This is an Opt In Archive . We would like to hear from you if you want your posts included. For the contact address see About this archive. All posts are copyright (c).

Previous Next

6000 6050 6100 6150 6200 6250 6300 6350 6400 6450 6500 6550 6600 6650 6700 6750 6800 6850 6900 6950

6700 - 6725 -

Message: 6700 - Contents - Hide Contents

Date: Mon, 31 Mar 2003 22:05:33

Subject: Re: 225/225 & 21/20 scales

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

>> [4, -3, 2, -14, -8, 13] [[1, 2, 2, 3], [0, -4, 3, -2]]
>> 
>> bad 2644.480844 comp 14.72969740 rms 12.18857055
>> graham 7 scale size 9 ratio 1.285714
> 
> What's this?


Tertiathirds[9]. Did I miss it?

Message: 6701 - Contents - Hide Contents

Date: Mon, 31 Mar 2003 22:13:16

Subject: Re: 225/224 & 21/20 scales

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...>
wrote:

Orwell[18]

> [7, -3, 8, -21, -7, 27] [[1, 0, 3, 1], [0, 7, -3, 8]]
> 
> bad 1673.187049 comp 25.42062964 rms 2.589237496
> graham 11 scale size 18 ratio 1.636364
> 
Catakleismic[23]
> [6, 5, 22, -6, 18, 37] [[1, 0, 1, -3], [0, 6, 5, 22]]
> 
> bad 1891.474472 comp 34.26986563 rms 1.610555448
> graham 22 scale size 23 ratio 1.045455
> 
Magic[16]
> [5, 1, 12, -10, 5, 25] [[1, 0, 2, -1], [0, 5, 1, 12]]
> 
> bad 1935.541443 comp 21.62473825 rms 4.139050792
> graham 12 scale size 16 ratio 1.333333
> 
Tertiathirds[9]
> [4, -3, 2, -14, -8, 13] [[1, 2, 2, 3], [0, -4, 3, -2]]
> 
> bad 2644.480844 comp 14.72969740 rms 12.18857055
> graham 7 scale size 9 ratio 1.285714
> 
Wizard[34]
> [12, -2, 20, -31, -2, 52] [[2, 1, 5, 2], [0, 6, -1, 10]]
> 
> bad 3656.269932 comp 45.66691577 rms 1.753213831
> graham 22 scale size 34 ratio 1.545455
> 
Slender[29]
> [13, -10, 6, -46, -27, 42] [[1, 2, 2, 3], [0, -13, 10, -6]]
> 
> bad 3872.384714 comp 48.03151022 rms 1.678518039
> graham 23 scale size 29 ratio 1.260870
> 
No Name1[25]
> [8, 1, 18, -17, 6, 39] [[1, -1, 2, -3], [0, 8, 1, 18]]
> 
> bad 3960.691733 comp 33.57393404 rms 3.513715352
> graham 18 scale size 25 ratio 1.388889
> 

No Name2[41]
> [13, 2, 30, -27, 11, 64] [[1, 6, 3, 13], [0, -13, -2, -30]]
> 
> bad 4674.708063 comp 55.18330983 rms 1.535108242
> graham 30 scale size 41 ratio 1.366667

etc.

Message: 6702 - Contents - Hide Contents

Date: Mon, 31 Mar 2003 14:26:46

Subject: Re: 225/225 & 21/20 scales

From: Carl Lumma

>>> >4, -3, 2, -14, -8, 13] [[1, 2, 2, 3], [0, -4, 3, -2]]
>>> 
>>> bad 2644.480844 comp 14.72969740 rms 12.18857055
>>> graham 7 scale size 9 ratio 1.285714
>> 
>> What's this?
>
>Tertiathirds[9].


Ah, tertiathirds.  What the hell is that?  Oh, Negri.  Wait,
it used to be called quadrafourths.


>Did I miss it?


No; for now it's all I can do to catalog your T[n] findings in
the n range I'm interested in.  Looks like this is still complete...


>Pelogic[7]
>
>135/128
>[1, 9/8, 5/4, 4/3, 3/2, 8/5, 15/8]
>[5/4, 15/8, 4/3, 1, 3/2, 9/8, 8/5]
//
>Dominant sevenths[7]
>rms error 20.163 cents
//
>Hemifourths[9]
>rms error 12.690
//
>Tertiathirds[9]
>rms error 12.189 cents
//
>Hexadecimal[9]
>rms error 18.585

-Carl

Message: 6703 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 20:34:47

Subject: Re: a proof?

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:


> 403 Forbidden * [with cont.]  (Wayb.)


There *is* a connection with physics, but that has lead to trouble in
the past, when people have assumed what is regarded as a known truth
by physicists has actually been proven.

Message: 6704 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 20:41:23

Subject: More scales (15/14)

From: Gene Ward Smith

This time, I give only scales where the ratio of the scale size to
Graham complexity is greater than 1.5. I generated the candidates using
standard vals less than 300, a filtered by the above criterion and
geometric badness < 10000 rms error < 30.


[58, 102, -2, 27, -166, -291] [[2, -8, -15, 6], [0, 29, 51, -1]]

bad 2887.493994 comp 232.3870662 rms .5346839936e-1
graham 104 scale size 162 ratio 1.557692


[114, 126, 24, -65, -282, -298] [[6, 15, 20, 18], [0, -19, -21, -4]]

bad 3761.835296 comp 345.4181813 rms .3152894148e-1
graham 126 scale size 216 ratio 1.714286


Superkleismic[22]
[9, 10, -3, -5, -30, -35] [[1, 4, 5, 2], [0, -9, -10, 3]]

bad 3840.251353 comp 30.78274748 rms 4.052704060
graham 13 scale size 22 ratio 1.692308


[23, 40, 1, 10, -63, -110] [[1, 6, 10, 3], [0, -23, -40, -1]]

bad 3956.265168 comp 90.19589386 rms .4863084980
graham 40 scale size 62 ratio 1.550000


[39, 30, -18, -43, -138, -126] [[3, 10, 11, 6], [0, -13, -10, 6]]

bad 4059.370482 comp 126.1804575 rms .2549614346
graham 57 scale size 87 ratio 1.526316


[96, 99, 6, -66, -260, -264] [[3, -2, 0, 8], [0, 32, 33, 2]]

bad 4393.600741 comp 292.1531807 rms .5147535508e-1
graham 99 scale size 189 ratio 1.909091


[35, 62, -3, 17, -103, -181] [[1, 11, 19, 2], [0, -35, -62, 3]]

bad 4941.261559 comp 142.2605120 rms .2441569598
graham 65 scale size 100 ratio 1.538462


[78, 72, -12, -67, -238, -230] [[6, 15, 19, 16], [0, -13, -12, 2]]

bad 4984.411853 comp 241.4906133 rms .8546994238e-1
graham 90 scale size 162 ratio 1.800000


[18, 15, -6, -18, -60, -56] [[3, 6, 8, 8], [0, -6, -5, 2]]

bad 5233.367262 comp 57.03464162 rms 1.608806378
graham 24 scale size 39 ratio 1.625000


[39, 42, 6, -24, -100, -104] [[3, 2, 4, 8], [0, 13, 14, 2]]

bad 6741.803387 comp 118.2809250 rms .4818886068
graham 42 scale size 75 ratio 1.785714


[57, 57, 0, -42, -160, -160] [[57, 90, 132, 160], [0, 1, 1, 0]]

bad 7545.107663 comp 174.1058254 rms .2489079892
graham 57 scale size 114 ratio 2.000000


[5, 6, -3, -2, -19, -24] [[1, 3, 4, 2], [0, -5, -6, 3]]

bad 7632.868860 comp 18.86661942 rms 21.44369508
graham 9 scale size 14 ratio 1.555556


[13, 9, 1, -16, -35, -23] [[1, 4, 4, 3], [0, -13, -9, -1]]

bad 8319.246343 comp 36.38471902 rms 6.284141184
graham 13 scale size 21 ratio 1.615385


[30, 25, -15, -30, -108, -105] [[5, 6, 10, 15], [0, 6, 5, -3]]

bad 8340.679677 comp 99.57644467 rms .8411785906
graham 45 scale size 70 ratio 1.555556


[19, 14, 4, -22, -47, -30] [[1, -7, -4, 1], [0, 19, 14, 4]]

bad 8342.374006 comp 52.44877833 rms 3.032626340
graham 19 scale size 29 ratio 1.526316


