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114 7-limit temperaments   Message List  
Reply | Forward Message #9048 of 17519 |
The true top 32 in log-flat?

I re-ranked Gene's top 64 using L_1 and got the following top 32.
Anything missing?

1.
> Ennealimmal
>
> [18, 27, 18, 1, -22, -34] [[9, 15, 22, 26], [0, -2, -3, -2]]
> TOP tuning [1200.036377, 1902.012656, 2786.350297, 3368.723784]
> TOP generators [133.3373752, 49.02398564]
> bad: 4.918774 comp: 11.628267 err: .036377

39.8287 -> bad = 57.7058

2.
> Meantone (Huygens)
>
> [1, 4, 10, 4, 13, 12] [[1, 2, 4, 7], [0, -1, -4, -10]]
> TOP tuning [1201.698521, 1899.262909, 2790.257556, 3370.548328]
> TOP generators [1201.698520, 504.1341314]
> bad: 21.551439 comp: 3.562072 err: 1.698521

11.7652 -> bad = 235.1092

3.
> Miracle
>
> [6, -7, -2, -25, -20, 15] [[1, 1, 3, 3], [0, 6, -7, -2]]
> TOP tuning [1200.631014, 1900.954868, 2784.848544, 3368.451756]
> TOP generators [1200.631014, 116.7206423]
> bad: 29.119472 comp: 6.793166 err: .631014

21.1019 --> bad = 280.9843

4.
> Hemiwuerschmidt
>
> [16, 2, 5, -34, -37, 6] [[1, -1, 2, 2], [0, 16, 2, 5]]
> TOP tuning [1199.692003, 1901.466838, 2787.028860, 3368.496143]
> TOP generators [1199.692003, 193.8224275]
> bad: 31.386908 comp: 10.094876 err: .307997

31.212 -> bad = 300.04

5.
> Dominant Seventh
>
> [1, 4, -2, 4, -6, -16] [[1, 2, 4, 2], [0, -1, -4, 2]]
> TOP tuning [1195.228951, 1894.576888, 2797.391744, 3382.219933]
> TOP generators [1195.228951, 495.8810151]
> bad: 28.744957 comp: 2.454561 err: 4.771049

7.9560 -> bad = 301.9952

6.
> Blackwood
>
> [0, 5, 0, 8, 0, -14] [[5, 8, 12, 14], [0, 0, -1, 0]]
> TOP tuning [1195.893464, 1913.429542, 2786.313713, 3348.501698]
> TOP generators [239.1786927, 83.83059859]
> bad: 34.210608 comp: 2.173813 err: 7.239629

6.4749 -> bad = 303.52

7.
> Magic
>
> [5, 1, 12, -10, 5, 25] [[1, 0, 2, -1], [0, 5, 1, 12]]
> TOP tuning [1201.276744, 1903.978592, 2783.349206, 3368.271877]
> TOP generators [1201.276744, 380.7957184]
> bad: 23.327687 comp: 4.274486 err: 1.276744

15.5360 -> bad = 308.1642

8.
> Beep
>
> [2, 3, 1, 0, -4, -6] [[1, 2, 3, 3], [0, -2, -3, -1]]
> TOP tuning [1194.642673, 1879.486406, 2819.229610, 3329.028548]
> TOP generators [1194.642673, 254.8994697]
> bad: 23.664749 comp: 1.292030 err: 14.176105

4.7295 -> bad = 317.0935

9.
> Pajara
>
> [2, -4, -4, -11, -12, 2] [[2, 3, 5, 6], [0, 1, -2, -2]]
> TOP tuning [1196.893422, 1901.906680, 2779.100462, 3377.547174]
> TOP generators [598.4467109, 106.5665459]
> bad: 27.754421 comp: 2.988993 err: 3.106578

10.4021 -> bad = 336.1437

10.
> Semisixths
>
> [7, 9, 13, -2, 1, 5] [[1, -1, -1, -2], [0, 7, 9, 13]]
> TOP tuning [1198.389531, 1903.732520, 2790.053107, 3364.304748]
> TOP generators [1198.389531, 443.1602931]
> bad: 34.533812 comp: 4.630693 err: 1.610469

14.459 -> bad = 336.67

11.
> Catakleismic
>
> [6, 5, 22, -6, 18, 37] [[1, 0, 1, -3], [0, 6, 5, 22]]
> TOP tuning [1200.536356, 1901.438376, 2785.068335, 3370.331646]
> TOP generators [1200.536355, 316.9063960]
> bad: 32.938503 comp: 7.836558 err: .536356

