TOP take on 7-limit temperaments

Here is my old list of 45 7-limit linear temperaments, this time using
top to sort it all out. The goodness winner is ennealimmal by a huge
margin, with meantone in second and magic coming up third. Ones with
badness under 30 are dominant seventh, augmented, pajara, meantone,
magic, miracle, schismic, and ennealimmal.

Decimal <4 2 2 -6 -8 -1]
[1207.657798 1914.092323 2768.532858 3372.361757]
[[2 4 5 6] [0 -2 -1 -1]] [600.0000000 249.0224992]
err: 7.657798 comp: 2.523719 bad: 48.773723

Dominant seventh <1 4 -2 4 -6 -16]
[1195.228951 1894.576888 2797.391744 3382.219933]
[[1 2 4 2] [0 -1 -4 2]] [1200. 497.7740225]
err: 4.771049 comp: 2.454561 bad: 28.744957

Diminished <4 4 4 -3 -5 -2]
[1194.128460 1892.648830 2788.245174 3385.309404]
[[4 6 9 11] [0 1 1 1]] [300.0000000 85.69820677]
err: 5.871540 comp: 2.523719 bad: 37.396767

Blackwood <0 5 0 8 0 -14]
[1195.893464 1913.429542 2786.313713 3348.501698]
[[5 8 12 14] [0 0 -1 0]] [240.0000000 90.61325640]
err: 7.239629 comp: 2.173813 bad: 34.210608

Augmented <3 0 6 -7 1 14]
[1199.976630 1892.649878 2799.945472 3385.307546]
[[3 5 7 9] [0 -1 0 -2]] [400.0000000 110.2596913]
err: 5.870879 comp: 2.147741 bad: 27.081145

Pajara <2 -4 -4 -11 -12 2]
[1196.893422 1901.906680 2779.100462 3377.547174]
[[2 3 5 6] [0 1 -2 -2]] [600.0000000 108.8143299]
err: 3.106578 comp: 2.988993 bad: 27.754421

Hexadecimal <1 -3 5 -7 5 20]
[1208.959294 1887.754858 2799.450479 3393.977822]
[[1 2 1 5] [0 -1 3 -5]] [1200. 526.8909182]
err: 8.959294 comp: 3.068202 bad: 84.341555

Negri <4 -3 2 -14 -8 13]
[1203.187308 1907.006766 2780.900506 3359.878000]
[[1 2 2 3] [0 -4 3 -2]] [1200. 125.4687958]
err: 3.187309 comp: 3.804173 bad: 46.125884

Kleismic <6 5 3 -6 -12 -7]
[1203.187308 1907.006766 2792.359613 3359.878000]
[[1 0 1 2] [0 6 5 3]] [1200. 316.6640534]
err: 3.187309 comp: 3.785579 bad: 45.676063

Tripletone <3 0 -6 -7 -18 -14]
[1197.060039 1902.640406 2793.140092 3377.079420]
[[3 5 7 8] [0 -1 0 2]] [400.0000000 88.72066409]
err: 2.939961 comp: 4.045351 bad: 48.112067

Hemifourth <2 8 1 8 -4 -20]
[1203.668842 1902.376967 2794.832500 3358.526166]
[[1 2 4 3] [0 -2 -8 -1]] [1200. 252.7423121]
err: 3.668842 comp: 3.445412 bad: 43.552336

Meantone <1 4 10 4 13 12]
[1201.698521 1899.262909 2790.257556 3370.548328]
[[1 2 4 7] [0 -1 -4 -10]] [1200. 503.3520320]
err: 1.698521 comp: 3.562072 bad: 21.551439

Injera <2 8 8 8 7 -4]
[1201.777814 1896.276546 2777.994928 3378.883835]
[[2 3 4 5] [0 1 4 4]] [600.0000000 93.65102578]
err: 3.582707 comp: 3.445412 bad: 42.529834

Double wide <8 6 6 -9 -13 -3]
[1198.553882 1907.135354 2778.724633 3378.001574]
[[2 5 6 7] [0 -4 -3 -3]] [600.0000000 274.3886321]
err: 3.268439 comp: 5.047438 bad: 83.268810

Porcupine <3 5 -6 1 -18 -28]
[1196.905961 1906.858938 2779.129576 3367.717888]
[[1 2 3 2] [0 -3 -5 6]] [1200. 162.3778142]
err: 3.094040 comp: 4.295482 bad: 57.088650