[20, 28, 2, -2, -53, -74] [[2, 7, 10, 6], [0, -10, -14, -1]]

bad 8365.352429 comp 68.41183346 rms 1.787400120
graham 28 scale size 46 ratio 1.642857


[21, 27, -7, -6, -70, -92] [[1, -8, -10, 6], [0, 21, 27, -7]]

bad 8474.527074 comp 75.92946628 rms 1.469923649
graham 34 scale size 55 ratio 1.617647


[27, 20, -9, -31, -90, -77] [[1, -11, -7, 7], [0, 27, 20, -9]]

bad 9664.899556 comp 83.79301090 rms 1.376517550
graham 36 scale size 56 ratio 1.555556


[15, 10, 0, -19, -42, -28] [[5, 7, 11, 14], [0, 3, 2, 0]]

bad 9904.666920 comp 42.41464423 rms 5.505645170
graham 15 scale size 25 ratio 1.666667

Message: 6705 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 20:42:33

Subject: More scales (21/20)

From: Gene Ward Smith

Orwell[18]
[7, -3, 8, -21, -7, 27] [[1, 0, 3, 1], [0, 7, -3, 8]]

bad 1673.187049 comp 25.42062964 rms 2.589237496
graham 11 scale size 18 ratio 1.636364


Wizard[34]
[12, -2, 20, -31, -2, 52] [[2, 1, 5, 2], [0, 6, -1, 10]]

bad 3656.269932 comp 45.66691577 rms 1.753213831
graham 22 scale size 34 ratio 1.545455


[11, -6, 10, -35, -15, 40] [[1, 4, 1, 5], [0, -11, 6, -10]]

bad 5333.482178 comp 39.77267622 rms 3.371640164
graham 17 scale size 27 ratio 1.588235


[23, -1, 13, -55, -44, 33] [[1, 9, 2, 7], [0, -23, 1, -13]]

bad 5401.759921 comp 66.37173527 rms 1.226221520
graham 24 scale size 37 ratio 1.541667


[17, 6, 15, -30, -24, 18] [[1, -5, 0, -3], [0, 17, 6, 15]]

bad 5437.329959 comp 46.92112111 rms 2.469726876
graham 17 scale size 26 ratio 1.529412


[9, 0, 9, -21, -11, 21] [[9, 14, 21, 25], [0, 1, 0, 1]]

bad 5972.212792 comp 27.49039349 rms 7.902661154
graham 9 scale size 18 ratio 2.000000


[45, -18, 45, -133, -55, 155] [[9, 14, 21, 25], [0, 5, -2, 5]]

bad 6149.867692 comp 156.9517242 rms .2496511612
graham 63 scale size 108 ratio 1.714286


[19, -5, 28, -52, -9, 79] [[1, -1, 3, -1], [0, 19, -5, 28]]

bad 7433.465748 comp 70.68042097 rms 1.487966281
graham 33 scale size 52 ratio 1.575758


[18, -9, 18, -56, -22, 67] [[9, 14, 21, 25], [0, 2, -1, 2]]

bad 7569.695667 comp 65.10901923 rms 1.785649073
graham 27 scale size 45 ratio 1.666667


[63, 9, 63, -132, -77, 121] [[9, 15, 21, 26], [0, -7, -1, -7]]

bad 7638.500292 comp 185.2199094 rms .2226551602
graham 63 scale size 117 ratio 1.857143


[52, 3, 82, -116, -16, 182] [[1, -4, 2, -6], [0, 52, 3, 82]]

bad 7639.174124 comp 181.3070820 rms .2323896986
graham 82 scale size 131 ratio 1.597561


[13, -3, 11, -35, -19, 34] [[1, 3, 2, 4], [0, -13, 3, -11]]

bad 7703.565761 comp 41.46170035 rms 4.481233532
graham 16 scale size 27 ratio 1.687500


[27, -9, 27, -77, -33, 88] [[9, 14, 21, 25], [0, 3, -1, 3]]

bad 7813.658642 comp 91.95432747 rms .9240811032
graham 36 scale size 63 ratio 1.750000


[20, -6, 19, -56, -26, 61] [[1, 6, 1, 7], [0, -20, 6, -19]]

bad 8132.442880 comp 66.64178162 rms 1.831166453
graham 26 scale size 45 ratio 1.730769


[75, -10, 124, -190, -14, 316] [[1, -11, 4, -18], [0, 75, -10, 124]]

bad 8390.566851 comp 281.6367635 rms .1057822042
graham 134 scale size 209 ratio 1.559701


[9, -2, 14, -24, -3, 38] [[1, 3, 2, 5], [0, -9, 2, -14]]

bad 8811.637847 comp 33.78049801 rms 7.721906590
graham 16 scale size 25 ratio 1.562500


[28, 12, 30, -46, -31, 36] [[2, -3, 2, -1], [0, 14, 6, 15]]

bad 9077.038437 comp 79.24358852 rms 1.445492711
graham 30 scale size 46 ratio 1.533333


[81, 36, 81, -131, -99, 87] [[9, 10, 19, 21], [0, 9, 4, 9]]

bad 9611.001444 comp 225.6179519 rms .1888084111
graham 81 scale size 126 ratio 1.555556

Message: 6706 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 05:57:50

Subject: a proof?

From: wallyesterpaulrus

403 Forbidden * [with cont.]  (Wayb.)

Message: 6707 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 20:53:39

Subject: More scales (36/35)

From: Gene Ward Smith

These are getting rather long, so I'll only give it up to badness 5000.

Quatraschismic[55]
[4, -32, -15, -60, -35, 55] [[1, 1, 7, 5], [0, 4, -32, -15]]

bad 806.2259448 comp 66.22833900 rms .1838099613
graham 36 scale size 55 ratio 1.527778


Miracle[21]
[6, -7, -2, -25, -20, 15] [[1, 1, 3, 3], [0, 6, -7, -2]]

bad 1017.380174 comp 24.92662918 rms 1.637405196
graham 13 scale size 21 ratio 1.615385


[22, -5, 3, -59, -57, 21] [[1, 3, 2, 3], [0, -22, 5, -3]]

bad 1096.707526 comp 65.79468212 rms .2533431918
graham 27 scale size 46 ratio 1.703704


Pajara[12]
[2, -4, -4, -11, -12, 2] [[2, 3, 5, 6], [0, 1, -2, -2]]

bad 1550.521632 comp 11.92510946 rms 10.90317748
graham 6 scale size 12 ratio 2.000000


Hemiwuerschmidt[25]
[16, 2, 5, -34, -37, 6] [[1, -1, 2, 2], [0, 16, 2, 5]]

bad 1682.562821 comp 43.84212121 rms .8753629708
graham 16 scale size 25 ratio 1.562500


Schismic[24]
[1, -8, -14, -15, -25, -10] [[1, 2, -1, -3], [0, -1, 8, 14]]

bad 1704.355358 comp 24.41447356 rms 2.859337512
graham 15 scale size 24 ratio 1.600000


[20, -30, -10, -94, -72, 61] [[10, 16, 23, 28], [0, -2, 3, 1]]

bad 1994.466122 comp 93.33508779 rms .2289479626
graham 50 scale size 80 ratio 1.600000


Beatles[17]
[2, -9, -4, -19, -12, 16] [[1, 1, 5, 4], [0, 2, -9, -4]]

bad 2483.820841 comp 19.94265310 rms 6.245315704
graham 11 scale size 17 ratio 1.545455


[2, -57, -28, -95, -50, 95] [[1, 1, 19, 11], [0, 2, -57, -28]]

bad 2515.083696 comp 111.6536821 rms .2017466548
graham 59 scale size 89 ratio 1.508475


[7, -56, -69, -105, -129, -3] [[1, 4, -17, -21], [0, -7, 56, 69]]

bad 2569.597244 comp 139.3093296 rms .1324050816
graham 76 scale size 139 ratio 1.828947


[38, -3, 8, -93, -94, 27] [[1, -7, 3, 1], [0, 38, -3, 8]]

bad 2717.059833 comp 108.9991134 rms .2286932106
graham 41 scale size 71 ratio 1.731707


[11, 83, 87, 106, 107, -31] [[1, 3, 13, 14], [0, -11, -83, -87]]

bad 2823.202696 comp 171.1977547 rms .9632653338e-1
graham 87 scale size 148 ratio 1.701149


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

bad 2839.251643 comp 32.44371033 rms 2.697384486
graham 17 scale size 33 ratio 1.941176


