|
|
| (2 intermediate revisions by the same user not shown) |
| Line 167: |
Line 167: |
| == Keenanismic (385/384) == | | == Keenanismic (385/384) == |
| {{Main| Keenanismic family }} | | {{Main| Keenanismic family }} |
|
| |
| [[Subgroup]]: 2.3.5.7.11
| |
|
| |
| [[Comma list]]: [[385/384]]
| |
|
| |
| {{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 1 | 0 0 1 0 -1 | 0 0 0 1 -1 }}
| |
| : Mapping generators: ~2, ~3, ~5, ~7
| |
|
| |
| [[Optimal tuning]]s:
| |
| * [[WE]]: ~2 = 1200.4104{{c}}, ~3/2 = 701.6916{{c}}, ~5/4 = 385.1761{{c}}, ~7/4 = 967.5421{{c}}
| |
| : [[error map]]: {{val| +0.410 +0.147 -0.317 -0.463 -0.703 }}
| |
| * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6933{{c}}, ~5/4 = 385.1491{{c}}, ~7/4 = 967.3004{{c}}
| |
| : error map: {{val| 0.000 -0.262 -1.165 -1.525 -2.074 }}
| |
|
| |
| [[Minimax tuning]]:
| |
| * [[11-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 }}, ~3 = {{monzo| 0 1 0 0 0 }}, ~5 = {{monzo| 7/3 1/3 2/3 -1/3 -1/3 }}, ~7 = {{monzo| 7/3 1/3 -1/3 2/3 -1/3 }}
| |
| : [[eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.3.7/5.11/5
| |
|
| |
| {{Optimal ET sequence|legend=1| 9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de }}
| |
|
| |
| [[Badness]] (Sintel): 0.277
| |
|
| |
| === Martwin ===
| |
| [[Subgroup]]: 2.3.5.7.11.13
| |
|
| |
| [[Comma list]]: 325/324, 385/384
| |
|
| |
| {{Mapping|legend=1| 1 0 0 0 7 2 | 0 1 0 0 1 4 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 0 }}
| |
|
| |
| Lattice basis:
| |
| : 4/3 length = 1.0820, 6/5 length = 1.3935, 10/9 length = 1.6247
| |
|
| |
| [[Optimal tuning]]s:
| |
| * [[WE]]: ~2 = 1200.3494{{c}}, ~3/2 = 702.2131{{c}}, ~5/4 = 384.8666{{c}}, ~7/4 = 967.8487{{c}}
| |
| : [[error map]]: {{val| +0.349 +0.608 -0.748 -0.278 -0.422 -0.710 }}
| |
| * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1659{{c}}, ~5/4 = 384.8721{{c}}, ~7/4 = 967.6109{{c}}
| |
| : error map: {{val| 0.000 +0.211 -1.442 -1.215 -1.635 -1.608 }}
| |
|
| |
| [[Minimax tuning]]:
| |
| * [[13-odd-limit|13-]] and [[15-odd-limit]]: ~2 = {{val| 1 0 0 0 0 0 }}, ~3 = {{val| 0 1 0 0 0 0 }}, ~5 = {{val| 2/3 4/3 1/3 0 0 -1/3 }}, ~7 = {{val| 19/6 -1/6 -1/6 1/2 -1/2 1/6 }}
| |
| : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/7.13/5
| |
|
| |
| {{Optimal ET sequence|legend=1| 12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff }}
| |
|
| |
| [[Badness]] (Sintel): 0.579
| |
|
| |
| === Ancient ===
| |
| [[Subgroup]]: 2.3.5.7.11.13
| |
|
| |
| [[Comma list]]: 385/384, 625/624
| |
|
| |
| {{Mapping|legend=1| 1 0 0 0 7 -4 | 0 1 0 0 1 -1 | 0 0 1 0 -1 4 | 0 0 0 1 -1 0 }}
| |
|
| |
| [[Optimal tuning]]s:
| |
| * [[WE]]: ~2 = 1200.4130{{c}}, ~3/2 = 701.6863{{c}}, ~5/4 = 385.2319{{c}}, ~7/4 = 967.5188{{c}}
| |
| : [[error map]]: {{val| +0.413 +0.144 -0.256 -0.481 -0.730 -0.047 }}
| |
| * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6838{{c}}, ~5/4 = 385.2497{{c}}, ~7/4 = 967.2556{{c}}