Superpythagorean <1 9 -2 12 -6 -30]
[1197.596121 1905.765059 2780.732078 3374.046608]
[[1 2 6 2] [0 -1 -9 2]] [1200. 489.6151808]
err: 2.403879 comp: 4.602303 bad: 50.917015

Muggles <5 1 -7 -10 -25 -19]
[1203.148010 1896.965522 2785.689126 3359.988323]
[[1 0 2 5] [0 5 1 -7]] [1200. 377.6398800]
err: 3.148011 comp: 5.618543 bad: 99.376477

Beatles <2 -9 -4 -19 -12 16]
[1197.104145 1906.544822 2793.037680 3369.535226]
[[1 1 5 4] [0 2 -9 -4]] [1200. 356.3080304]
err: 2.895855 comp: 5.162806 bad: 77.187771

Flattone <1 4 -9 4 -17 -32]
[1202.536420 1897.934872 2781.593812 3361.705278]
[[1 2 4 -1] [0 -1 -4 9]] [1200. 506.5439220]
err: 2.536420 comp: 4.909123 bad: 61.126418

Magic <5 1 12 -10 5 25]
[1201.276744 1903.978592 2783.349206 3368.271877]
[[1 0 2 -1] [0 5 1 12]] [1200. 380.5064473]
err: 1.276744 comp: 4.274486 bad: 23.327687

Nonkleismic <10 9 7 -9 -17 -9]
[1198.828458 1900.098151 2789.033948 3368.077085]
[[1 -1 0 1] [0 10 9 7]] [1200. 309.9514712]
err: 1.171542 comp: 6.309298 bad: 46.635848

Semisixths <7 9 13 -2 1 5]
[1198.389531 1903.732520 2790.053106 3364.304748]
[[1 -1 -1 -2] [0 7 9 13]] [1200. 443.6203855]
err: 1.610469 comp: 4.630693 bad: 34.533812

Orwell <7 -3 8 -21 -7 27]
[1199.532657 1900.455530 2784.117029 3371.481834]
[[1 0 3 1] [0 7 -3 8]] [1200. 271.3263635]
err: .946061 comp: 5.706260 bad: 30.805067

Miracle <6 -7 -2 -25 -20 15]
[1200.631014 1900.954868 2784.848544 3368.451756]
[[1 1 3 3] [0 6 -7 -2]] [1200. 116.5729472]
err: .631014 comp: 6.793166 bad: 29.119472

Quartaminorthirds <9 5 -3 -13 -30 -21]
[1199.792743 1900.291122 2788.751252 3365.878770]
[[1 1 2 3] [0 9 5 -3]] [1200. 77.70708732]
err: 1.049791 comp: 6.742251 bad: 47.721346

Supermajor seconds <3 12 -1 12 -10 -36]
[1201.698521 1899.262909 2790.257556 3372.574099]
[[1 1 0 3] [0 3 12 -1]] [1200. 232.1235474]
err: 1.698521 comp: 5.522763 bad: 51.806440

Schismic <1 -8 -14 -15 -25 -10]
[1200.760625 1903.401919 2784.194017 3371.388750]
[[1 2 -1 -3] [0 -1 8 14]] [1200. 497.8598384]
err: .912904 comp: 5.618543 bad: 28.818563

Superkleismic <9 10 -3 -5 -30 -35]
[1201.371918 1904.129438 2783.128219 3369.863245]
[[1 4 5 2] [0 -9 -10 3]] [1200. 321.8581276]
err: 1.371918 comp: 6.742251 bad: 62.364566

Squares <4 16 9 16 3 -24]
[1201.698521 1899.262909 2790.257556 3372.067656]
[[1 3 8 6] [0 -4 -16 -9]] [1200. 425.9591136]
err: 1.698521 comp: 6.890825 bad: 80.651668

Semififth <2 8 -11 8 -23 -48]
[1201.698521 1899.262909 2790.257556 3373.586984]
[[1 1 0 6] [0 2 8 -11]] [1200. 348.3528922]
err: 1.698521 comp: 7.363684 bad: 92.100337

