Obvious things proven

Everything you already knew about maximally even scales:

http://x31eq.com/proof.html

Graham

--- In tuning-math@yahoogroups.com, Graham Breed <graham@m...> wrote:

> Everything you already knew about maximally even scales:

Great stuff!

By the way, what would you and Carl think of starting a web ring? You
only need four websites for a webring.com website.

>> Everything you already knew about maximally even scales:
>
>Great stuff!
>
>By the way, what would you and Carl think of starting a web ring?
>You only need four websites for a webring.com website.

I don't have a site, yet. But I also prefer just linking to
friends in the conventional way, or using google's similar
pages feature.

-Carl

> Everything you already knew about maximally even scales:
>
> http://x31eq.com/proof.html

Great stuff, indeed. That's everything I've ever suspected,
and more.

-Carl

Nice indeed. Was the formula p(n) = floor(na/b) proven by Clough and
Douthett?
Because I remember the definition being in terms of interval sizes.

Manuel

Manuel Op de Coul wrote:
> Nice indeed. Was the formula p(n) = floor(na/b) proven by Clough and > Douthett?
> Because I remember the definition being in terms of interval sizes.

I don't have that paper. I got it from equation 1.1 in Aytan Agmon's 1996 one. He says in Note 17 "In theorems 1.2 and 1.5 Clough and Douthett establish that 'being a J-set' (Definition 1.9) is equivalent to 'having the property that the spectrum of each dlen is either a single integer or two consecutive integers' (Definition 1.7). Thus Clough and Douthett's 'maximal evenness' ... and the present relation (1.1) are the same ..."

Graham

Ah, so Agmon proved it then, good.

Manuel