25.127 -> bad = 338.65

12.
> Diminished
>
> [4, 4, 4, -3, -5, -2] [[4, 6, 9, 11], [0, 1, 1, 1]]
> TOP tuning [1194.128460, 1892.648830, 2788.245174, 3385.309404]
> TOP generators [298.5321149, 101.4561401]
> bad: 37.396767 comp: 2.523719 err: 5.871540

7.917 -> bad = 368.02

13.
> Schismic
>
> [1, -8, -14, -15, -25, -10] [[1, 2, -1, -3], [0, -1, 8, 14]]
> TOP tuning [1200.760625, 1903.401919, 2784.194017, 3371.388750]
> TOP generators [1200.760624, 498.1193303]
> bad: 28.818558 comp: 5.618543 err: .912904

20.2918 --> bad = 375.8947

14.
> Orwell
>
> [7, -3, 8, -21, -7, 27] [[1, 0, 3, 1], [0, 7, -3, 8]]
> TOP tuning [1199.532657, 1900.455530, 2784.117029, 3371.481834]
> TOP generators [1199.532657, 271.4936472]
> bad: 30.805067 comp: 5.706260 err: .946061

19.9797 -> bad = 377.6573

15.
> Hemififths
>
> [2, 25, 13, 35, 15, -40] [[1, 1, -5, -1], [0, 2, 25, 13]]
> TOP tuning [1199.700353, 1902.429930, 2785.617954, 3368.041901]
> TOP generators [1199.700353, 351.3647888]
> bad: 34.737019 comp: 10.766914 err: .299647

35.677 -> bad = 381.41

16.
> Father
>
> [1, -1, 3, -4, 2, 10] [[1, 2, 2, 4], [0, -1, 1, -3]]
> TOP tuning [1185.869125, 1924.351908, 2819.124589, 3401.317477]
> TOP generators [1185.869125, 447.3863410]
> bad: 33.256527 comp: 1.534101 err: 14.130876

5.2007 -> bad = 382.2

17.
> Amity
>
> [5, 13, -17, 9, -41, -76] [[1, 3, 6, -2], [0, -5, -13, 17]]
> TOP tuning [1199.723894, 1902.392618, 2786.717797, 3369.601033]
> TOP generators [1199.723894, 339.3558130]
> bad: 37.532790 comp: 11.659166 err: .276106

38.128 -> bad = 401.39

18.
> Augmented
>
> [3, 0, 6, -7, 1, 14] [[3, 5, 7, 9], [0, -1, 0, -2]]
> TOP tuning [1199.976630, 1892.649878, 2799.945472, 3385.307546]
> TOP generators [399.9922103, 107.3111730]
> bad: 27.081145 comp: 2.147741 err: 5.870879

8.3046 -> bad = 404.8933

19.
> Parakleismic
>
> [13, 14, 35, -8, 19, 42] [[1, 5, 6, 12], [0, -13, -14, -35]]
> TOP tuning [1199.738066, 1902.291445, 2786.921905, 3368.090564]
> TOP generators [1199.738066, 315.1076065]
> bad: 40.713036 comp: 12.467252 err: .261934

39.586 -> bad = 410.46

20.
> Tripletone
>
> [3, 0, -6, -7, -18, -14] [[3, 5, 7, 8], [0, -1, 0, 2]]
> TOP tuning [1197.060039, 1902.640406, 2793.140092, 3377.079420]
> TOP generators [399.0200131, 92.45965769]
> bad: 48.112067 comp: 4.045351 err: 2.939961

12.125 -> bad = 432.24

21.
> {21/20, 28/27}
>
> [1, 4, 3, 4, 2, -4] [[1, 2, 4, 4], [0, -1, -4, -3]]
> TOP tuning [1214.253642, 1919.106053, 2819.409644, 3328.810876]
> TOP generators [1214.253642, 509.4012304]
> bad: 42.300772 comp: 1.722706 err: 14.253642

5.5723 -> bad = 442.58

22.
> Decimal
>
> [4, 2, 2, -6, -8, -1] [[2, 4, 5, 6], [0, -2, -1, -1]]
> TOP tuning [1207.657798, 1914.092323, 2768.532858, 3372.361757]
> TOP generators [603.8288989, 250.6116362]
> bad: 48.773723 comp: 2.523719 err: 7.657798