Diaschismic <2 -4 -16 -11 -31 -26]
[1198.732403 1901.885616 2789.256983 3365.267311]
[[2 3 5 7] [0 1 -2 -8]] [600.0000000 103.7370914]
err: 1.267597 comp: 6.966993 bad: 61.527901

Octacot <8 18 11 10 -5 -25]
[1199.031259 1903.490418 2784.064367 3366.693863]
[[1 1 1 2] [0 8 18 11]] [1200. 88.14540671]
err: .968741 comp: 7.752178 bad: 58.217715

Tritonic <5 -11 -12 -29 -33 3]
[1201.023211 1900.333250 2785.201472 3365.953391]
[[1 4 -3 -3] [0 -5 11 12]] [1200. 580.4242150]
err: 1.023211 comp: 7.880073 bad: 63.536850

Supersupermajor <3 17 -1 20 -10 -50]
[1200.231588 1903.372996 2784.236389 3366.314293]
[[1 1 -1 3] [0 3 17 -1]] [1200. 234.4104084]
err: .894655 comp: 7.670504 bad: 52.638504

Shrutar <4 -8 14 -22 11 55]
[1198.920873 1903.665377 2786.734051 3365.796415]
[[2 3 5 5] [0 2 -4 7]] [600.0000000 52.89351739]
err: 1.079127 comp: 8.437555 bad: 76.825572

Catakleismic <6 5 22 -6 18 37]
[1200.536356 1901.438376 2785.068335 3370.331646]
[[1 0 1 -3] [0 6 5 22]] [1200. 316.7238784]
err: .536356 comp: 7.836558 bad: 32.938503

Hemiwuerschmidt <16 2 5 -34 -37 6]
[1199.692003 1901.466838 2787.028860 3368.496143]
[[1 -1 2 2] [0 16 2 5]] [1200. 193.9099372]
err: .307997 comp: 10.094876 bad: 31.386987

Hemikleismic <12 10 -9 -12 -48 -49]
[1199.411231 1902.888178 2785.151380 3370.478790]
[[1 0 1 4] [0 12 10 -9]] [1200. 158.7324720]
err: .588769 comp: 10.787602 bad: 68.516458

Hemithird <15 -2 -5 -38 -50 -6]
[1200.363229 1901.194685 2787.427555 3367.479202]
[[1 4 2 2] [0 -15 2 5]] [1200. 193.2841225]
err: .479706 comp: 11.237086 bad: 60.573479

Wizard <12 -2 20 -31 -2 52]
[1200.639571 1900.941305 2784.828674 3368.342104]
[[2 1 5 2] [0 6 -1 10]] [600.0000000 216.7129477]
err: .639571 comp: 8.423526 bad: 45.381303

Duodecimal <0 12 24 19 38 22]
[1200.617051 1900.976998 2785.844725 3370.558188]
[[12 19 28 34] [0 0 -1 -2]] [100.0000000 15.94743281]
err: .617051 comp: 8.548972 bad: 45.097159

Slender <13 -10 6 -46 -27 42]
[1200.337238 1901.055858 2784.996493 3370.418508]
[[1 2 2 3] [0 -13 10 -6]] [1200. 38.46612667]
err: .567296 comp: 12.499426 bad: 88.631905

Amity <5 13 -17 9 -41 -76]
[1199.723894 1902.392618 2786.717797 3369.601033]
[[1 3 6 -2] [0 -5 -13 17]] [1200. 339.4147297]
err: .276106 comp: 11.659166 bad: 37.532790

Hemififth <2 25 13 35 15 -40]
[1199.700353 1902.429930 2785.617954 3368.041901]
[[1 1 -5 -1] [0 2 25 13]] [1200. 351.4712147]
err: .299647 comp: 10.766914 bad: 34.737019

Ennealimmal <18 27 18 1 -22 -34]
[1200.036377 1902.012658 2786.350298 3368.723784]
[[9 15 22 26] [0 -2 -3 -2]] [133.3333333 48.99915090]
err: .036377 comp: 11.628267 bad: 4.918774

I appreciate this work, Gene.

How about a worked-out, hand-holding example for one of these error
and complexity calculations?