[25, -29, -51, -104, -151, -37] [[1, 1, 3, 4], [0, 25, -29, -51]]

bad 2999.836419 comp 128.1794899 rms .1825830659
graham 76 scale size 130 ratio 1.710526


[26, -37, -12, -119, -92, 76] [[1, -1, 6, 4], [0, 26, -37, -12]]

bad 3100.719951 comp 118.1864165 rms .2219869346
graham 63 scale size 101 ratio 1.603175


[42, -35, -7, -153, -129, 82] [[7, 9, 18, 20], [0, 6, -5, -1]]

bad 3179.506415 comp 154.6706492 rms .1329057862
graham 77 scale size 126 ratio 1.636364


Nameless1[24]
[5, -4, -10, -18, -30, -12] [[1, 2, 2, 2], [0, -5, 4, 10]]

bad 3559.349903 comp 24.27272427 rms 6.041345016
graham 15 scale size 24 ratio 1.600000


Hemithird[37]
[15, -2, -5, -38, -50, -6] [[1, 4, 2, 2], [0, -15, 2, 5]]

bad 3633.506097 comp 45.81266906 rms 1.731229740
graham 20 scale size 37 ratio 1.850000


[7, -15, -16, -40, -45, 5] [[1, 5, -5, -5], [0, -7, 15, 16]]

bad 3753.682125 comp 44.35287385 rms 1.908156371
graham 23 scale size 45 ratio 1.956522


[14, -23, -8, -69, -52, 46] [[1, 3, 0, 2], [0, -14, 23, 8]]

bad 3923.865486 comp 68.53846993 rms .8353054234
graham 37 scale size 59 ratio 1.594595


Nameless2[21]
[3, -7, -8, -18, -21, 1] [[1, 3, -1, -1], [0, -3, 7, 8]]

bad 4088.324637 comp 20.55304683 rms 9.678163406
graham 11 scale size 21 ratio 1.909091


[8, -16, -6, -44, -32, 31] [[2, 4, 3, 5], [0, -4, 8, 3]]

bad 4109.453916 comp 43.88939274 rms 2.133364042
graham 24 scale size 38 ratio 1.583333


Nameless3[17]
[3, -5, -6, -15, -18, 0] [[1, 3, 0, 0], [0, -3, 5, 6]]

bad 4123.788393 comp 16.70536648 rms 14.77693479
graham 9 scale size 17 ratio 1.888889


[10, -39, -17, -85, -55, 70] [[1, 5, -11, -3], [0, -10, 39, 17]]

bad 4138.593302 comp 88.64147767 rms .5267187470
graham 49 scale size 76 ratio 1.551020


[2, -6, -6, -14, -15, 3] [[2, 3, 5, 6], [0, 1, -3, -3]]

bad 4244.507950 comp 15.87113261 rms 16.85045028
graham 8 scale size 16 ratio 2.000000


[6, -2, -2, -17, -20, 1] [[2, 2, 5, 6], [0, 3, -1, -1]]

bad 4316.252443 comp 19.12683103 rms 11.79833694
graham 8 scale size 16 ratio 2.000000


[6, -19, -26, -44, -58, -7] [[1, 2, 1, 1], [0, -6, 19, 26]]

bad 4581.275208 comp 55.50097057 rms 1.487254275
graham 32 scale size 57 ratio 1.781250


[43, -2, -33, -103, -173, -71] [[1, -13, 3, 14], [0, 43, -2, -33]]

bad 4698.397626 comp 142.7492493 rms .2305696298
graham 76 scale size 121 ratio 1.592105


[1, 33, 27, 50, 40, -30] [[1, 2, 16, 14], [0, -1, -33, -27]]

bad 4988.312470 comp 65.75753976 rms 1.153619365
graham 33 scale size 58 ratio 1.757576


[8, -11, -6, -36, -32, 17] [[1, 4, -1, 1], [0, -8, 11, 6]]

bad 4988.607974 comp 36.19566507 rms 3.807730956
graham 19 scale size 33 ratio 1.736842

Message: 6708 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 20:56:49

Subject: More scales (49/48)

From: Gene Ward Smith

Meantone[19]
[1, 4, 10, 4, 13, 12] [[1, 2, 4, 7], [0, -1, -4, -10]]

bad 835.8644295 comp 15.10180564 rms 3.665034700
graham 10 scale size 19 ratio 1.900000


[15, 51, 72, 46, 72, 24] [[3, 3, 1, 0], [0, 5, 17, 24]]

bad 1103.703155 comp 119.5590291 rms .7721248404e-1
graham 72 scale size 129 ratio 1.791667


[19, 19, 57, -14, 37, 79] [[19, 30, 44, 53], [0, 1, 1, 3]]

bad 1128.943760 comp 89.73537466 rms .1401990099
graham 57 scale size 95 ratio 1.666667


Infraschismic[77]
[1, -8, 39, -15, 59, 113] [[1, 2, -1, 19], [0, -1, 8, -39]]

bad 1159.472962 comp 72.04051068 rms .2234122900
graham 47 scale size 77 ratio 1.638298


[3, -24, -54, -45, -94, -58] [[3, 5, 5, 4], [0, -1, 8, 18]]

bad 1162.373338 comp 88.95093793 rms .1469077057
graham 57 scale size 111 ratio 1.947368


[37, 46, 75, -13, 15, 45] [[1, 15, 19, 30], [0, -37, -46, -75]]

bad 1251.495304 comp 133.5646435 rms .7015299320e-1
graham 75 scale size 113 ratio 1.506667


Pajara[10]
[2, -4, -4, -11, -12, 2] [[2, 3, 5, 6], [0, 1, -2, -2]]

bad 1550.521632 comp 11.92510946 rms 10.90317748
graham 6 scale size 10 ratio 1.666667


Augmented[15]
[3, 0, -6, -7, -18, -14] [[3, 5, 7, 8], [0, -1, 0, 2]]

bad 1626.237930 comp 14.16874337 rms 8.100678900
graham 9 scale size 15 ratio 1.666667


Schismic[29]
[1, -8, -14, -15, -25, -10] [[1, 2, -1, -3], [0, -1, 8, 14]]

bad 1704.355358 comp 24.41447356 rms 2.859337512
graham 15 scale size 29 ratio 1.933333


[21, 3, -36, -44, -116, -92] [[3, 5, 7, 8], [0, -7, -1, 12]]

bad 1875.441808 comp 91.94917886 rms .2218236682
graham 57 scale size 93 ratio 1.631579


Catakleismic[38]
[6, 5, 22, -6, 18, 37] [[1, 0, 1, -3], [0, 6, 5, 22]]

bad 1891.474472 comp 34.26986563 rms 1.610555448
graham 22 scale size 38 ratio 1.727273


Magic[19]
[5, 1, 12, -10, 5, 25] [[1, 0, 2, -1], [0, 5, 1, 12]]

bad 1935.541443 comp 21.62473825 rms 4.139050792
graham 12 scale size 19 ratio 1.583333



Duodecimal[48] ?
[0, 12, 24, 19, 38, 22] [[12, 19, 28, 34], [0, 0, -1, -2]]

bad 2254.400881 comp 38.80790989 rms 1.496892592
graham 24 scale size 48 ratio 2.000000


[3, -12, -30, -26, -56, -36] [[3, 5, 6, 6], [0, -1, 4, 10]]

bad 2280.649235 comp 50.50205396 rms .8942118330
graham 33 scale size 63 ratio 1.909091


Check this out Carl[10]
[2, 1, -4, -3, -12, -12] [[1, 1, 2, 4], [0, 2, 1, -4]]

bad 2431.810368 comp 9.849243627 rms 25.06824586
graham 6 scale size 10 ratio 1.666667


[4, 21, -56, 24, -100, -189] [[1, 0, -6, 25], [0, 4, 21, -56]]

bad 2524.338456 comp 116.4675612 rms .1860962494
graham 77 scale size 116 ratio 1.506494


[7, -56, -69, -105, -129, -3] [[1, 4, -17, -21], [0, -7, 56, 69]]

bad 2569.597244 comp 139.3093296 rms .1324050816
graham 76 scale size 145 ratio 1.907895


[13, 14, 35, -8, 19, 42] [[1, 5, 6, 12], [0, -13, -14, -35]]

bad 2640.470526 comp 56.11257541 rms .8386117054
graham 35 scale size 57 ratio 1.628571


Here's another Carl[10]
[2, 6, 6, 5, 4, -3] [[2, 3, 4, 5], [0, 1, 3, 3]]

bad 2682.600306 comp 11.92510946 rms 18.86388854
graham 6 scale size 10 ratio 1.666667


