Very high accuracy temperaments: Difference between revisions
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Below are listed some very high accuracy temperaments ([[Tenney-Euclidean temperament measures|TE error]] < 0.005 cents/octave). | |||
=Rank two temperaments= | =Rank two temperaments= | ||
Revision as of 15:09, 15 January 2019
Below are listed some very high accuracy temperaments (TE error < 0.005 cents/octave).
Rank two temperaments
Astro
Comma: |91 -12 -31>
POTE generator: ~296630859375/274877906944 = 132.1947
Map: [<1 5 1|, <0 31 -12|]
EDOs: 118, 935, 1053, 1171, 1289, 1407, 2224, 2460
Badness: 0.0628
Whoosh
Comma: |37 25 -33>
POTE generator: ~864/625 = 560.5468
Map: [<1 -16 -11|, <0 33 25|]
EDOs: 289, 441, 730, 1171, 1612, 1901, 2631
Badness: 0.0257
Monzismic
Comma: |54 -37 2> = 450359962737049600 / 450283905890997363
POTE generator: ~387420489/335544320 = 249.0184
Map: [<1 0 -27|, <0 2 37|]
EDOs: 53, 506, 559, 612, 1783, 2954, 6520
Badness: 0.0104
Egads
Comma: |-36 -52 51>
POTE generator: ~6/5 = 315.6479
Map: [<1 15 16|, <0 -51 -52|]
EDOs: 441, 901, 1342, 1783, 2224, 3125, 4467, 4908
Badness: 0.0418
Fortune
Comma: |-107 47 14>
POTE generator: ~8388608/7381125 = 221.5679
Map: [<1 -1 11|, <0 14 -47|]
EDOs: 612, 1289, 1901, 2513, 3125, 3737, 4414, 5638
Badness: 0.0279
7-limit
Commas: 78125000/78121827, |-52 17 12 -1>
POTE generator: ~8388608/7381125 = 221.5680
Map: [<1 -1 11 63|, <0 14 -47 -326|]
EDOs: 612, 2513, 3125, 3737, 4349, 5638, 6862, 9987
Badness: 0.0237
11-limit
Commas: 151263/151250, 21437500/21434787, 369140625/369098752
POTE generator: ~8388608/7381125 = 221.5681
Map: [<1 -1 11 63 134|, <0 14 -47 -326 -707|]
EDOs: 612, 2513, 3125, 3737, 4349, 4961, 6862, 8086
Badness: 0.0366
Senior
Comma: |-17 62 -35>
POTE generator: ~94143178827/78125000000 = 322.8014
Map: [<1 11 19|, <0 -35 -62|]
EDOs: 171, 1171, 1342, 2513, 3684, 3855, 4855, 6197
Badness: 0.0212
Gross
Comma: |144 -22 -47>
POTE generator: ~1953125000000000/1853020188851841 = 91.5310
Map: [<1 -2 4|, <0 47 -22|]
EDOs: 118, 1783, 1901, 3684, 5467, 5585, 7250
Badness: 0.0463
Raider
Comma: |71 -99 37>
POTE generator: ~8000/6561 = 343.2961
Map: [<1 -9 -26|, <0 37 99|]
EDOs: 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355
Badness: 0.0129
Pirate
Comma: |-90 -15 49>
POTE generator: ~1358954496/1220703125 = 185.7542
Map: [<1 -6 0|, <0 49 15|]
EDOs: 730, 1783, 2513, 4296, 6079, 6809, 10375, 11105
Badness: 0.0057
Atomic
Comma: |161 -84 -12>
POTE generator: ~32805/32768 = 1.95516
Map: [<12 0 161|, <0 1 -7|]
EDOs: 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 3684, 4296, 4308, 4908, 7980, 12276, 16572, 20868, 25164, 29460, 33756, 46032
Badness: 0.0038
7-limit
Commas: 250047/250000, |-55 30 2 1>
POTE generator: ~32805/32768 = 1.94961
Map: [<12 0 161 338|, <0 1 -7 -16|]
EDOs: 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 4308
Badness: 0.0458
11-limit
Commas: 9801/9800, 151263/151250, 184549376/184528125
POTE generator: ~32805/32768 = 1.94799
Map: [<12 0 161 338 517|, <0 1 -7 -16 -25|]
EDOs: 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 4308
Badness: 0.0160
Rank three temperaments
171 & 1106 & 3566
Comma: 282475249000/282429536481
Map: [<1 0 9 -3|, <0 1 8 0|, <0 0 10 -3|]
EDOs: 171, 935, 1106, 1277, 2289, 2460, 3395, 3566, 3737
Badness: 0.000281
171 & 2019 & 3566
Comma: 13841287201/13839609375
Map: [<1 0 0 0|, <0 1 7 5|, <0 0 12 7|]
EDOs: 171, 1547, 1677, 1718, 1848, 2019, 3395, 3566, 3737
Badness: 0.000135
171 & 441 & 4973
Comma: |-7 19 -16 5> = 19534128475869/19531250000000
Map: [<1 0 3 11|, <0 1 4 9|, <0 0 5 16|]
EDOs: 171, 270, 441, 612, 783, 4802, 4973, 5144
Badness: 0.000297
171 & 1547 & 3125
Comma: 3955078125/3954653486
Map: [<1 3 0 1|, <0 11 0 4|, <0 0 1 1|]
EDOs: 171, 1407, 1547, 1578, 1718, 2783, 2954, 3125, 3296
Badness: 0.000114
Starscape
Comma: 645700815/645657712
Map: [<1 0 4 0|, <0 1 1 2|, <0 0 9 1|]
EDOs: 171, 1848, 2019, 2783, 2954, 3125, 3296, 4973, 5144
Badness: 0.000545
171 & 3566 & 4973
Comma: 6104007655641/6103515625000
Map: [<1 0 13 16|, <0 1 10 12|, <0 0 14 17|]
EDOs: 171, 1236, 1407, 3566, 3737, 3908, 4802, 4973, 8539, 8710
Badness: 0.000223
Euzenius
Comma: 78125000/78121827
Map: [<1 0 0 -5|, <0 2 0 -13|, <0 0 1 5|]
EDOs: 171, 441, 612, 2954, 3125, 3566, 3737, 6520, 6691
Badness: 0.000205
612 & 1848 & 3125
Comma: |-55 30 2 1>
Map: [<1 0 0 55|, <0 1 0 -30|, <0 0 1 -2|]
EDOs: 612, 665, 1236, 1277, 1848, 1889, 2460, 2513, 3125, 3737, 4973, 5585, 6862, 8098, 8710, 11835, 14960
Badness: 0.000366
171 & 1547 & 4973
Comma: |1 -15 -18 23>
Map: [<1 0 9 7|, <0 1 3 3|, <0 0 23 18|]
EDOs: 171, 1547, 4802, 4973, 5144, 6520, 6691, 6862, 11493, 11664, 11835, 18184, 18355, 18526, 25046, 30019, 30190, 48545
Badness: 0.000114
441 & 1848 & 3125
Comma: |51 -13 -1 -10>
Map: [<1 0 1 5|, <0 1 7 -2|, <0 0 10 -1|]
EDOs: 441, 1848, 3125, 3566, 4973, 6691, 8098, 8539, 9816, 11664, 14789, 15230, 18355, 21480, 30019, 33144, 39835, 51499
Badness: 0.000263