc, 163bc | {{Optimal ET sequence|legend=1| 19e, 22, 27e, 46, 68, 95, 141bc, 163bc }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 1.05 | ||
=== Shrusic === | === Shrusic === | ||
| Line 141: | Line 175: | ||
Mapping: {{mapping| 1 0 0 0 -4 1 | 0 1 1 2 4 1 | 0 0 2 -1 3 3 }} | Mapping: {{mapping| 1 0 0 0 -4 1 | 0 1 1 2 4 1 | 0 0 2 -1 3 3 }} | ||
{{Optimal ET sequence|legend=0| 22, 46 | Optimal tunings: | ||
* WE: ~2 = 1199.7256{{c}}, ~3/2 = 704.9071{{c}}, ~9/7 = 443.1303{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.9572{{c}}, ~9/7 = 443.2018{{c}} | |||
{{Optimal ET sequence|legend=0| 19e, 22, 27e, 46 }} | |||
Badness ( | Badness (Sintel): 1.05 | ||
== Bisector == | == Bisector == | ||
| Line 151: | Line 189: | ||
{{Mapping|legend=1| 2 0 0 0 3 | 0 1 1 2 1 | 0 0 2 -1 1 }} | {{Mapping|legend=1| 2 0 0 0 3 | 0 1 1 2 1 | 0 0 2 -1 1 }} | ||
: mapping generators: ~77/54, ~3, ~9/7 | : mapping generators: ~77/54, ~3, ~9/7 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 600.3096{{c}}, ~3/2 = 703.4512{{c}}, ~9/7 = 441.3336{{c}} | |||
: [[error map]]: {{val| +0.619 +2.115 +0.424 -2.019 -4.985 }} | |||
* [[CWE]]: ~2 = 600.0000{{c}}, ~3/2 = 703.5671{{c}}, ~9/7 = 441.2436{{c}} | |||
: error map: {{val| 0.000 +1.612 -0.259 -2.935 -6.507 }} | |||
<!-- * [[POTE]]: ~77/54 = 600.0000{{c}}, ~3/2 = 703.0884{{c}}, ~9/7 = 441.1060{{c}} --> | |||
{{Optimal ET sequence|legend=1| 22, 46, 68 | {{Optimal ET sequence|legend=1| 8d, 14c, 22, 38d, 46, 60e, 68, 106de, 128e, 174e }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 1.31 | ||
== Sensigh == | == Sensigh == | ||
| Line 166: | Line 208: | ||
Mapping: {{mapping| 1 6 8 11 0 10 | 0 -7 -9 -13 0 -10 | 0 0 0 0 1 0 }} | Mapping: {{mapping| 1 6 8 11 0 10 | 0 -7 -9 -13 0 -10 | 0 0 0 0 1 0 }} | ||
: mapping generators: ~2, ~9/7, ~11 | |||
: | Optimal tunings: | ||
* WE: ~2 = 1200.0000{{c}}, ~9/7 = 443.4379{{c}}, ~11/8 = 550.3462{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~9/7 = 443.3581{{c}}, ~11/8 = 550.7092{{c}} | |||
{{Optimal ET sequence|legend=0| | {{Optimal ET sequence|legend=0| 27e, 38df, 46, 111df }} | ||
Badness ( | Badness (Sintel): 0.878 | ||
=== 17-limit === | === 17-limit === | ||
| Line 180: | Line 225: | ||
Mapping: {{mapping| 1 6 8 11 0 10 0 | 0 -7 -9 -13 0 -10 1 | 0 0 0 0 1 0 1 }} | Mapping: {{mapping| 1 6 8 11 0 10 0 | 0 -7 -9 -13 0 -10 1 | 0 0 0 0 1 0 1 }} | ||
{{Optimal ET sequence|legend=0| | Optimal tunings: | ||
* WE: ~2 = 1200.2286{{c}}, ~9/7 = 443.4291{{c}}, ~11/8 = 549.2790{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~9/7 = 443.3707{{c}}, ~11/8 = 549.5775{{c}} | |||
{{Optimal ET sequence|legend=0| 27eg, 38df, 46 }} | |||
Badness (Sintel): 0.917 | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||