[2, -4, -16, -11, -31, -26] [[2, 3, 5, 7], [0, 1, -2, -8]]

bad 2780.393711 comp 26.97297092 rms 3.821630806
graham 18 scale size 34 ratio 1.888889


[11, 83, 87, 106, 107, -31] [[1, 3, 13, 14], [0, -11, -83, -87]]

bad 2823.202696 comp 171.1977547 rms .9632653338e-1
graham 87 scale size 163 ratio 1.873563


[2, 8, 8, 8, 7, -4] [[2, 3, 4, 5], [0, 1, 4, 4]]

bad 2825.971089 comp 15.87113261 rms 11.21894125
graham 8 scale size 14 ratio 1.750000


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

bad 2839.251643 comp 32.44371033 rms 2.697384486
graham 17 scale size 29 ratio 1.705882


[4, -8, -20, -22, -43, -24] [[4, 6, 10, 13], [0, 1, -2, -5]]

bad 2979.183549 comp 36.62986166 rms 2.220376920
graham 24 scale size 44 ratio 1.833333


[25, -29, -51, -104, -151, -37] [[1, 1, 3, 4], [0, 25, -29, -51]]

bad 2999.836419 comp 128.1794899 rms .1825830659
graham 76 scale size 127 ratio 1.671053


[14, 6, 74, -23, 78, 155] [[2, 4, 5, 10], [0, -7, -3, -37]]

bad 3105.726517 comp 118.0421791 rms .2228890708
graham 74 scale size 134 ratio 1.810811


[6, 5, -31, -6, -66, -86] [[1, 0, 1, 11], [0, 6, 5, -31]]

bad 3127.379354 comp 60.20409280 rms .8628365462
graham 37 scale size 68 ratio 1.837838


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

bad 3484.642607 comp 19.98216005 rms 8.727168798
graham 12 scale size 19 ratio 1.583333


[5, -4, -10, -18, -30, -12] [[1, 2, 2, 2], [0, -5, 4, 10]]

bad 3559.349903 comp 24.27272427 rms 6.041345016
graham 15 scale size 25 ratio 1.666667


[3, 0, 9, -7, 6, 21] [[3, 5, 7, 9], [0, -1, 0, -3]]

bad 3577.956662 comp 15.95957268 rms 14.04729032
graham 9 scale size 15 ratio 1.666667


[7, -15, -16, -40, -45, 5] [[1, 5, -5, -5], [0, -7, 15, 16]]

bad 3753.682125 comp 44.35287385 rms 1.908156371
graham 23 scale size 39 ratio 1.695652


[7, 9, 32, -2, 31, 49] [[1, -1, -1, -9], [0, 7, 9, 32]]

bad 3793.215226 comp 48.34611818 rms 1.622871997
graham 32 scale size 57 ratio 1.781250


[4, -20, -44, -41, -81, -46] [[4, 6, 11, 15], [0, 1, -5, -11]]

bad 3844.761675 comp 74.60232426 rms .6908196906
graham 48 scale size 92 ratio 1.916667


[8, 1, -13, -17, -43, -33] [[1, -1, 2, 7], [0, 8, 1, -13]]

bad 3868.273092 comp 34.07459350 rms 3.331622296
graham 21 scale size 34 ratio 1.619048


[12, 10, 25, -12, 6, 30] [[1, 6, 6, 12], [0, -12, -10, -25]]

bad 3886.016957 comp 43.45704720 rms 2.057710454
graham 25 scale size 38 ratio 1.520000


[0, 0, 12, 0, 19, 28] [[12, 19, 28, 34], [0, 0, 0, -1]]

bad 3914.199361 comp 19.94372148 rms 9.840803064
graham 12 scale size 24 ratio 2.000000


[24, -9, -66, -70, -172, -128] [[3, 2, 8, 16], [0, 8, -3, -22]]

bad 4033.584203 comp 136.9571741 rms .2150411404
graham 90 scale size 156 ratio 1.733333


[2, -16, -40, -30, -69, -48] [[2, 3, 6, 9], [0, 1, -8, -20]]

bad 4064.299560 comp 64.92532025 rms .9641786468
graham 42 scale size 82 ratio 1.952381



[3, -7, -8, -18, -21, 1] [[1, 3, -1, -1], [0, -3, 7, 8]]

bad 4088.324637 comp 20.55304683 rms 9.678163406
graham 11 scale size 19 ratio 1.727273


[3, -5, -6, -15, -18, 0] [[1, 3, 0, 0], [0, -3, 5, 6]]

bad 4123.788393 comp 16.70536648 rms 14.77693479
graham 9 scale size 15 ratio 1.666667


[2, -6, -6, -14, -15, 3] [[2, 3, 5, 6], [0, 1, -3, -3]]

bad 4244.507950 comp 15.87113261 rms 16.85045028
graham 8 scale size 14 ratio 1.750000


[5, 8, 14, 1, 8, 10] [[1, 2, 3, 4], [0, -5, -8, -14]]

bad 4438.739309 comp 22.70605088 rms 8.609470174
graham 14 scale size 23 ratio 1.642857


[42, 18, -48, -69, -194, -162] [[6, 12, 15, 14], [0, -7, -3, 8]]

bad 4446.741506 comp 158.1758818 rms .1777302516
graham 90 scale size 138 ratio 1.533333


[3, 5, 16, 1, 17, 23] [[1, 2, 3, 5], [0, -3, -5, -16]]

bad 4475.490403 comp 23.94716411 rms 7.804272934
graham 16 scale size 29 ratio 1.812500


[8, 13, 23, 2, 14, 17] [[1, 2, 3, 4], [0, -8, -13, -23]]

bad 4517.316135 comp 37.08137627 rms 3.285252812
graham 23 scale size 38 ratio 1.652174


[6, -36, -84, -71, -150, -94] [[6, 10, 11, 10], [0, -1, 6, 14]]

bad 4524.688632 comp 139.3535064 rms .2329983774
graham 90 scale size 174 ratio 1.933333


[6, -19, -26, -44, -58, -7] [[1, 2, 1, 1], [0, -6, 19, 26]]

bad 4581.275208 comp 55.50097057 rms 1.487254275
graham 32 scale size 58 ratio 1.812500


[13, 2, 30, -27, 11, 64] [[1, 6, 3, 13], [0, -13, -2, -30]]

bad 4674.708063 comp 55.18330983 rms 1.535108242
graham 30 scale size 47 ratio 1.566667


[0, 0, 19, 0, 30, 44] [[19, 30, 44, 53], [0, 0, 0, 1]]

bad 4848.358890 comp 31.57755902 rms 4.862254076
graham 19 scale size 38 ratio 2.000000


[1, 16, 34, 23, 51, 34] [[1, 2, 9, 17], [0, -1, -16, -34]]

bad 4849.147837 comp 53.59263278 rms 1.688321844
graham 34 scale size 67 ratio 1.970588


[3, 12, 11, 12, 9, -8] [[1, 3, 8, 8], [0, -3, -12, -11]]

bad 4859.392907 comp 23.16666620 rms 9.054301108
graham 12 scale size 19 ratio 1.583333


[15, 39, 48, 27, 34, 2] [[3, 4, 5, 6], [0, 5, 13, 16]]

bad 4873.326095 comp 84.95415769 rms .6752369450
graham 48 scale size 81 ratio 1.687500


[7, 26, 25, 25, 20, -15] [[1, 5, 15, 15], [0, -7, -26, -25]]

bad 4890.319502 comp 50.87738861 rms 1.889242078
graham 26 scale size 43 ratio 1.653846


[1, 33, 27, 50, 40, -30] [[1, 2, 16, 14], [0, -1, -33, -27]]

bad 4988.312470 comp 65.75753976 rms 1.153619365
graham 33 scale size 53 ratio 1.606061


[3, 12, 18, 12, 20, 8] [[3, 5, 8, 10], [0, -1, -4, -6]]

bad 4991.565409 comp 29.37953135 rms 5.782918062
graham 18 scale size 33 ratio 1.833333


[32, 33, 92, -22, 56, 121] [[1, 10, 11, 27], [0, -32, -33, -92]]

bad 4997.016683 comp 145.6972665 rms .2354008310
graham 92 scale size 152 ratio 1.652174

Message: 6709 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 20:48:29

Subject: More scales (25/24)