7.6792 -> bad = 451.58

23.
> Hemifourths
>
> [2, 8, 1, 8, -4, -20] [[1, 2, 4, 3], [0, -2, -8, -1]]
> TOP tuning [1203.668842, 1902.376967, 2794.832500, 3358.526166]
> TOP generators [1203.668841, 252.4803582]
> bad: 43.552336 comp: 3.445412 err: 3.668842

11.204 -> bad = 460.59

24.
> Negri
>
> [4, -3, 2, -14, -8, 13] [[1, 2, 2, 3], [0, -4, 3, -2]]
> TOP tuning [1203.187308, 1907.006766, 2780.900506, 3359.878000]
> TOP generators [1203.187309, 124.8419629]
> bad: 46.125886 comp: 3.804173 err: 3.187309

12.125 -> bad = 468.55

25.
> Nonkleismic
>
> [10, 9, 7, -9, -17, -9] [[1, -1, 0, 1], [0, 10, 9, 7]]
> TOP tuning [1198.828458, 1900.098151, 2789.033948, 3368.077085]
> TOP generators [1198.828458, 309.8926610]
> bad: 46.635848 comp: 6.309298 err: 1.171542

20.326 -> bad = 484

26.
> Kleismic
>
> [6, 5, 3, -6, -12, -7] [[1, 0, 1, 2], [0, 6, 5, 3]]
> TOP tuning [1203.187308, 1907.006766, 2792.359613, 3359.878000]
> TOP generators [1203.187309, 317.8344609]
> bad: 45.676063 comp: 3.785579 err: 3.187309

12.409 -> bad = 490.77

27.
> Dicot
>
> [2, 1, 6, -3, 4, 11] [[1, 1, 2, 1], [0, 2, 1, 6]]
> TOP tuning [1204.048158, 1916.847810, 2764.496143, 3342.447113]
> TOP generators [1204.048159, 356.3998255]
> bad: 42.920570 comp: 2.137243 err: 9.396316

7.2314 -> bad = 491.37

28.
> Superpythagorean
>
> [1, 9, -2, 12, -6, -30] [[1, 2, 6, 2], [0, -1, -9, 2]]
> TOP tuning [1197.596121, 1905.765059, 2780.732078, 3374.046608]
> TOP generators [1197.596121, 489.4271829]
> bad: 50.917015 comp: 4.602303 err: 2.403879

14.431 -> bad = 500.61

29.
> Injera
>
> [2, 8, 8, 8, 7, -4] [[2, 3, 4, 5], [0, 1, 4, 4]]
> TOP tuning [1201.777814, 1896.276546, 2777.994928, 3378.883835]
> TOP generators [600.8889070, 93.60982493]
> bad: 42.529834 comp: 3.445412 err: 3.582707

11.918 -> bad = 508.85

30.
> {25/24, 81/80} Jamesbond?
>
> [0, 0, 7, 0, 11, 16] [[7, 11, 16, 20], [0, 0, 0, -1]]
> TOP tuning [1209.431411, 1900.535075, 2764.414655, 3368.825906]
> TOP generators [172.7759159, 86.69241190]
> bad: 58.637859 comp: 2.493450 err: 9.431411

7.4202 -> bad = 519.28

31.
> Quartaminorthirds
>
> [9, 5, -3, -13, -30, -21] [[1, 1, 2, 3], [0, 9, 5, -3]]
> TOP tuning [1199.792743, 1900.291122, 2788.751252, 3365.878770]
> TOP generators [1199.792743, 77.83315314]
> bad: 47.721352 comp: 6.742251 err: 1.049791

22.397 -> bad = 526.59

32.
> Pelogic
>
> [1, -3, -4, -7, -9, -1] [[1, 2, 1, 1], [0, -1, 3, 4]]
> TOP tuning [1209.734056, 1886.526887, 2808.557731, 3341.498957]
> TOP generators [1209.734056, 532.9412251]
> bad: 39.824125 comp: 2.022675 err: 9.734056

7.426 -> bad = 536.78






**********************************************************************














> Number 43
>
> [6, 10, 10, 2, -1, -5] [[2, 4, 6, 7], [0, -3, -5, -5]]
> TOP tuning [1196.893422, 1906.838962, 2779.100462, 3377.547174]
> TOP generators [598.4467109, 162.3159606]
> bad: 57.621529 comp: 4.306766 err: 3.106578