| |
| : error map: {{val| 0.000 -0.271 -1.064 -1.570 -2.139 -1.213 }}
| |
|
| |
| {{Optimal ET sequence|legend=1| 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def }}
| |
|
| |
| [[Badness]] (Sintel): 0.675
| |
|
| |
|
| === Commas 351/350, 385/384 === | | === Commas 351/350, 385/384 === |
| Line 246: |
Line 184: |
|
| |
|
| [[Badness]] (Sintel): 0.781 | | [[Badness]] (Sintel): 0.781 |
|
| |
| === Zaxa ===
| |
| [[Subgroup]]: 2.3.5.7.11.13
| |
|
| |
| [[Comma list]]: 352/351, 385/384
| |
|
| |
| {{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 1 -2 | 0 0 1 0 -1 -1 | 0 0 0 1 -1 -1 }}
| |
|
| |
| [[Optimal tuning]]s:
| |
| * [[WE]]: ~2 = 1200.1117{{c}}, ~3/2 = 702.6588{{c}}, ~5/4 = 385.6821{{c}}, ~7/4 = 968.0061{{c}}
| |
| : [[error map]]: {{val| +0.112 +0.815 -0.408 -0.596 -1.901 +1.137 }}
| |
| * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.6029{{c}}, ~5/4 = 385.6441{{c}}, ~7/4 = 967.9030{{c}}
| |
| : error map: {{val| 0.000 +0.648 -0.670 -0.923 -2.262 +0.720 }}
| |
|
| |
| {{Optimal ET sequence|legend=1| 22, 31, 41, 46, 53, 77, 87, 118, 140, 258e, 461e }}
| |
|
| |
| [[Badness]] (Sintel): 0.880
| |
|
| |
|
| === Commas 364/363, 385/384 === | | === Commas 364/363, 385/384 === |
| Line 407: |
Line 328: |
| Comma list: 273/272, 441/440, 561/560 | | Comma list: 273/272, 441/440, 561/560 |
|
| |
|
| Mapping: {{mapping| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }}
| | {{Mapping|legend=0| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }} |
|
| |
|
| Optimal tunings: | | Optimal tunings: |
| Line 633: |
Line 554: |
|
| |
|
| == Vishdelismic (5632/5625) == | | == Vishdelismic (5632/5625) == |
| | Vishdelismic tempers out 5632/5625, the [[vishdelisma]], and adds to [[vishdelic]] an independent generator for prime 7. From 5632/5625 = ([[176/175]])/([[225/224]]), vishdelismic has the feature of making [[14/9]], [[25/16]], and [[11/7]] equidistant. |
| | |
| [[Subgroup]]: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
|
| |
|
| Line 911: |
Line 834: |
| Comma list: 1216/1215, 1540/1539, 2080/2079 | | Comma list: 1216/1215, 1540/1539, 2080/2079 |
|
| |
|
| Mapping: {{mapping| 1 0 0 0 -8 -13 -6 | 0 1 0 0 9 12 5 | 0 0 1 0 0 -1 1 | 0 0 0 1 -1 0 0 }}
| | {{Mapping|legend=0| 1 0 0 0 -8 -13 -6 | 0 1 0 0 9 12 5 | 0 0 1 0 0 -1 1 | 0 0 0 1 -1 0 0 }} |
|
| |
|
| Optimal tunings: | | Optimal tunings: |
| Line 1,022: |
Line 945: |
| Comma list: 2080/2079, 3510/3509, 4096/4095 | | Comma list: 2080/2079, 3510/3509, 4096/4095 |
|
| |
|
| Mapping: {{mapping| 1 0 0 0 17 12 -21 | 0 1 0 0 -5 -2 11 | 0 0 1 0 0 -1 0 | 0 0 0 1 -2 -1 3 }}
| | {{Mapping|legend=0| 1 0 0 0 17 12 -21 | 0 1 0 0 -5 -2 11 | 0 0 1 0 0 -1 0 | 0 0 0 1 -2 -1 3 }} |
|
| |
|
| Optimal tunings: | | Optimal tunings: |
| Line 1,041: |
Line 964: |
| Comma list: 2080/2079, 3250/3249, 4096/4095 | | Comma list: 2080/2079, 3250/3249, 4096/4095 |