From: Gene Ward Smith

Quatraschismic[68]
[4, -32, -15, -60, -35, 55] [[1, 1, 7, 5], [0, 4, -32, -15]]

bad 806.2259448 comp 66.22833900 rms .1838099613
graham 36 scale size 68 ratio 1.888889


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

bad 1017.380174 comp 24.92662918 rms 1.637405196
graham 13 scale size 20 ratio 1.538462


Hemififth[48]
[2, 25, 13, 35, 15, -40] [[1, 1, -5, -1], [0, 2, 25, 13]]

bad 1262.620150 comp 46.45156504 rms .5851564738
graham 25 scale size 48 ratio 1.920000


Pajara[10]
[2, -4, -4, -11, -12, 2] [[2, 3, 5, 6], [0, 1, -2, -2]]

bad 1550.521632 comp 11.92510946 rms 10.90317748
graham 6 scale size 10 ratio 1.666667


[14, 59, 33, 61, 13, -89] [[1, -3, -17, -8], [0, 14, 59, 33]]

bad 1635.576289 comp 106.6204474 rms .1438764803
graham 59 scale size 104 ratio 1.762712


Blackwood[10]
[0, 5, 0, 8, 0, -14] [[5, 8, 12, 14], [0, 0, -1, 0]]

bad 1662.988586 comp 10.25428060 rms 15.81535241
graham 5 scale size 10 ratio 2.000000


[20, -30, -10, -94, -72, 61] [[10, 16, 23, 28], [0, -2, 3, 1]]

bad 1994.466122 comp 93.33508779 rms .2289479626
graham 50 scale size 80 ratio 1.600000


Supermajor seconds[21]
[3, 12, -1, 12, -10, -36] [[1, 1, 0, 3], [0, 3, 12, -1]]

bad 2171.962763 comp 24.63368766 rms 3.579262202
graham 13 scale size 21 ratio 1.615385


[12, 34, 20, 26, -2, -49] [[2, 4, 7, 7], [0, -6, -17, -10]]

bad 2344.370133 comp 62.49168223 rms .6003185294
graham 34 scale size 56 ratio 1.647059


Octafifths[28]
[8, 18, 11, 10, -5, -25] [[1, 1, 1, 2], [0, 8, 18, 11]]

bad 2419.357927 comp 34.23414359 rms 2.064339812
graham 18 scale size 28 ratio 1.555556

Superpythagorean[17]
[1, 9, -2, 12, -6, -30] [[1, 2, 6, 2], [0, -1, -9, 2]]

bad 2430.162102 comp 19.47032028 rms 6.410457906
graham 11 scale size 17 ratio 1.545455


Beatles[20]
[2, -9, -4, -19, -12, 16] [[1, 1, 5, 4], [0, 2, -9, -4]]

bad 2483.820841 comp 19.94265310 rms 6.245315704
graham 11 scale size 20 ratio 1.818182


[2, -57, -28, -95, -50, 95] [[1, 1, 19, 11], [0, 2, -57, -28]]

bad 2515.083696 comp 111.6536821 rms .2017466548
graham 59 scale size 116 ratio 1.966102


[7, -56, -69, -105, -129, -3] [[1, 4, -17, -21], [0, -7, 56, 69]]

bad 2569.597244 comp 139.3093296 rms .1324050816
graham 76 scale size 119 ratio 1.565789


NB Carl
[2, 6, 6, 5, 4, -3] [[2, 3, 4, 5], [0, 1, 3, 3]]

bad 2682.600306 comp 11.92510946 rms 18.86388854
graham 6 scale size 10 ratio 1.666667


[11, 83, 87, 106, 107, -31] [[1, 3, 13, 14], [0, -11, -83, -87]]

bad 2823.202696 comp 171.1977547 rms .9632653338e-1
graham 87 scale size 155 ratio 1.781609


NB Carl
[2, 8, 8, 8, 7, -4] [[2, 3, 4, 5], [0, 1, 4, 4]]

bad 2825.971089 comp 15.87113261 rms 11.21894125
graham 8 scale size 14 ratio 1.750000


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

bad 2839.251643 comp 32.44371033 rms 2.697384486
graham 17 scale size 27 ratio 1.588235


Squares[28]
[4, 16, 9, 16, 3, -24] [[1, 3, 8, 6], [0, -4, -16, -9]]

bad 2880.870812 comp 28.92292245 rms 3.443812018
graham 16 scale size 28 ratio 1.750000


Hemifourths[14]
[2, 8, 1, 8, -4, -20] [[1, 2, 4, 3], [0, -2, -8, -1]]

bad 2970.086939 comp 15.29862606 rms 12.69007834
graham 8 scale size 14 ratio 1.750000


[26, -37, -12, -119, -92, 76] [[1, -1, 6, 4], [0, 26, -37, -12]]

bad 3100.719951 comp 118.1864165 rms .2219869346
graham 63 scale size 100 ratio 1.587302


[20, 52, 31, 36, -7, -74] [[1, 3, 6, 5], [0, -20, -52, -31]]

bad 3218.975776 comp 96.52895125 rms .3454637898
graham 52 scale size 84 ratio 1.615385


Supersupermajor[31]
[3, 17, -1, 20, -10, -50] [[1, 1, -1, 3], [0, 3, 17, -1]]

bad 3230.112914 comp 34.40312184 rms 2.729116010
graham 18 scale size 31 ratio 1.722222


[7, -15, -16, -40, -45, 5] [[1, 5, -5, -5], [0, -7, 15, 16]]

bad 3753.682125 comp 44.35287385 rms 1.908156371
graham 23 scale size 37 ratio 1.608696


[7, 38, -4, 44, -26, -116] [[1, 3, 10, 2], [0, -7, -38, 4]]

bad 3828.476155 comp 78.25908571 rms .6251099432
graham 42 scale size 69 ratio 1.642857


[14, -23, -8, -69, -52, 46] [[1, 3, 0, 2], [0, -14, 23, 8]]

bad 3923.865486 comp 68.53846993 rms .8353054234
graham 37 scale size 60 ratio 1.621622


[3, -7, -8, -18, -21, 1] [[1, 3, -1, -1], [0, -3, 7, 8]]

bad 4088.324637 comp 20.55304683 rms 9.678163406
graham 11 scale size 17 ratio 1.545455


[8, -16, -6, -44, -32, 31] [[2, 4, 3, 5], [0, -4, 8, 3]]

bad 4109.453916 comp 43.88939274 rms 2.133364042
graham 24 scale size 40 ratio 1.666667


[10, -39, -17, -85, -55, 70] [[1, 5, -11, -3], [0, -10, 39, 17]]

bad 4138.593302 comp 88.64147767 rms .5267187470
graham 49 scale size 88 ratio 1.795918


[16, 84, 46, 96, 28, -129] [[2, 4, 9, 8], [0, -8, -42, -23]]

bad 4175.315972 comp 152.1385061 rms .1803894157
graham 84 scale size 152 ratio 1.809524


[2, -6, -6, -14, -15, 3] [[2, 3, 5, 6], [0, 1, -3, -3]]

bad 4244.507950 comp 15.87113261 rms 16.85045028
graham 8 scale size 14 ratio 1.750000


[13, 67, -6, 76, -46, -202] [[1, -1, -11, 4], [0, 13, 67, -6]]

bad 4551.129119 comp 137.1901910 rms .2418093198
graham 73 scale size 121 ratio 1.657534


[6, 29, -2, 32, -20, -86] [[1, 4, 14, 2], [0, -6, -29, 2]]

bad 4693.393783 comp 58.95452867 rms 1.350369594
graham 31 scale size 52 ratio 1.677419


[3, -24, -1, -45, -10, 65] [[1, 1, 7, 3], [0, 3, -24, -1]]

bad 4789.919936 comp 51.59695464 rms 1.799202788
graham 27 scale size 51 ratio 1.888889


[30, 61, 38, 27, -24, -83] [[1, -3, -7, -3], [0, 30, 61, 38]]

bad 4806.311234 comp 118.8004970 rms .3405456798
graham 61 scale size 92 ratio 1.508197


[3, 12, 11, 12, 9, -8] [[1, 3, 8, 8], [0, -3, -12, -11]]

bad 4859.392907 comp 23.16666620 rms 9.054301108
graham 12 scale size 21 ratio 1.750000


[7, 26, 25, 25, 20, -15] [[1, 5, 15, 15], [0, -7, -26, -25]]

bad 4890.319502 comp 50.87738861 rms 1.889242078
graham 26 scale size 45 ratio 1.730769


