Re: [tuning] 3&7 based scales (was: Re: [MMM] lost in appalachia)

In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> writes:

> Let's make this precise, since I think you're a physicist.

Dang, my cover's blown already!

> Firstly, 12-equal is consistent in the 7-limit. Knowing that, it's
> pretty unobjectionable to write the covector for the 12-equal pitch
> contours as
>
> <12 19 28 34]

And for an EDO which is not consistent in the specified limit? Are
you dead in the water, or is it just harder, or does it just not make
sense to go there?

> More later -- and should we stay at this level of mathematics,
> perhaps we should move it to tuning-math

I was afraid of that...

- Rich Holmes

--- In tuning-math@yahoogroups.com, Rich Holmes<rsholmes@m...> wrote:
> In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> writes:
>
> > Let's make this precise, since I think you're a physicist.
>
> Dang, my cover's blown already!
>
> > Firstly, 12-equal is consistent in the 7-limit. Knowing that, it's
> > pretty unobjectionable to write the covector for the 12-equal
pitch
> > contours as
> >
> > <12 19 28 34]

> And for an EDO which is not consistent in the specified limit?

Then you have to specify the mapping to the acoustical primes that
you have in mind. And beyond 34-equal or so, consistency doesn't
necessarily matter. For example, if you look at

/tuning-math/files/152br2.gif

and compare with Fig. 5 in my new paper, you can see why I might be
interested in using 152-equal in any of the incarnations shown, such
as
<152 240 352],
<152 241 354],
etc.

All of them work -- you just have to be "consistent" if you want the
math to work out :)