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

> 7-limit Blackwood 243:252:256 lcm 435,456

I just found this for Blackwood:

189:192:196 lcm 84,672

I guess "by inspection" doesn't cut it.

I'll have to do this systematically.

Here's my Matlab program to convert from tratios to wedgies:

function out=trat2wedg(a1,a2,a3);
j=factor(a1);
a12=sum(j==2);
a13=sum(j==3);
a15=sum(j==5);
a17=sum(j==7);
j=factor(a2);
a22=sum(j==2);
a23=sum(j==3);
a25=sum(j==5);
a27=sum(j==7);
j=factor(a3);
a32=sum(j==2);
a33=sum(j==3);
a35=sum(j==5);
a37=sum(j==7);
w=([det([a22-a12 a23-a13;a22-a32 a23-a33]) det([a22-a12 a25-a15;a22-
a32 a25-a35]) det([a22-a12 a27-a17;a22-a32 a27-a37]) det([a23-a13 a25-
a15;a23-a33 a25-a35]) det([a23-a13 a27-a17;a23-a33 a27-a37]) det([a25-
a15 a27-a17;a25-a35 a27-a37])]);
g=gcd(w(1),gcd(w(2),gcd(w(3),gcd(w(4),gcd(w(5),w(6))))));
out=w/g;


> Dominant Sevenths 245:252:256 lcm 564,480
> 7-limit Diminished 343:350:360 lcm 617,400
> Pajara 441:448:450 lcm 705,600
> Semifourths 240:243:245 lcm 952,560
> Tripletone 125:126:128 lcm 1,008,000
> Injera 392:400:405 lcm 1,587,600
> meantone 1120:1125:1134 lcm 2,268,000
> 7-limit Augmented:
> 1125:1152:1176 lcm 7,056,000
> BUT ALSO
> 1568:1575:1620 lcm 3,175,200
> (any simpler tratio?)
> OldKleismic 1000:1008:1029 lcm 6,174,000
> Catler -- same as 12-equal -- 625:648:640 lcm 6,480,000
> Negri 672:675:686 lcm 7,408,800
> semisixths 3375:3402:3430 lcm 20,837,250
> Superpythagorean 1701:1715:1728 lcm 26,671,680
> magic 6048:6075:6125 lcm 47,628,000
> miracle 7168:7200:7203 lcm 553,190,400
> orwell 12005:12096:12150 lcm 933,508,800
> (septimal) schismic 27783:28000:28125 lcm 2,778,300,000
> ennealimmal 419904:420000:420175 lcm 4,410,829,080,000
>
> What's bigger -- the lcm of ennealimmal or the national debt?