Amended best list

I had a problem merging lists (I neglected to consider that two different temperaments can have the same complexity.) This led to the only addition to my list, which I'm calling "supersharp" because of its very very sharp fifth generator of 17/28, being left off.

Decimal
[4, 2, 2, -1, 8, -6] [[2, 0, 3, 4], [0, 2, 1, 1]]

bad 184.7010517 g 2.777313996 rms 23.94525150

1/2 950.9775006

Dominant seventh
[1, 4, -2, -16, 6, 4] [[1, 0, -4, 6], [0, 1, 4, -2]]

bad 197.3456024 g 3.128478105 rms 20.16328150

1 1902.225978

Diminished
[4, 4, 4, -2, 5, -3] [[4, 0, 3, 5], [0, 1, 1, 1]]

bad 189.2082747 g 3.144366918 rms 19.13699259

1/4 1885.698207

Quintal
[0, 5, 0, -14, 0, 8] [[5, 8, 0, 14], [0, 0, 1, 0]]

bad 171.2126805 g 3.290247187 rms 15.81535241

1/5 2789.386745

Augmented
[3, 0, 6, 14, -1, -7] [[3, 0, 7, -1], [0, 1, 0, 2]]

bad 224.2088808 g 3.675273386 rms 16.59867843

1/3 1889.740309

Pajara
[2, -4, -4, 2, 12, -11] [[2, 0, 11, 12], [0, 1, -2, -2]]

bad 169.1429833 g 3.938677761 rms 10.90317755

1/2 1908.814330

Supersharp
[2, 6, 6, -3, -4, 5] [[2, 0, -5, -4], [0, 1, 3, 3]]

bad 292.6389492 g 3.938677761 rms 18.86388876

1/2 1928.512337

Hexadecimal
[1, -3, 5, 20, -5, -7] [[1, 0, 7, -5], [0, 1, -3, 5]]

bad 296.7523121 g 3.995964429 rms 18.58450012

1 1873.109081

Tertiathirds
[4, -3, 2, 13, 8, -14] [[1, 2, 2, 3], [0, 4, -3, 2]]

bad 225.9663420 g 4.305717081 rms 12.18857055

1 -125.4687958

Kleismic
[6, 5, 3, -7, 12, -6] [[1, 0, 1, 2], [0, 6, 5, 3]]

bad 234.2754881 g 4.368916409 rms 12.27380956

1 316.6640534

Tripletone
[3, 0, -6, -14, 18, -7] [[3, 0, 7, 18], [0, 1, 0, -2]]

bad 173.7904007 g 4.631825456 rms 8.100678834

1/3 1911.279336

[2, 8, 1, -20, 4, 8] [[1, 0, -4, 2], [0, 2, 8, 1]]

bad 293.7346084 g 4.811111338 rms 12.69007837

1 947.2576878

Meantone
[1, 4, 10, 12, -13, 4] [[1, 0, -4, -13], [0, 1, 4, 10]]

bad 103.8247475 g 5.322447240 rms 3.665035228

1 1896.647968

Injera
[2, 8, 8, -4, -7, 8] [[2, 0, -8, -7], [0, 1, 4, 4]]

bad 320.3524287 g 5.343650829 rms 11.21894132

1/2 1893.651026

Double wide
[8, 6, 6, -3, 13, -9] [[2, 1, 3, 4], [0, 4, 3, 3]]

bad 334.6430427 g 5.746952448 rms 10.13226624

1/2 325.6113679

Porcupine
[3, 5, -6, -28, 18, 1] [[1, 2, 3, 2], [0, 3, 5, -6]]

bad 231.9225067 g 5.836211169 rms 6.808961862

1 -162.3778142

Superpythagorean
[1, 9, -2, -30, 6, 12] [[1, 0, -12, 6], [0, 1, 9, -2]]

bad 246.9834642 g 6.207109365 rms 6.410458352

1 1910.384820

[5, 1, -7, -19, 25, -10] [[1, 0, 2, 5], [0, 5, 1, -7]]

bad 347.0112248 g 6.305725722 rms 8.727168682

1 377.6398806

Neutral thirds
[2, -9, -4, 16, 12, -19] [[1, 1, 5, 4], [0, 2, -9, -4]]

bad 265.2522216 g 6.517068879 rms 6.245315858

1 356.3080310

Flattone
[1, 4, -9, -32, 17, 4] [[1, 0, -4, 17], [0, 1, 4, -9]]

bad 329.1049270 g 6.557956330 rms 7.652394368

1 1893.456080

Magic
[5, 1, 12, 25, -5, -10] [[1, 0, 2, -1], [0, 5, 1, 12]]

bad 190.6152791 g 6.786228469 rms 4.139050792

1 380.5064474

Small diesic
[10, 9, 7, -9, 17, -9] [[1, 9, 9, 8], [0, 10, 9, 7]]

bad 181.6005942 g 7.395689110 rms 3.320167332

1 -890.0485289

Semisixths (tiny diesic)
[7, 9, 13, 5, -1, -2] [[1, 6, 8, 11], [0, 7, 9, 13]]

bad 278.2627568 g 7.420887650 rms 5.052931030

1 -756.3796144

Orwell
[7, -3, 8, 27, 7, -21] [[1, 0, 3, 1], [0, 7, -3, 8]]