13.19 -> bad = 540.44

> Number 36 Supersupermajor
>
> [3, 17, -1, 20, -10, -50] [[1, 1, -1, 3], [0, 3, 17, -1]]
> TOP tuning [1200.231588, 1903.372996, 2784.236389, 3366.314293]
> TOP generators [1200.231587, 234.3804692]
> bad: 52.638504 comp: 7.670504 err: .894655

24.923 -> bad = 555.72

> Number 47
>
> [12, 34, 20, 26, -2, -49] [[2, 4, 7, 7], [0, -6, -17, -10]]
> TOP tuning [1200.284965, 1901.503343, 2786.975381, 3369.219732]
> TOP generators [600.1424823, 83.17776441]
> bad: 61.101493 comp: 14.643003 err: .284965

44.37 -> bad = 561

> Number 46 Hemithirds
>
> [15, -2, -5, -38, -50, -6] [[1, 4, 2, 2], [0, -15, 2, 5]]
> TOP tuning [1200.363229, 1901.194685, 2787.427555, 3367.479202]
> TOP generators [1200.363229, 193.3505488]
> bad: 60.573479 comp: 11.237086 err: .479706

34.589 -> bad = 573.94

> Number 44 Octacot
>
> [8, 18, 11, 10, -5, -25] [[1, 1, 1, 2], [0, 8, 18, 11]]
> TOP tuning [1199.031259, 1903.490418, 2784.064367, 3366.693863]
> TOP generators [1199.031259, 88.05739491]
> bad: 58.217715 comp: 7.752178 err: .968741

24.394 -> bad = 576.47

> Number 35 Supermajor seconds
>
> [3, 12, -1, 12, -10, -36] [[1, 1, 0, 3], [0, 3, 12, -1]]
> TOP tuning [1201.698521, 1899.262909, 2790.257556, 3372.574099]
> TOP generators [1201.698520, 232.5214630]
> bad: 51.806440 comp: 5.522763 err: 1.698521

18.448 -> bad = 578.06

> Number 25 Waage? Compton? Duodecimal?
>
> [0, 12, 24, 19, 38, 22] [[12, 19, 28, 34], [0, 0, -1, -2]]
> TOP tuning [1200.617051, 1900.976998, 2785.844725, 3370.558188]
> TOP generators [100.0514209, 16.55882096]
> bad: 45.097159 comp: 8.548972 err: .617051

30.795 -> bad = 585.17

> Number 55
>
> [0, 0, 12, 0, 19, 28] [[12, 19, 28, 34], [0, 0, 0, -1]]
> TOP tuning [1197.674070, 1896.317278, 2794.572829, 3368.825906]
> TOP generators [99.80617249, 24.58395811]
> bad: 65.630949 comp: 4.295482 err: 3.557008

12.84 -> bad = 586.43

> Number 48 Flattone
>
> [1, 4, -9, 4, -17, -32] [[1, 2, 4, -1], [0, -1, -4, 9]]
> TOP tuning [1202.536420, 1897.934872, 2781.593812, 3361.705278]
> TOP generators [1202.536419, 507.1379663]
> bad: 61.126418 comp: 4.909123 err: 2.536420

15.376 -> bad = 599.67

> Number 38 {3136/3125, 5120/5103} Misty
>
> [3, -12, -30, -26, -56, -36] [[3, 5, 6, 6], [0, -1, 4, 10]]
> TOP tuning [1199.661465, 1902.491566, 2787.099767, 3368.765021]
> TOP generators [399.8871550, 96.94420930]
> bad: 53.622498 comp: 12.585536 err: .338535

42.92 -> bad = 623.63

> Number 41 {28/27, 50/49}
>
> [2, 6, 6, 5, 4, -3] [[2, 3, 4, 5], [0, 1, 3, 3]]
> TOP tuning [1191.599639, 1915.269258, 2766.808679, 3362.608498]
> TOP generators [595.7998193, 127.8698005]
> bad: 56.092257 comp: 2.584059 err: 8.400361

8.701 -> bad = 635.97

> Number 63
>
> [8, 13, 23, 2, 14, 17] [[1, 2, 3, 4], [0, -8, -13, -23]]
> TOP tuning [1198.975478, 1900.576277, 2788.692580, 3365.949709]
> TOP generators [1198.975478, 62.17183489]
> bad: 68.767371 comp: 8.192765 err: 1.024522