[1, 33, 27, 50, 40, -30] [[1, 2, 16, 14], [0, -1, -33, -27]]

bad 4988.312470 comp 65.75753976 rms 1.153619365
graham 33 scale size 65 ratio 1.969697


[8, -11, -6, -36, -32, 17] [[1, 4, -1, 1], [0, -8, 11, 6]]

bad 4988.607974 comp 36.19566507 rms 3.807730956
graham 19 scale size 30 ratio 1.578947


[4, 21, -3, 24, -16, -66] [[1, 0, -6, 4], [0, 4, 21, -3]]

bad 5155.606183 comp 43.89813671 rms 2.675392852
graham 24 scale size 38 ratio 1.583333


[6, -12, -2, -33, -20, 29] [[2, 2, 7, 6], [0, 3, -6, -1]]

bad 5210.520687 comp 32.97178432 rms 4.792876340
graham 18 scale size 30 ratio 1.666667


[6, 41, 22, 51, 18, -64] [[1, 3, 12, 8], [0, -6, -41, -22]]

bad 5272.772051 comp 74.77203531 rms .9431061824
graham 41 scale size 76 ratio 1.853659


[1, -8, -2, -15, -6, 18] [[1, 2, -1, 2], [0, -1, 8, 2]]

bad 5451.864616 comp 16.64869341 rms 19.66911190
graham 9 scale size 17 ratio 1.888889


[8, 66, 35, 86, 33, -104] [[1, 3, 14, 9], [0, -8, -66, -35]]

bad 5508.324105 comp 121.0812738 rms .3757210468
graham 66 scale size 124 ratio 1.878788

[27, -45, 27, -134, -33, 189] [[9, 13, 23, 24], [0, 3, -5, 3]]

bad 5580.116645 comp 147.9383210 rms .2549657862
graham 72 scale size 117 ratio 1.625000


[5, 18, 17, 17, 13, -11] [[1, 4, 11, 11], [0, -5, -18, -17]]

bad 5619.674186 comp 35.02857965 rms 4.580006366
graham 18 scale size 31 ratio 1.722222


[1, -37, -43, -61, -71, 4] [[1, 2, -13, -15], [0, -1, 37, 43]]

bad 5627.373521 comp 85.06872292 rms .7776173046
graham 44 scale size 75 ratio 1.704545


[29, -61, -66, -164, -186, 18] [[1, 16, -28, -30], [0, -29, 61, 66]]

bad 5677.494450 comp 182.1474610 rms .1711238232
graham 95 scale size 151 ratio 1.589474


[20, 105, -10, 120, -72, -318] [[5, 8, 12, 14], [0, -4, -21, 2]]

bad 5830.074186 comp 215.4428685 rms .1256058409
graham 115 scale size 190 ratio 1.652174


[5, -9, -10, -26, -30, 2] [[1, 4, -2, -2], [0, -5, 9, 10]]

bad 5929.557384 comp 28.59776268 rms 7.250336456
graham 15 scale size 23 ratio 1.533333


[1, 14, -2, 20, -6, -44] [[1, 2, 8, 2], [0, -1, -14, 2]]

bad 5995.726244 comp 29.52506360 rms 6.877967380
graham 16 scale size 27 ratio 1.687500


[5, -40, -29, -75, -60, 45] [[1, 0, 15, 12], [0, 5, -40, -29]]

bad 6123.389477 comp 85.45333864 rms .8385593644
graham 45 scale size 85 ratio 1.888889


[9, -36, 9, -78, -11, 122] [[9, 14, 22, 25], [0, 1, -4, 1]]

bad 6153.784420 comp 89.20724695 rms .7732893066
graham 45 scale size 81 ratio 1.800000


[12, 116, 61, 156, 63, -184] [[1, 3, 16, 10], [0, -12, -116, -61]]

bad 6165.308451 comp 213.8850099 rms .1347702745
graham 116 scale size 220 ratio 1.896552


[18, -55, -23, -129, -87, 101] [[1, 3, -2, 1], [0, -18, 55, 23]]

bad 6235.360091 comp 131.9448098 rms .3581598638
graham 73 scale size 128 ratio 1.753425


[4, -13, -8, -30, -24, 18] [[1, 2, 1, 2], [0, -4, 13, 8]]

bad 6241.865596 comp 31.21994596 rms 6.403982242
graham 17 scale size 30 ratio 1.764706


[9, -72, 9, -135, -11, 223] [[9, 14, 23, 25], [0, 1, -8, 1]]

bad 6319.559467 comp 161.4376788 rms .2424805988
graham 81 scale size 153 ratio 1.888889


[4, 26, -3, 32, -16, -80] [[1, 0, -8, 4], [0, 4, 26, -3]]

bad 6500.850211 comp 53.77070178 rms 2.248426784
graham 29 scale size 48 ratio 1.655172


[4, -8, 2, -22, -8, 27] [[2, 4, 3, 6], [0, -2, 4, -1]]

bad 6596.418400 comp 23.07411531 rms 12.38962259
graham 12 scale size 20 ratio 1.666667


[6, -48, 10, -90, -1, 158] [[2, 4, -2, 7], [0, -3, 24, -5]]

bad 6680.634414 comp 110.3759122 rms .5483642010
graham 58 scale size 102 ratio 1.758621


[0, 14, 7, 22, 11, -23] [[7, 11, 17, 20], [0, 0, -2, -1]]

bad 6796.021281 comp 26.92065616 rms 9.377421730
graham 14 scale size 28 ratio 2.000000


[34, 111, 64, 97, 6, -163] [[1, 7, 20, 13], [0, -34, -111, -64]]

bad 6807.242767 comp 201.8667373 rms .1670481659
graham 111 scale size 188 ratio 1.693694


[2, -45, -57, -76, -96, -6] [[1, 2, -7, -9], [0, -2, 45, 57]]

bad 6992.965578 comp 108.7289132 rms .5915225374
graham 59 scale size 92 ratio 1.559322


[10, 43, 24, 45, 10, -65] [[1, 5, 17, 11], [0, -10, -43, -24]]

bad 7147.639216 comp 77.70529019 rms 1.183753973
graham 43 scale size 76 ratio 1.767442


[4, 26, 31, 32, 38, -1] [[1, 2, 5, 6], [0, -4, -26, -31]]

bad 7230.978192 comp 56.46645405 rms 2.267858844
graham 31 scale size 48 ratio 1.548387


[13, -22, -18, -65, -65, 20] [[1, 0, 5, 5], [0, 13, -22, -18]]

bad 7345.749516 comp 67.68280434 rms 1.603538626
graham 35 scale size 57 ratio 1.628571


[10, 50, -5, 56, -36, -152] [[5, 8, 12, 14], [0, -2, -10, 1]]

bad 7412.155328 comp 102.8169138 rms .7011571780
graham 55 scale size 90 ratio 1.636364


[12, 46, 44, 45, 36, -27] [[2, 3, 4, 5], [0, 6, 23, 22]]

bad 7491.753129 comp 89.88643879 rms .9272463000
graham 46 scale size 80 ratio 1.739130


[0, 36, 0, 57, 0, -101] [[36, 57, 84, 101], [0, 0, -1, 0]]

bad 7503.143539 comp 73.83082033 rms 1.376473539
graham 36 scale size 72 ratio 2.000000


[2, -14, -4, -27, -12, 30] [[2, 3, 6, 6], [0, 1, -7, -2]]

bad 7572.429503 comp 29.38555991 rms 8.769347874
graham 16 scale size 30 ratio 1.875000


[2, 13, 1, 16, -4, -34] [[1, 2, 5, 3], [0, -2, -13, -1]]

bad 7614.478971 comp 25.17178952 rms 12.01744127
graham 13 scale size 24 ratio 1.846154


[0, 29, 29, 46, 46, -14] [[29, 46, 67, 81], [0, 0, 1, 1]]

bad 7839.831477 comp 61.99622330 rms 2.039746796
graham 29 scale size 58 ratio 2.000000


[9, -31, -3, -70, -30, 80] [[1, 4, -6, 2], [0, -9, 31, 3]]

bad 7888.155773 comp 73.37295378 rms 1.465222141
graham 40 scale size 71 ratio 1.775000


[2, -11, 1, -22, -4, 33] [[1, 2, 0, 3], [0, -2, 11, -1]]

bad 7938.051784 comp 25.17178952 rms 12.52811538
graham 13 scale size 24 ratio 1.846154