P.S. Instead of using log-flat badness, why don't we use the same
function of error and complexity that yielded epimericity in the
codimension-1 case?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> Here is my old list of 45 7-limit linear temperaments, this time
using
> top to sort it all out. The goodness winner is ennealimmal by a huge
> margin, with meantone in second and magic coming up third. Ones with
> badness under 30 are dominant seventh, augmented, pajara, meantone,
> magic, miracle, schismic, and ennealimmal.
>
> Decimal <4 2 2 -6 -8 -1]
> [1207.657798 1914.092323 2768.532858 3372.361757]
> [[2 4 5 6] [0 -2 -1 -1]] [600.0000000 249.0224992]
> err: 7.657798 comp: 2.523719 bad: 48.773723
>
>
> Dominant seventh <1 4 -2 4 -6 -16]
> [1195.228951 1894.576888 2797.391744 3382.219933]
> [[1 2 4 2] [0 -1 -4 2]] [1200. 497.7740225]
> err: 4.771049 comp: 2.454561 bad: 28.744957
>
>
> Diminished <4 4 4 -3 -5 -2]
> [1194.128460 1892.648830 2788.245174 3385.309404]
> [[4 6 9 11] [0 1 1 1]] [300.0000000 85.69820677]
> err: 5.871540 comp: 2.523719 bad: 37.396767
>
>
> Blackwood <0 5 0 8 0 -14]
> [1195.893464 1913.429542 2786.313713 3348.501698]
> [[5 8 12 14] [0 0 -1 0]] [240.0000000 90.61325640]
> err: 7.239629 comp: 2.173813 bad: 34.210608
>
>
> Augmented <3 0 6 -7 1 14]
> [1199.976630 1892.649878 2799.945472 3385.307546]
> [[3 5 7 9] [0 -1 0 -2]] [400.0000000 110.2596913]
> err: 5.870879 comp: 2.147741 bad: 27.081145
>
>
> Pajara <2 -4 -4 -11 -12 2]
> [1196.893422 1901.906680 2779.100462 3377.547174]
> [[2 3 5 6] [0 1 -2 -2]] [600.0000000 108.8143299]
> err: 3.106578 comp: 2.988993 bad: 27.754421
>
>
> Hexadecimal <1 -3 5 -7 5 20]
> [1208.959294 1887.754858 2799.450479 3393.977822]
> [[1 2 1 5] [0 -1 3 -5]] [1200. 526.8909182]
> err: 8.959294 comp: 3.068202 bad: 84.341555
>
>
> Negri <4 -3 2 -14 -8 13]
> [1203.187308 1907.006766 2780.900506 3359.878000]
> [[1 2 2 3] [0 -4 3 -2]] [1200. 125.4687958]
> err: 3.187309 comp: 3.804173 bad: 46.125884
>
>
> Kleismic <6 5 3 -6 -12 -7]
> [1203.187308 1907.006766 2792.359613 3359.878000]
> [[1 0 1 2] [0 6 5 3]] [1200. 316.6640534]
> err: 3.187309 comp: 3.785579 bad: 45.676063
>
>
> Tripletone <3 0 -6 -7 -18 -14]
> [1197.060039 1902.640406 2793.140092 3377.079420]
> [[3 5 7 8] [0 -1 0 2]] [400.0000000 88.72066409]
> err: 2.939961 comp: 4.045351 bad: 48.112067
>
>
> Hemifourth <2 8 1 8 -4 -20]
> [1203.668842 1902.376967 2794.832500 3358.526166]
> [[1 2 4 3] [0 -2 -8 -1]] [1200. 252.7423121]
> err: 3.668842 comp: 3.445412 bad: 43.552336
>
>
> Meantone <1 4 10 4 13 12]
> [1201.698521 1899.262909 2790.257556 3370.548328]
> [[1 2 4 7] [0 -1 -4 -10]] [1200. 503.3520320]
> err: 1.698521 comp: 3.562072 bad: 21.551439
>
>
> Injera <2 8 8 8 7 -4]
> [1201.777814 1896.276546 2777.994928 3378.883835]
> [[2 3 4 5] [0 1 4 4]] [600.0000000 93.65102578]
> err: 3.582707 comp: 3.445412 bad: 42.529834
>
>
> Double wide <8 6 6 -9 -13 -3]