25.137 -> bad = 647.35

> Number 49 Diaschismic
>
> [2, -4, -16, -11, -31, -26] [[2, 3, 5, 7], [0, 1, -2, -8]]
> TOP tuning [1198.732403, 1901.885616, 2789.256983, 3365.267311]
> TOP generators [599.3662015, 103.7870123]
> bad: 61.527901 comp: 6.966993 err: 1.267597

22.629 -> bad = 649.07

> Number 57
>
> [2, -2, 1, -8, -4, 8] [[1, 2, 2, 3], [0, -2, 2, -1]]
> TOP tuning [1185.869125, 1924.351909, 2819.124589, 3333.914203]
> TOP generators [1185.869125, 223.6931705]
> bad: 66.774944 comp: 2.173813 err: 14.130876

6.7795 -> bad = 649.47

> Number 59
>
> [3, 5, 9, 1, 6, 7] [[1, 2, 3, 4], [0, -3, -5, -9]]
> TOP tuning [1193.415676, 1912.390908, 2789.512955, 3350.341372]
> TOP generators [1193.415676, 158.1468146]
> bad: 67.670842 comp: 3.205865 err: 6.584324

9.9461 -> bad = 651.35

> Number 56
>
> [2, 1, -4, -3, -12, -12] [[1, 1, 2, 4], [0, 2, 1, -4]]
> TOP tuning [1204.567524, 1916.451342, 2765.076958, 3394.502460]
> TOP generators [1204.567524, 355.9419091]
> bad: 66.522610 comp: 2.696901 err: 9.146173

8.4704 -> bad = 656.21

> Number 26 Wizard
>
> [12, -2, 20, -31, -2, 52] [[2, 1, 5, 2], [0, 6, -1, 10]]
> TOP tuning [1200.639571, 1900.941305, 2784.828674, 3368.342104]
> TOP generators [600.3197857, 216.7702531]
> bad: 45.381303 comp: 8.423526 err: .639571

32.407 -> bad = 671.69

> Number 37 {6144/6125, 10976/10935} Hendecatonic?
>
> [11, -11, 22, -43, 4, 82] [[11, 17, 26, 30], [0, 1, -1, 2]]
> TOP tuning [1199.662182, 1902.490429, 2787.098101, 3368.740066]
> TOP generators [109.0601984, 48.46705632]
> bad: 53.458690 comp: 12.579627 err: .337818

44.677 -> bad = 674.3

> Number 42 Porcupine
>
> [3, 5, -6, 1, -18, -28] [[1, 2, 3, 2], [0, -3, -5, 6]]
> TOP tuning [1196.905961, 1906.858938, 2779.129576, 3367.717888]
> TOP generators [1196.905960, 162.3176609]
> bad: 57.088650 comp: 4.295482 err: 3.094040

14.796 -> bad = 677.35

> Number 33 {1029/1024, 4375/4374}
>
> [12, 22, -4, 7, -40, -71] [[2, 5, 8, 5], [0, -6, -11, 2]]
> TOP tuning [1200.421488, 1901.286959, 2785.446889, 3367.642640]
> TOP generators [600.2107440, 183.2944602]
> bad: 50.004574 comp: 10.892116 err: .421488

40.255 -> bad = 683

> Number 39 {1728/1715, 4000/3993}
>
> [11, 18, 5, 3, -23, -39] [[1, 2, 3, 3], [0, -11, -18, -5]]
> TOP tuning [1199.083445, 1901.293958, 2784.185538, 3371.399002]
> TOP generators [1199.083445, 45.17026643]
> bad: 55.081549 comp: 7.752178 err: .916555

28.441 -> bad = 741.38

> Number 62
>
> [2, -2, -2, -8, -9, 1] [[2, 3, 5, 6], [0, 1, -1, -1]]
> TOP tuning [1185.468457, 1924.986952, 2816.886876, 3409.621105]
> TOP generators [592.7342285, 146.7842660]
> bad: 68.668284 comp: 2.173813 err: 14.531543

7.1855 -> bad = 750.29

> Number 40 {36/35, 160/147} Hystrix?
>
> [3, 5, 1, 1, -7, -12] [[1, 2, 3, 3], [0, -3, -5, -1]]
> TOP tuning [1187.933715, 1892.564743, 2758.296667, 3402.700250]
> TOP generators [1187.933715, 161.1008955]
> bad: 55.952057 comp: 2.153383 err: 12.066285

