A <2,3,7> group "best" list

This was done in a way exactly comparable to the most recent 5-limit
search.

567/512

map [[0, -1, 4], [1, 2, 1]]

generators 535.897694119756 1200.

badness 670.137142647868 rms 27.2570556594034 g_w 2.90778025274862

243/224

map [[0, -1, -5], [1, 2, 5]]

generators 528.248377247002 1200.

badness 534.715045110858 rms 21.7489179735939 g_w 2.90778025274862

343/324

map [[0, 3, 4], [1, 1, 2]]

generators 240.309212849092 1200.

badness 493.563423167166 rms 19.3483699528574 g_w 2.94374053640771

256/243

map [[0, 0, -1], [5, 8, 15]]

generators 222.151593963576 240.

badness 378.244754205085 rms 12.7597412545895 g_w 3.09487905565715

28/27

map [[0, -1, -3], [1, 2, 4]]

generators 475.558962037126 1200.

badness 91.4596348840926 rms 16.8270093610171 g_w 1.75822388550304

16807/16384

map [[0, -1, 0], [5, 10, 14]]

generators 502.457952369172 240.

badness 550.435696708892 rms 6.24085831443580 g_w 4.45130571562582

19683/19208

map [[0, -4, -9], [1, 3, 6]]

generators 425.724527133587 1200.

badness 626.695380808806 rms 3.82888181257598 g_w 5.47009468947274

49/48

map [[0, -2, -1], [1, 2, 3]]

generators 249.022499567306 1200.

badness 67.8093075322853 rms 14.5731625037549 g_w 1.66946954361805

64/63

map [[0, -1, 2], [1, 2, 2]]

generators 488.307823491718 1200.

badness 39.6049568556885 rms 7.28663503411012 g_w 1.75822388550304

531441/524288

map [[0, 0, -1], [12, 19, 36]]

generators 232.151593963576 100.

badness 566.495842771669 rms 1.38239436914426 g_w 7.42770973357716

537824/531441

map [[0, 5, 12], [1, 0, -1]]

generators 380.751294592580 1200.

badness 524.893579245064 rms 1.39991667198979 g_w 7.21090363091141

65536/64827

map [[0, 4, -3], [1, 0, 4]]

generators 476.124945200378 1200.

badness 206.568540713651 rms 2.18910247435947 g_w 4.55266851389582

177147/175616

map [[0, -3, -11], [1, 3, 8]]

generators 566.505581347493 1200.

badness 281.673403211886 rms 1.07889655377572 g_w 6.39129227512076

1605632/1594323

map [[0, 2, 13], [1, 1, -1]]

generators 351.476961726092 1200.

badness 314.893972274088 rms .713664767134272 g_w 7.61301520051980

67108864/66706983

map [[0, -7, 4], [1, 3, 2]]

generators 242.458056889570 1200.

badness 316.903243699017 rms .762466103296028 g_w 7.46280420851729

13841287201/13759414272

map [[0, 3, 2], [4, 3, 9]]

generators 334.046136423623 300.

badness 705.581672022668 rms .686251415126464 g_w 10.0930249317794

1029/1024

map [[0, 3, -1], [1, 1, 3]]

generators 233.444441296619 1200.

badness 42.1870934730102 rms 1.65379250859746 g_w 2.94374053640771

118098/117649

map [[0, 3, 5], [2, 1, 2]]

generators 433.782535424977 600.

badness 155.357296461064 rms .534890245526000 g_w 6.62250546977042

70632088586703/70368744177664

map [[0, 13, -6], [1, -1, 4]]

generators 238.589951176615 1200.

badness 643.457389814532 rms .271819428385752 g_w 13.3274306917460

94450499584/94143178827

map [[0, -8, -23], [1, 2, 4]]

generators 62.2228613205755 1200.

badness 487.989402670565 rms .197276010332117 g_w 13.5242141244344

4760622968832/4747561509943

map [[0, 15, 19], [1, -3, -3]]

generators 366.784885146694 1200.

badness 579.210669002310 rms .193857182595423 g_w 14.4029532849298

34451725707/34359738368

map [[0, 4, -15], [1, 1, 5]]

generators 175.423395680988 1200.

badness 253.815642297510 rms .188649236250683 g_w 11.0396281212545

33554432/33480783

map [[0, -1, 14], [1, 2, -3]]

generators 497.783581217437 1200.

badness 135.621744048494 rms .185179785930646 g_w 9.01388298147804

282429536481/281974669312

map [[0, 5, 24], [1, 1, 0]]

generators 140.366054018771 1200.

badness 244.087415237322 rms .899689577077160e-1 g_w 13.
9471102220917

68719476736/68641485507

map [[0, 2, -1], [5, 6, 15]]

generators 231.033669889318 240.

badness 117.928158169825 rms .105083431144134 g_w 10.3918871916168

40353607/40310784

map [[0, -1, -1], [9, 18, 29]]

generators 497.942879666076 133.333333333333

badness 74.2853761882641 rms .144418737385944 g_w 8.01235028812647

5559060566555523/5556003412779008

map [[0, 14, 33], [1, -3, -8]]

generators 392.994636775254 1200.

badness 184.673444690140 rms .234734105085574e-1 g_w 19.
8888383853365

1153470752371588581/1152921504606846976

map [[0, 5, -29], [1, 0, 12]]

generators 380.385861981302 1200.

badness 145.368173525748 rms .183370867638466e-1 g_w 19.
9394418821855

11399736556781568/11398895185373143

map [[0, 19, 4], [1, -7, 1]]

generators 542.208280827679 1200.

badness 22.2288637273498 rms .520794634506544e-2 g_w 16.
2212227246308

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> This was done in a way exactly comparable to the most recent 5-limit
> search.

I'll have a much better feel for this if we do the full 7-limit first.
But have we agreed on the 5-limit list yet. Do you agree the weighted
complexity cutoff can be reduced to 13, to give us a list of 20?

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> I'll have a much better feel for this if we do the full 7-limit first.
> But have we agreed on the 5-limit list yet. Do you agree the weighted
> complexity cutoff can be reduced to 13, to give us a list of 20?

It looks OK; hemithirds, ennealimmal and the 10485760000/10460353203
system are really best thought of as 7-limit temperaments.

On Fri, 22 Mar 2002 06:07:25 -0000, "genewardsmith"
<genewardsmith@juno.com> wrote:

>This was done in a way exactly comparable to the most recent 5-limit
>search.

A suggestion: it might be easier to recognize some of the unison vectors if
you supply the prime factorization in addition to the ratio. Here's one I
didn't recognize right away:

>531441/524288

But expressed as 2^-19 * 3^12, it's clear that this is the familiar
Pythagorean comma. As many times as I've seen "531441/524288", it somehow
never stuck in my memory.