[1, -18, -2, -31, -6, 46] [[1, 2, -5, 2], [0, -1, 18, 2]]

bad 8056.407803 comp 36.78114028 rms 5.955127490
graham 19 scale size 37 ratio 1.947368


[26, 93, 53, 87, 11, -138] [[1, 11, 36, 22], [0, -26, -93, -53]]

bad 8093.774001 comp 168.4889089 rms .2851073660
graham 93 scale size 160 ratio 1.720430


[5, 15, 0, 12, -14, -42] [[5, 8, 12, 14], [0, -1, -3, 0]]

bad 8182.982260 comp 30.39899189 rms 8.855095446
graham 15 scale size 25 ratio 1.666667


[22, -46, 15, -124, -38, 164] [[1, -4, 14, -1], [0, 22, -46, 15]]

bad 8351.983090 comp 132.8105018 rms .4735052200
graham 68 scale size 114 ratio 1.676471


[1, 21, 15, 31, 21, -24] [[1, 2, 11, 9], [0, -1, -21, -15]]

bad 8383.389707 comp 40.52787716 rms 5.104015010
graham 21 scale size 41 ratio 1.952381


[22, -87, -38, -189, -122, 156] [[1, 9, -27, -10], [0, -22, 87, 38]]

bad 8385.446065 comp 197.2149324 rms .2155989194
graham 109 scale size 196 ratio 1.798165


[5, 20, 0, 20, -14, -56] [[5, 8, 12, 14], [0, -1, -4, 0]]

bad 8399.610364 comp 39.81174637 rms 5.299521806
graham 20 scale size 35 ratio 1.750000


[3, -14, -1, -29, -10, 37] [[1, 1, 5, 3], [0, 3, -14, -1]]

bad 8586.941076 comp 31.58687897 rms 8.606469818
graham 17 scale size 31 ratio 1.823529


[4, -6, -6, -19, -21, 3] [[2, 3, 5, 6], [0, 2, -3, -3]]

bad 8668.698698 comp 20.10736235 rms 21.44093398
graham 10 scale size 16 ratio 1.600000


[14, -18, -8, -61, -52, 32] [[2, 6, 1, 4], [0, -7, 9, 4]]

bad 8816.158261 comp 60.99768675 rms 2.369477816
graham 32 scale size 50 ratio 1.562500


[12, -19, -4, -58, -40, 44] [[1, -2, 8, 4], [0, 12, -19, -4]]

bad 8836.553840 comp 57.54824529 rms 2.668202310
graham 31 scale size 50 ratio 1.612903


[24, -50, -54, -135, -153, 15] [[2, 3, 5, 6], [0, 12, -25, -27]]

bad 8882.978187 comp 149.7085231 rms .3963378450
graham 78 scale size 124 ratio 1.589744


[12, -26, -28, -69, -78, 8] [[2, 3, 5, 6], [0, 6, -13, -14]]

bad 8889.387895 comp 76.79410970 rms 1.507356707
graham 40 scale size 64 ratio 1.600000


[6, -48, -55, -90, -104, 7] [[1, 2, -1, -1], [0, -6, 48, 55]]

bad 8897.127867 comp 115.7156147 rms .6644554968
graham 61 scale size 102 ratio 1.672131


[11, -47, -31, -100, -80, 60] [[1, 4, -8, -4], [0, -11, 47, 31]]

bad 8956.989107 comp 107.3460098 rms .7773028044
graham 58 scale size 105 ratio 1.810345


[9, 27, 9, 22, -11, -55] [[9, 14, 20, 25], [0, 1, 3, 1]]

bad 8959.675660 comp 50.08480578 rms 3.571743808
graham 27 scale size 45 ratio 1.666667


[5, 20, 7, 20, -3, -40] [[1, 1, 0, 2], [0, 5, 20, 7]]

bad 9017.955004 comp 36.46768805 rms 6.780966544
graham 20 scale size 35 ratio 1.750000


[11, 35, 10, 30, -15, -75] [[1, 4, 10, 5], [0, -11, -35, -10]]

bad 9042.553516 comp 65.14194852 rms 2.130932032
graham 35 scale size 59 ratio 1.685714


[14, 30, 4, 15, -33, -75] [[2, 1, 0, 5], [0, 7, 15, 2]]

bad 9063.321564 comp 61.52250182 rms 2.394525208
graham 30 scale size 46 ratio 1.533333


[4, -10, -10, -25, -27, 5] [[2, 3, 5, 6], [0, 2, -5, -5]]

bad 9074.144988 comp 27.74745759 rms 11.78580691
graham 14 scale size 24 ratio 1.714286


[32, -44, -14, -144, -112, 91] [[2, 0, 9, 7], [0, 16, -22, -7]]

bad 9171.116574 comp 143.0639478 rms .4480864422
graham 76 scale size 120 ratio 1.578947


[10, 38, 36, 37, 29, -23] [[2, 3, 4, 5], [0, 5, 19, 18]]

bad 9246.679618 comp 74.03029640 rms 1.687201038
graham 38 scale size 66 ratio 1.736842


[3, 58, 40, 85, 55, -70] [[1, 1, -9, -5], [0, 3, 58, 40]]

bad 9420.219585 comp 111.2094301 rms .7616891970
graham 58 scale size 113 ratio 1.948276


[16, -46, -19, -110, -75, 85] [[1, 9, -19, -6], [0, -16, 46, 19]]

bad 9446.600087 comp 112.1209344 rms .7514535032
graham 62 scale size 108 ratio 1.741935


[17, -35, -38, -95, -108, 10] [[1, 10, -15, -16], [0, -17, 35, 38]]

bad 9461.679755 comp 105.3585759 rms .8523705986
graham 55 scale size 87 ratio 1.581818


[3, -9, -1, -21, -10, 23] [[1, 1, 4, 3], [0, 3, -9, -1]]

bad 9725.542432 comp 21.92998710 rms 20.22260414
graham 12 scale size 21 ratio 1.750000


[7, -13, -14, -37, -42, 4] [[1, 5, -4, -4], [0, -7, 13, 14]]

bad 9771.889199 comp 40.50939722 rms 5.954797154
graham 21 scale size 33 ratio 1.571429


[6, -41, -19, -79, -47, 71] [[1, -1, 20, 11], [0, 6, -41, -19]]

bad 9872.563354 comp 86.08168623 rms 1.332319542
graham 47 scale size 88 ratio 1.872340


[62, -65, -17, -247, -201, 143] [[1, -21, 26, 9], [0, 62, -65, -17]]

bad 9873.649021 comp 246.8601962 rms .1620225808
graham 127 scale size 192 ratio 1.511811


[10, -20, -10, -55, -44, 33] [[10, 16, 23, 28], [0, -1, 2, 1]]

bad 9980.657784 comp 55.22531575 rms 3.272523316
graham 30 scale size 50 ratio 1.666667

Message: 6710 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 13:03:03

Subject: updated list

From: Carl Lumma

Pelogic[7]
135/128
[1, 9/8, 5/4, 4/3, 3/2, 8/5, 15/8]
[5/4, 15/8, 4/3, 1, 3/2, 9/8, 8/5]

---

Dominant sevenths[7]
rms error 20.163 cents

---

Hemifourths[9]
rms error 12.690

---

Tertiathirds[9]
rms error 12.189 cents

---

Hexadecimal[9]
rms error 18.585

---

Pajara[10]
[2, -4, -4, -11, -12, 2] [[2, 3, 5, 6], [0, 1, -2, -2]]

bad 1550.521632 comp 11.92510946 rms 10.90317748
graham 6 scale size 10 ratio 1.666667

---

Check this out Carl[10]
[2, 1, -4, -3, -12, -12] [[1, 1, 2, 4], [0, 2, 1, -4]]

bad 2431.810368 comp 9.849243627 rms 25.06824586
graham 6 scale size 10 ratio 1.666667

---

Here's another Carl[10]
[2, 6, 6, 5, 4, -3] [[2, 3, 4, 5], [0, 1, 3, 3]]

bad 2682.600306 comp 11.92510946 rms 18.86388854
graham 6 scale size 10 ratio 1.666667

-Carl

Message: 6711 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 13:07:30

Subject: Re: More scales (25/24)

From: Carl Lumma

>NB Carl

Note bene?

-C.

Message: 6712 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 21:16:53

Subject: Re: More scales (25/24)

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

>> NB Carl
> 
> Note bene?


Yes; it was in your interest range, but not known.

