Re: EDO classification by families of scale patterns

--- In tuning@yahoogroups.com, Graham Breed <gbreed@g...> wrote:
> Igliashon Jones wrote:
>
> > In case it's not obvious what I mean by "scale shapes", I'm referring
> > specifically to n-tone MOS scales with x number of large steps (l) and
> > y number of small steps (s), where n=x+y. Thus I'd group EDOs
> > together that all support, say, 7-note scales with 5(l)+2(s)...or
> > 8-note scales with 3(l)+5(s) [written such to include all possible
> > modes/permutations of l's and s's]. For the moment I'm going to limit
> > myself to EDOs < 36, and scales of no more than 10 steps. Also, the
> > ratio of l:s shouldn't exceed 5:1, because most listeners would find
> > such scales rather lopsided and unpleasant (I think?).
>
> So what are "l" and "s"? You only defined "x" and "y".
>

l and s are the sizes of the large and the small step, in units of the smallest
step of the EDO, or not?

Well, if you take k as the subdivision of the EDO, the values x, y, l and s
fulfill

x*l + y*s = k

which is a linear Diophantine equation. It appears to me that this probably has
been done before - dunno though. Maybe I will try to do it...
In any case, you might check the archives in tuning-math for "diophantine".
I cross-posted this to tuning-math.

BTW, is "City of the Asleep" not on soundclick any more? I am missing it...

Hans Straub