> [1198.553882 1907.135354 2778.724633 3378.001574]
> [[2 5 6 7] [0 -4 -3 -3]] [600.0000000 274.3886321]
> err: 3.268439 comp: 5.047438 bad: 83.268810
>
>
> Porcupine <3 5 -6 1 -18 -28]
> [1196.905961 1906.858938 2779.129576 3367.717888]
> [[1 2 3 2] [0 -3 -5 6]] [1200. 162.3778142]
> err: 3.094040 comp: 4.295482 bad: 57.088650
>
>
> Superpythagorean <1 9 -2 12 -6 -30]
> [1197.596121 1905.765059 2780.732078 3374.046608]
> [[1 2 6 2] [0 -1 -9 2]] [1200. 489.6151808]
> err: 2.403879 comp: 4.602303 bad: 50.917015
>
>
> Muggles <5 1 -7 -10 -25 -19]
> [1203.148010 1896.965522 2785.689126 3359.988323]
> [[1 0 2 5] [0 5 1 -7]] [1200. 377.6398800]
> err: 3.148011 comp: 5.618543 bad: 99.376477
>
>
> Beatles <2 -9 -4 -19 -12 16]
> [1197.104145 1906.544822 2793.037680 3369.535226]
> [[1 1 5 4] [0 2 -9 -4]] [1200. 356.3080304]
> err: 2.895855 comp: 5.162806 bad: 77.187771
>
>
> Flattone <1 4 -9 4 -17 -32]
> [1202.536420 1897.934872 2781.593812 3361.705278]
> [[1 2 4 -1] [0 -1 -4 9]] [1200. 506.5439220]
> err: 2.536420 comp: 4.909123 bad: 61.126418
>
>
> Magic <5 1 12 -10 5 25]
> [1201.276744 1903.978592 2783.349206 3368.271877]
> [[1 0 2 -1] [0 5 1 12]] [1200. 380.5064473]
> err: 1.276744 comp: 4.274486 bad: 23.327687
>
>
> Nonkleismic <10 9 7 -9 -17 -9]
> [1198.828458 1900.098151 2789.033948 3368.077085]
> [[1 -1 0 1] [0 10 9 7]] [1200. 309.9514712]
> err: 1.171542 comp: 6.309298 bad: 46.635848
>
>
> Semisixths <7 9 13 -2 1 5]
> [1198.389531 1903.732520 2790.053106 3364.304748]
> [[1 -1 -1 -2] [0 7 9 13]] [1200. 443.6203855]
> err: 1.610469 comp: 4.630693 bad: 34.533812
>
>
> Orwell <7 -3 8 -21 -7 27]
> [1199.532657 1900.455530 2784.117029 3371.481834]
> [[1 0 3 1] [0 7 -3 8]] [1200. 271.3263635]
> err: .946061 comp: 5.706260 bad: 30.805067
>
>
> Miracle <6 -7 -2 -25 -20 15]
> [1200.631014 1900.954868 2784.848544 3368.451756]
> [[1 1 3 3] [0 6 -7 -2]] [1200. 116.5729472]
> err: .631014 comp: 6.793166 bad: 29.119472
>
>
> Quartaminorthirds <9 5 -3 -13 -30 -21]
> [1199.792743 1900.291122 2788.751252 3365.878770]
> [[1 1 2 3] [0 9 5 -3]] [1200. 77.70708732]
> err: 1.049791 comp: 6.742251 bad: 47.721346
>
>
> Supermajor seconds <3 12 -1 12 -10 -36]
> [1201.698521 1899.262909 2790.257556 3372.574099]
> [[1 1 0 3] [0 3 12 -1]] [1200. 232.1235474]
> err: 1.698521 comp: 5.522763 bad: 51.806440
>
>
> Schismic <1 -8 -14 -15 -25 -10]
> [1200.760625 1903.401919 2784.194017 3371.388750]
> [[1 2 -1 -3] [0 -1 8 14]] [1200. 497.8598384]
> err: .912904 comp: 5.618543 bad: 28.818563
>
>
> Superkleismic <9 10 -3 -5 -30 -35]
> [1201.371918 1904.129438 2783.128219 3369.863245]
> [[1 4 5 2] [0 -9 -10 3]] [1200. 321.8581276]
> err: 1.371918 comp: 6.742251 bad: 62.364566
>
>
> Squares <4 16 9 16 3 -24]
> [1201.698521 1899.262909 2790.257556 3372.067656]
> [[1 3 8 6] [0 -4 -16 -9]] [1200. 425.9591136]
> err: 1.698521 comp: 6.890825 bad: 80.651668
>
>
> Semififth <2 8 -11 8 -23 -48]