Message: 6713 - Contents - Hide Contents

Date: Tue, 01 Apr 2003 21:19:23

Subject: Re: updated list

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:


> Tertiathirds[9]
> rms error 12.189 cents


Calling this Tertiathirds rather than Negri was my mistake. In the
course of my computer problems, I had to revert to old versions of
the files with names of temperaments.

Message: 6714 - Contents - Hide Contents

Date: Wed, 02 Apr 2003 04:57:05

Subject: question for graham on 9-limit temperaments

From: wallyesterpaulrus

hi graham :)

5 12 19 22 26 27 29 31 41 46 50 53 58 60 68 70... * [with cont.]  (Wayb.)

what's that third temperament?

that fifth one -- we all know what it is, but how come it's not 
consistent with anything, even 22?

-paul

Message: 6715 - Contents - Hide Contents

Date: Wed, 02 Apr 2003 05:02:39

Subject: question for gene

From: wallyesterpaulrus

what are the best 7-, 9-, 11-, and 13-limit extensions of 
diaschismic? how can we "well-temper" them so that chords near the 
1/1------3/2 center are just? shrutar was actually an example of 
this, rather than being a regular temperament.

Message: 6716 - Contents - Hide Contents

Date: Wed, 02 Apr 2003 06:52:55

Subject: Re: question for graham on 9-limit temperaments

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> hi graham :)
> 
> 5 12 19 22 26 27 29 31 41 46 50 53 58 60 68 70... * [with cont.]  (Wayb.)
> 
> what's that third temperament?


It's what I've been calling hemififths. It has 2401/2400 and 5120/5103
for a TM comma basis, and showed up in the recent choma postings as
having Hemififths[48] for 25/24 and Hemififths[34] for 36/35.


> that fifth one -- we all know what it is, but how come it's not 
> consistent with anything, even 22?


It's probably not worth bothering about, Paul. No one's ever likely to
use it. :)

Message: 6717 - Contents - Hide Contents

Date: Wed, 02 Apr 2003 09:51:58

Subject: Re: question for graham on 9-limit temperaments

From: Graham Breed

wallyesterpaulrus wrote:


> that fifth one -- we all know what it is, but how come it's not 
> consistent with anything, even 22?


It looks like there was a bug, which isn't in the current version, that 
stops the reverse ET lookup working where the period and octave are not 
the same.  The static files have been phased out in favor of the CGI 
script, which doesn't even show the ETs for now.


                            Graham

Message: 6718 - Contents - Hide Contents

Date: Wed, 02 Apr 2003 09:02:24

Subject: The diaschismic family

From: Gene Ward Smith

Here is a new analysis of the family in the 7-limit, and old stuff
showing what I've called "diaschismic" in the 11 and 13 limits. I'm
afraid the 13 limit badness is not geometric badness; however both
diaschismic and hemififths come out with low badness figures in the 13
limit and are important 13-limit systems.

7 limit 

Pajara [50/49, 64/63]
[2, -4, -4, -11, -12, 2] [[2, 3, 5, 6], [0, 1, -2, -2]]

bad 1550.521632 comp 11.92510946 rms 10.90317748


Shrutar [245/243, 2048/2025]
[4, -8, 14, -22, 11, 55] [[2, 3, 5, 5], [0, 2, -4, 7]]

bad 2740.920108 comp 34.89878326 rms 2.250483358


Diaschismic [126/125, 2048/2025]
[2, -4, -16, -11, -31, -26] [[2, 3, 5, 7], [0, 1, -2, -8]]

bad 2780.393711 comp 26.97297092 rms 3.821630806


Ragar [2048/2025, 3136/3125]
[4, -8, -20, -22, -43, -24] [[4, 6, 10, 13], [0, 1, -2, -5]]

bad 2979.183549 comp 36.62986166 rms 2.220376920


Diaquatra [2048/2025, 2401/2400]
[8, -16, -6, -44, -32, 31] [[2, 4, 3, 5], [0, -4, 8, 3]]

bad 4109.453916 comp 43.88939274 rms 2.133364042


11 limit


Diaschismic

[2, -4, -16, -24, -11, -31, -45, -26, -42, -12]

[[2, 3, 5, 7, 9], [0, 1, -2, -8, -12]]

[600.000000000000, 103.783535998448]



bad 4368.478167 comp 76.308394 rms 3.182069


13 limit


Diaschismic

[2, -4, -16, -24, -30, -11, -31, -45, -55, -26, -42, -55, -12, -25, -15]

[[2, 3, 5, 7, 9, 10], [0, 1, -2, -8, -12, -15]]

[600., 103.786589235317]

[46, 58]

unweighted badness 251.546815 unweighted complexity 19.682480 rms
error 2.880707

Message: 6721 - Contents - Hide Contents

Date: Thu, 03 Apr 2003 02:30:38

Subject: viggo brun's algorithm produces periodicity blocks . . . gene tell us more

From: wallyesterpaulrus

--- In SpecMus@xxxxxxxxxxx.xxxx "wallyesterpaulrus" 
<wallyesterpaulrus@y...> wrote:
--- In SpecMus@xxxxxxxxxxx.xxxx Kraig Grady <kraiggrady@a...> wrote:

>  %PDF-1.3 * [with cont.]  (Wayb.)
> has some 10 tone scales as well as the indian 22


%PDF-1.3 * [with cont.]  (Wayb.) is cool! i've never seen it 
before. when i sent erv my paper, he sent me a few things and all the 
10-tone scales in there were non-CS. but his note said (and only 
said) i should take a second look at vigo's algorithms. now i know 
why!

wonder if gene has any thoughts on this . . .
--- End forwarded message ---

Message: 6722 - Contents - Hide Contents

Date: Fri, 04 Apr 2003 01:47:54

Subject: Scales to chromas

From: Gene Ward Smith

We can reverse the proceedure I've been following, and from a T[n] for
temperament T, get a TM-reduced chroma. Here's what the miracle MOS
give, for the 7 and the 11-limit:

10: 48/49, 44/45

11: 21/20, 21/20

21: 36/35, 33/32

31: 81/80, 81/80

41: 243/245, 99/100

72: 4374/4375, 3993/4000

Message: 6723 - Contents - Hide Contents

Date: Fri, 04 Apr 2003 10:05:53

Subject: Re: 45/44 & 49/48

From: Carl Lumma

>Here are 11-limit scales for which both 45/44 and 49/48 are chromas


I guess what I just wrote on specmus is wrong.  Can you show how
these two chroma arise?


>the scale degree is greater than the // Graham complexity


?  The "scale degree"?


>Heptadec[9] [36/35, 56/55, 77/75]
>[5, 3, 7, 4, -7, -3, -11, 8, -1, -13] [[1, 1, 2, 2, 3], [0, 5, 3, 7, 4]]
>
>bad 6400.766110 comp 32.19555159 rms 19.64440328
>graham 7 scale size 9
>
>
>Fourththirds[5] [16/15, 28/27, 77/75]
>[1, -1, 3, -4, -4, 2, -10, 10, -6, -22] [[1, 2, 2, 4, 2], [0, -1, 1,
>-3, 4]]
>
>bad 6476.838089 comp 20.25383770 rms 43.03787612
>graham 7 scale size 5
>
>
>Pajarous[10] [50/49, 55/54, 64/63]
>[2, -4, -4, 10, -11, -12, 9, 2, 37, 42] [[2, 3, 5, 6, 6], [0, 1, -2,
>-2, 5]]
>
>bad 6667.906202 comp 43.76707564 rms 12.26714784
>graham 14 scale size 10

Say,


When you post lists of scales, could you post a template at the
top, so we know what all this notation is?  I know it's pretty
standard every time, but still, for achives' sake.

-Carl

Message: 6724 - Contents - Hide Contents

Date: Fri, 04 Apr 2003 04:59:45

Subject: Re: Scales to chromas

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:

> We can reverse the proceedure I've been following, and from a T[n] 
for
> temperament T, get a TM-reduced chroma. Here's what the miracle MOS
> give, for the 7 and the 11-limit:
> 
> 10: 48/49, 44/45
> 
> 11: 21/20, 21/20
> 
> 21: 36/35, 33/32
> 
> 31: 81/80, 81/80
> 
> 41: 243/245, 99/100
> 
> 72: 4374/4375, 3993/4000

cool!

Previous Next

6000 6050 6100 6150 6200 6250 6300 6350 6400 6450 6500 6550 6600 6650 6700 6750 6800 6850 6900 6950

6700 - 6725 -