|
| |
|
| Mapping: {{mapping| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}
| | {{Mapping|legend=0| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }} |
|
| |
|
| Optimal tunings: | | Optimal tunings: |
| Line 1,058: |
Line 981: |
| Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095 | | Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095 |
|
| |
|
| Mapping: {{mapping| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}
| | {{Mapping|legend=0| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }} |
|
| |
|
| Optimal tunings: | | Optimal tunings: |
| Line 1,077: |
Line 1,000: |
| Comma list: 2080/2079, 4096/4095, 35000/34969 | | Comma list: 2080/2079, 4096/4095, 35000/34969 |
|
| |
|
| Mapping: {{mapping| 1 0 0 1 15 11 -13 | 0 1 0 0 -5 -2 5 | 0 0 1 0 0 -1 2 | 0 0 0 2 -4 -2 5 }}
| | {{Mapping|legend=0| 1 0 0 1 15 11 -13 | 0 1 0 0 -5 -2 5 | 0 0 1 0 0 -1 2 | 0 0 0 2 -4 -2 5 }} |
| : mapping generators: ~2, ~3, ~5, ~187/100 | | : mapping generators: ~2, ~3, ~5, ~187/100 |
|
| |
|
| Line 1,095: |
Line 1,018: |
| Comma list: 2080/2079, 3250/3249, 4096/4095, 4200/4199 | | Comma list: 2080/2079, 3250/3249, 4096/4095, 4200/4199 |
|
| |
|
| Mapping: {{mapping| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}
| | {{Mapping|legend=0| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }} |
|
| |
|
| Optimal tunings: | | Optimal tunings: |
| Line 1,112: |
Line 1,035: |
| Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095, 4200/4199 | | Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095, 4200/4199 |
|
| |
|
| Mapping: {{mapping| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}
| | {{Mapping|legend=0| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }} |
|
| |
|
| Optimal tunings: | | Optimal tunings: |
| Line 1,202: |
Line 1,125: |
| Comma list: 352/351, 715/714, 155771/155520 | | Comma list: 352/351, 715/714, 155771/155520 |
|
| |
|
| Mapping: {{mapping| 1 0 -6 0 1 6 0 | 0 1 3 0 2 -1 3 | 0 0 5 0 -1 -1 3 | 0 0 0 1 0 0 -1 }}
| | {{Mapping|legend=0| 1 0 -6 0 1 6 0 | 0 1 3 0 2 -1 3 | 0 0 5 0 -1 -1 3 | 0 0 0 1 0 0 -1 }} |
|
| |
|
| Optimal tunings: | | Optimal tunings: |
| Line 1,217: |
Line 1,140: |
| Comma list: 352/351, 715/714, 1463/1458, 2057/2052 | | Comma list: 352/351, 715/714, 1463/1458, 2057/2052 |
|
| |
|
| Mapping: {{mapping| 1 0 -6 0 1 6 0 0 | 0 1 3 0 2 -1 3 4 | 0 0 5 0 -1 -1 3 1 | 0 0 0 1 0 0 -1 -1 }}
| | {{Mapping|legend=0| 1 0 -6 0 1 6 0 0 | 0 1 3 0 2 -1 3 4 | 0 0 5 0 -1 -1 3 1 | 0 0 0 1 0 0 -1 -1 }} |
|
| |
|
| Optimal tunings: | | Optimal tunings: |
| Line 1,250: |
Line 1,173: |
| Comma list: 676/675, 6656/6655 | | Comma list: 676/675, 6656/6655 |
|
| |
|
| Mapping: {{mapping| 3 0 0 0 8 -3 | 0 2 0 0 1 3 | 0 0 1 0 0 1 | 0 0 0 1 0 0 }}
| | {{Mapping|legend=0| 3 0 0 0 8 -3 | 0 2 0 0 1 3 | 0 0 1 0 0 1 | 0 0 0 1 0 0 }} |
|
| |
|
| Optimal tunings: | | Optimal tunings: |