> [1201.698521 1899.262909 2790.257556 3373.586984]
> [[1 1 0 6] [0 2 8 -11]] [1200. 348.3528922]
> err: 1.698521 comp: 7.363684 bad: 92.100337
>
>
> Diaschismic <2 -4 -16 -11 -31 -26]
> [1198.732403 1901.885616 2789.256983 3365.267311]
> [[2 3 5 7] [0 1 -2 -8]] [600.0000000 103.7370914]
> err: 1.267597 comp: 6.966993 bad: 61.527901
>
>
> Octacot <8 18 11 10 -5 -25]
> [1199.031259 1903.490418 2784.064367 3366.693863]
> [[1 1 1 2] [0 8 18 11]] [1200. 88.14540671]
> err: .968741 comp: 7.752178 bad: 58.217715
>
>
> Tritonic <5 -11 -12 -29 -33 3]
> [1201.023211 1900.333250 2785.201472 3365.953391]
> [[1 4 -3 -3] [0 -5 11 12]] [1200. 580.4242150]
> err: 1.023211 comp: 7.880073 bad: 63.536850
>
>
> Supersupermajor <3 17 -1 20 -10 -50]
> [1200.231588 1903.372996 2784.236389 3366.314293]
> [[1 1 -1 3] [0 3 17 -1]] [1200. 234.4104084]
> err: .894655 comp: 7.670504 bad: 52.638504
>
>
> Shrutar <4 -8 14 -22 11 55]
> [1198.920873 1903.665377 2786.734051 3365.796415]
> [[2 3 5 5] [0 2 -4 7]] [600.0000000 52.89351739]
> err: 1.079127 comp: 8.437555 bad: 76.825572
>
>
> Catakleismic <6 5 22 -6 18 37]
> [1200.536356 1901.438376 2785.068335 3370.331646]
> [[1 0 1 -3] [0 6 5 22]] [1200. 316.7238784]
> err: .536356 comp: 7.836558 bad: 32.938503
>
>
> Hemiwuerschmidt <16 2 5 -34 -37 6]
> [1199.692003 1901.466838 2787.028860 3368.496143]
> [[1 -1 2 2] [0 16 2 5]] [1200. 193.9099372]
> err: .307997 comp: 10.094876 bad: 31.386987
>
>
> Hemikleismic <12 10 -9 -12 -48 -49]
> [1199.411231 1902.888178 2785.151380 3370.478790]
> [[1 0 1 4] [0 12 10 -9]] [1200. 158.7324720]
> err: .588769 comp: 10.787602 bad: 68.516458
>
>
> Hemithird <15 -2 -5 -38 -50 -6]
> [1200.363229 1901.194685 2787.427555 3367.479202]
> [[1 4 2 2] [0 -15 2 5]] [1200. 193.2841225]
> err: .479706 comp: 11.237086 bad: 60.573479
>
>
> Wizard <12 -2 20 -31 -2 52]
> [1200.639571 1900.941305 2784.828674 3368.342104]
> [[2 1 5 2] [0 6 -1 10]] [600.0000000 216.7129477]
> err: .639571 comp: 8.423526 bad: 45.381303
>
>
> Duodecimal <0 12 24 19 38 22]
> [1200.617051 1900.976998 2785.844725 3370.558188]
> [[12 19 28 34] [0 0 -1 -2]] [100.0000000 15.94743281]
> err: .617051 comp: 8.548972 bad: 45.097159
>
>
> Slender <13 -10 6 -46 -27 42]
> [1200.337238 1901.055858 2784.996493 3370.418508]
> [[1 2 2 3] [0 -13 10 -6]] [1200. 38.46612667]
> err: .567296 comp: 12.499426 bad: 88.631905
>
>
> Amity <5 13 -17 9 -41 -76]
> [1199.723894 1902.392618 2786.717797 3369.601033]
> [[1 3 6 -2] [0 -5 -13 17]] [1200. 339.4147297]
> err: .276106 comp: 11.659166 bad: 37.532790
>
>
> Hemififth <2 25 13 35 15 -40]
> [1199.700353 1902.429930 2785.617954 3368.041901]
> [[1 1 -5 -1] [0 2 25 13]] [1200. 351.4712147]
> err: .299647 comp: 10.766914 bad: 34.737019
>
>
> Ennealimmal <18 27 18 1 -22 -34]
> [1200.036377 1902.012658 2786.350298 3368.723784]
> [[9 15 22 26] [0 -2 -3 -2]] [133.3333333 48.99915090]
> err: .036377 comp: 11.628267 bad: 4.918774

