xenharmony.org

Funny; the DNS doesn't seem to be available yet.

http://66.246.86.148/~xenharmo/intval.html

I understand everything here but the last paragraph.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> Funny; the DNS doesn't seem to be available yet.

I've written to complain. I'll poke them again.

> http://66.246.86.148/~xenharmo/intval.html
>
> I understand everything here but the last paragraph.

This?

Given the p-limit group Np of intervals, there is a non-canonically
isomorphic dual group Vp of vals. A val is a homomorphism of Np to
the integers Z. Just as an interval may be regarded as a Z-linear
combination of basis elements representing the prime numbers, a val
may be regarded as a Z-linear combination of a dual basis, consisting
of the p-adic valuations. For a given prime p, the corresponding p-
adic valuation vp gives the p-exponent of an interval q, so for
instance v2(5/4) = -2, v3(5/4) = 0, v5(5/4) = 1. If an interval is
written as a row vector of intervals, a val is simply a column vector
of intervals.

It does read a lot like math, now that I look at it. Maybe I need a
translator.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

If an interval is
> written as a row vector of intervals, a val is simply a column
vector
> of intervals.

I see I said "intervals" twice when I mean "integers". That could be
a teeny-weeny problem. :)

Keep up the good work, Carl.