Re: [tuning-math] Re: geometric complexity
- From: Gene W Smith <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Thu, 18 Jul 2002 21:46:40 -0700
On Fri, 19 Jul 2002 00:36:20 -0400 "Paul H. Erlich"
<PErlich@xxxxxxxxxxxxxxxxx> writes:
>
> First of all, i don't know where you're getting just linear ones
> from.
What's your definition of complexity in general?
> Secondly, i don't see what there is about a Euclidean, as opposed to
> a
> triangular-taxicab, metric that is going to be reflective of how we
> hear. In
> fact, it would seem especially important at the 9-limit and above to
> deviate
> from Euclid.
I was proposing using a Euclidean metric which did not give the same size
to all prime numbers; prime p would have length ln(p), and if p and q are
odd primes, with q>p, then
length p/q = length q/p = ln(q). This uniquely determines a Euclidean
metric.
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