bad 142.6121910 g 7.421511799 rms 2.589237496

1 271.3263633

Miracle
[6, -7, -2, 15, 20, -25] [[1, 1, 3, 3], [0, 6, -7, -2]]

bad 94.80434091 g 7.609147969 rms 1.637405196

1 116.5729472

Quartaminorthirds
[9, 5, -3, -21, 30, -13] [[1, 1, 2, 3], [0, 9, 5, -3]]

bad 179.6938179 g 7.655669978 rms 3.065961726

1 77.70708740

Supermajor seconds
[3, 12, -1, -36, 10, 12] [[1, 1, 0, 3], [0, 3, 12, -1]]

bad 214.5541544 g 7.742330569 rms 3.579262150

1 232.1235474

Schismic
[1, -8, -14, -10, 25, -15] [[1, 0, 15, 25], [0, 1, -8, -14]]

bad 212.0930465 g 8.612526914 rms 2.859336356

1 1902.140161

[9, 10, -3, -35, 30, -5] [[1, 4, 5, 2], [0, 9, 10, -3]]

bad 323.7195354 g 8.937416729 rms 4.052704060

1 -321.8581275

[4, 16, 9, -24, -3, 16] [[1, 3, 8, 6], [0, 4, 16, 9]]

bad 300.2293184 g 9.336988664 rms 3.443812018

1 -425.9591136

[2, 8, -11, -48, 23, 8] [[1, 1, 0, 6], [0, 2, 8, -11]]

bad 333.5422522 g 9.453300867 rms 3.732363180

1 348.3528923

Diaschismic
[2, -4, -16, -26, 31, -11] [[2, 0, 11, 31], [0, 1, -2, -8]]

bad 342.7141199 g 9.469818377 rms 3.821630536

1/2 1903.737092

Octafifths
[8, 18, 11, -25, 5, 10] [[1, 1, 1, 2], [0, 8, 18, 11]]

bad 227.7375065 g 10.50332216 rms 2.064339812

1 88.14540670

[5, -11, -12, 3, 33, -29] [[1, 4, -3, -3], [0, 5, -11, -12]]

bad 316.6090581 g 10.83403515 rms 2.697384486

1 -580.4242148

[3, 17, -1, -50, 10, 20] [[1, 1, -1, 3], [0, 3, 17, -1]]

bad 324.7554230 g 10.90855391 rms 2.729116326

1 234.4104087

Shrutar
[4, -8, 14, 55, -11, -22] [[2, 1, 9, -2], [0, 2, -4, 7]]

bad 281.7169931 g 11.18841619 rms 2.250483424

1/2 652.8935173

Catakleismic
[6, 5, 22, 37, -18, -6] [[1, 0, 1, -3], [0, 6, 5, 22]]

bad 209.7321406 g 11.41155044 rms 1.610555448

1 316.7238784

Hemiwuerschmidt
[16, 2, 5, 6, 37, -34] [[1, 15, 4, 7], [0, 16, 2, 5]]

bad 120.8100402 g 11.74782291 rms .8753631224

1 -1006.090063

Hemikleismic
[12, 10, -9, -49, 48, -12] [[1, 0, 1, 4], [0, 12, 10, -9]]

bad 311.1962901 g 12.80971160 rms 1.896512488

1 158.7324720

Hemithird
[15, -2, -5, -6, 50, -38] [[1, 4, 2, 2], [0, 15, -2, -5]]

bad 299.6293822 g 13.15572684 rms 1.731229740

1 -193.2841226

[12, -2, 20, 52, 2, -31] [[2, 1, 5, 2], [0, 6, -1, 10]]

bad 327.4131763 g 13.66566083 rms 1.753213789

1/2 216.7129478

[0, 12, 24, 22, -38, 19] [[12, 19, 0, -22], [0, 0, 1, 2]]

bad 283.6535726 g 13.76571634 rms 1.496892545

1/12 2784.052566

[13, -10, 6, 42, 27, -46] [[1, 2, 2, 3], [0, 13, -10, 6]]

bad 331.7213164 g 14.05800468 rms 1.678518039

1 -38.46612668

Amt
[5, 13, -17, -76, 41, 9] [[1, 3, 6, -2], [0, 5, 13, -17]]

bad 195.3007298 g 15.19489337 rms .8458796028

1 -339.4147298

[2, 25, 13, -40, -15, 35] [[1, 1, -5, -1], [0, 2, 25, 13]]

bad 137.7813896 g 15.34473078 rms .5851564738

1 351.4712147

Ennealimmal
[18, 27, 18, -34, 22, 1] [[9, 1, 1, 12], [0, 2, 3, 2]]

bad 37.51193854 g 16.95758830 rms .1304491741

1/9 884.3341826

>I had a problem merging lists (I neglected to consider that two different
>temperaments can have the same complexity.) This led to the only addition
>to my list, which I'm calling "supersharp" because of its very very sharp
>fifth generator of 17/28, being left off.

For someone who doesn't understand why everyone else thinks weighted
complexity is better, could we see the same thing with unweighted
complexity?

-Carl

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> For someone who doesn't understand why everyone else thinks weighted
> complexity is better, could we see the same thing with unweighted
> complexity?

It still has the property which screwed me up before--the same complexity as pajara. This time the value in question is sqrt(18) =
4.242640686.