8.0882 -> bad = 789.37

> Number 61 Hemikleismic
>
> [12, 10, -9, -12, -48, -49] [[1, 0, 1, 4], [0, 12, 10, -9]]
> TOP tuning [1199.411231, 1902.888178, 2785.151380, 3370.478790]
> TOP generators [1199.411231, 158.5740148]
> bad: 68.516458 comp: 10.787602 err: .588769

36.649 -> bad = 790.81

> Number 52 Tritonic
>
> [5, -11, -12, -29, -33, 3] [[1, 4, -3, -3], [0, -5, 11, 12]]
> TOP tuning [1201.023211, 1900.333250, 2785.201472, 3365.953391]
> TOP generators [1201.023211, 580.7519186]
> bad: 63.536850 comp: 7.880073 err: 1.023211

27.923 -> bad = 797.81

> Number 50 Superkleismic
>
> [9, 10, -3, -5, -30, -35] [[1, 4, 5, 2], [0, -9, -10, 3]]
> TOP tuning [1201.371917, 1904.129438, 2783.128219, 3369.863245]
> TOP generators [1201.371918, 322.3731369]
> bad: 62.364585 comp: 6.742251 err: 1.371918

24.524 -> bad = 825.11

> Number 54
>
> [6, 10, 3, 2, -12, -21] [[1, 2, 3, 3], [0, -6, -10, -3]]
> TOP tuning [1202.659696, 1907.471368, 2778.232381, 3359.055076]
> TOP generators [1202.659696, 82.97467050]
> bad: 64.556006 comp: 4.306766 err: 3.480440

15.623 -> bad = 849.49

> Number 53
>
> [1, 33, 27, 50, 40, -30] [[1, 2, 16, 14], [0, -1, -33, -27]]
> TOP tuning [1199.680495, 1902.108988, 2785.571846, 3369.722869]
> TOP generators [1199.680495, 497.2520023]
> bad: 64.536886 comp: 14.212326 err: .319505

51.639 -> bad = 851.99

> Number 51
>
> [8, 1, 18, -17, 6, 39] [[1, -1, 2, -3], [0, 8, 1, 18]]
> TOP tuning [1201.135544, 1899.537544, 2789.855225, 3373.107814]
> TOP generators [1201.135545, 387.5841360]
> bad: 62.703297 comp: 6.411729 err: 1.525246

23.841 -> bad = 866.91

> Number 60
>
> [3, 0, 9, -7, 6, 21] [[3, 5, 7, 9], [0, -1, 0, -3]]
> TOP tuning [1193.415676, 1912.390908, 2784.636577, 3350.341372]
> TOP generators [397.8052253, 76.63521863]
> bad: 68.337269 comp: 3.221612 err: 6.584324

11.571 -> bad = 881.53

> Number 64
>
> [3, -7, -8, -18, -21, 1] [[1, 3, -1, -1], [0, -3, 7, 8]]
> TOP tuning [1202.900537, 1897.357759, 2790.235118, 3360.683070]
> TOP generators [1202.900537, 570.4479508]
> bad: 69.388565 comp: 4.891080 err: 2.900537

17.521 -> bad = 890.45

> Number 58
>
> [5, 8, 2, 1, -11, -18] [[1, 2, 3, 3], [0, -5, -8, -2]]
> TOP tuning [1194.335372, 1892.976778, 2789.895770, 3384.728528]
> TOP generators [1194.335372, 99.13879319]
> bad: 67.244049 comp: 3.445412 err: 5.664628

12.818 -> bad = 930.67




Sat Jan 31, 2004 7:23 pm

paulerlich
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If someone could help explain this, and/or generalize it to higher dimensions, I'd be thrilled . . . pleeeeeeeeeeeease? Also would like to understand the...
Paul Erlich
paulerlich
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May 25, 2004
6:19 pm

I re-ranked Gene's top 64 using L_1 and got the following top 32. Anything missing? 1. ... 39.8287 -> bad = 57.7058 2. ... 11.7652 -> bad = 235.1092 3. ... ...
Paul Erlich
paulerlich
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Jan 31, 2004
7:23 pm

There's something VERY CREEPY about my complexity values. I'm going to have to accept this as *the* correct scaling for complexity (I'm already convinced this...
Paul Erlich
paulerlich
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Feb 1, 2004
4:41 am