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> I appreciate this work, Gene.
>
> How about a worked-out, hand-holding example for one of these error
> and complexity calculations?
>
> P.S. Instead of using log-flat badness, why don't we use the same
> function of error and complexity that yielded epimericity in the
> codimension-1 case?

What's your proposal specifically?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> > I appreciate this work, Gene.
> >
> > How about a worked-out, hand-holding example for one of these
error
> > and complexity calculations?
> >
> > P.S. Instead of using log-flat badness, why don't we use the same
> > function of error and complexity that yielded epimericity in the
> > codimension-1 case?
>
> What's your proposal specifically?

Hrm. Well, I'm trying to use your webpages as a substitute for hand-
holding, but why is the codimension one case here:

http://66.98.148.43/~xenharmo/top.htm

so complicated? I thought we agreed that if there's only one comma
n/d, we simply temper each prime p from cents(p) to

cents(p) - log(p)*cents(n/d)/log(n*d)
if p is a factor of n, and to

cents(p) + log(p)*cents(n/d)/log(n*d)
if p is a factor of d.

If p is not a factor of n or d, we probably wouldn't want to temper
it at all, but it *is* tempered on all the vertices of your ball,
isn't it?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> > I appreciate this work, Gene.
> >
> > How about a worked-out, hand-holding example for one of these
error
> > and complexity calculations?
> >
> > P.S. Instead of using log-flat badness, why don't we use the same
> > function of error and complexity that yielded epimericity in the
> > codimension-1 case?
>
> What's your proposal specifically?

In the P.S., what I was referring to was this:

/tuning/topicId_51065.html#51221

This is a function of complexity and error, so can be applied even if
the actual number of commas is greater than 1. So why not use it as a
badness function? Maybe it's screwy, but I think it would be
informative to see what results.

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

> This is a function of complexity and error, so can be applied even if
> the actual number of commas is greater than 1. So why not use it as a
> badness function? Maybe it's screwy, but I think it would be
> informative to see what results.

It can be applied to commas individually, but how do you make it
independent of the comma basis if you apply it to wedgies?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
>
> > This is a function of complexity and error, so can be applied
even if
> > the actual number of commas is greater than 1. So why not use it
as a
> > badness function? Maybe it's screwy, but I think it would be
> > informative to see what results.
>
> It can be applied to commas individually, but how do you make it
> independent of the comma basis if you apply it to wedgies?

*You yourself* already posted the complexity and error for various
codimension-2 wedgies!!!! Those results weren't independent of the
comma basis?????????

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:

> *You yourself* already posted the complexity and error for various
> codimension-2 wedgies!!!! Those results weren't independent of the
> comma basis?????????

Yes they were, but I thought you didn't like what I did and were
suggesting we try something else.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
>
> > *You yourself* already posted the complexity and error for
various
> > codimension-2 wedgies!!!! Those results weren't independent of
the
> > comma basis?????????
>
> Yes they were, but I thought you didn't like what I did and were
> suggesting we try something else.

It was the *badness* function you used that I didn't like, which is
why I was suggesting this *other* function of complexity and error
which, as well, *you yourself* posted.

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:

> It was the *badness* function you used that I didn't like, which is
> why I was suggesting this *other* function of complexity and error
> which, as well, *you yourself* posted.

That was in a discussion of commas, not wedgies. How do you apply it
to wedgies?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
>
> > It was the *badness* function you used that I didn't like, which
is
> > why I was suggesting this *other* function of complexity and
error
> > which, as well, *you yourself* posted.
>
> That was in a discussion of commas, not wedgies.

You gave a function of complexity and error, in which you managed to
eliminate all reference to the original comma, so that I could plot
the contours over the whole graph regardless of how few commas were
actually in the vicinity.

> How do you apply it
> to wedgies?

Compute the complexity and error from the wedgie, and the compute
that same function of complexity and error.