Sorry I skipped this: 4. ... 31.212 -> bad = 300.04 31.212 --> 31 -? 31-note proper MOS ... norm,...
Paul Erlich
paulerlich
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Feb 1, 2004
4:50 am

... Woah! Yes....
Dave Keenan
dkeenanuqnetau
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Feb 1, 2004
5:32 am

... going ... (I'm ... norm, ... So when I explained this as the number of notes in the bivector, I must have been onto something. It's interesting how the...
Paul Erlich
paulerlich
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Feb 1, 2004
5:58 am

... seem ... Except Blackjack . . ....
Paul Erlich
paulerlich
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Feb 1, 2004
6:19 am

... Wow dude. What sort of DES are these? Not the smallest apparently. -Carl...
Carl Lumma
clumma
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Feb 1, 2004
1:30 pm

... So how are these generators being chosen? Hermite? I confess I don't know how to 'refactor' a generator basis. -Carl...
Carl Lumma
clumma
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Feb 1, 2004
1:43 pm

... No, just assume octave repetition, find the period (easy) and then the unique generator that is between 0 and 1/2 period. ... What do you have in mind?...
Paul Erlich
paulerlich
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Feb 2, 2004
2:33 am

... Isn't it possible to find alternate generator pairs that give the same temperament when carried out to infinity? -Carl...
Carl Lumma
clumma
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Feb 2, 2004
3:19 am

... Yup! You can assume tritave-equivalence instead of octave- equivalence, for one thing . . ....
Paul Erlich
paulerlich
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Feb 2, 2004
3:56 am

... And can doing so change the DES series? -Carl...
Carl Lumma
clumma
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Feb 2, 2004
4:29 am

... then ... Well of course . . . can you think of any octave-repeating DESs that are also tritave-repeating?...
Paul Erlich
paulerlich
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Feb 2, 2004
5:14 am

... Right, so when trying to explain a creepy coincidence between complexity and DES cardinalities, might not we take this into account? -Carl...
Carl Lumma
clumma
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Feb 2, 2004
5:26 am

... Sure . . . some of the ones that 'don't work' may be working for tritave-DESs rather than octave-DESs, is that what you were thinking?...
Paul Erlich
paulerlich
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Feb 2, 2004
5:33 am

... Yep! -Carl...
Carl Lumma
clumma
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Feb 2, 2004
5:40 am

... norm, ... That's great, Paul. So what's the scaling?...
Gene Ward Smith
genewardsmith
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Feb 1, 2004
6:56 pm

... going ... (I'm ... I'm using your formula from http://groups.yahoo.com/group/tuning-math/message/8806 but instead of "max", I'm using "sum" . . ....
Paul Erlich
paulerlich
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Feb 2, 2004
3:01 am

... So these cosmically great answers are coming from the L1 norm applied to the scaling we got from vals, where we divide by log2(p)'s. What does that mean, I...
Gene Ward Smith
genewardsmith
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Feb 2, 2004
5:18 am

... applied ... The formulas, I think, are basically the same ones being used in the "cross-check" post -- did you have a chance to think about it? ...
Paul Erlich
paulerlich
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Feb 2, 2004
6:04 am

... are ... like ... even ... Gene, how does 4000/3993 (with its factors of 11) get into the description of a 7-limit temperament?...
Paul Erlich
paulerlich
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Mar 2, 2005
6:31 pm

... He did? I can't find this message from Gene Ward Smith, either in my in box or in the Yahoo Groups archive. Is it really out there? Can someone sent me a...
Rich Holmes
rsholmes
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Mar 2, 2005
8:10 pm

... http://www.robertinventor.com/tuning-math/s__10/msg_9350-9374.html Starting around the middle of that page. The original post was from 1/21/2004, and has...
Herman Miller
teamousechan...
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Mar 3, 2005
2:03 am

... <gwsmith@s...> ... top ... or ... That's odd, Rich. All you have to do is click on "Up Thread" in my message, and it takes you right to Gene's original: ...
Paul Erlich
paulerlich
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Mar 3, 2005
7:11 pm

... For some reason I wrote 4000/3993 when I should have written 4000/3969. Apparently I had commas too much on the brain and pulled another familiar one out...
Gene Ward Smith
genewardsmith
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Mar 3, 2005
8:57 am
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