Re: [tuning] Digest Number 3578

<>Hi Gene!
Could you define epimorphic again.
As far as a constant structure . Partch's tuning comes out well as a 41 tone scale with two variables.
This is what Erv noticed in the the way Harry would use intervals and observations he made in the course of the two discussing certain relations Harry would pull out of his tuning by ear.
of which his ear was his final guide.

From: "Gene Ward Smith" <gwsmith@svpal.org>
Subject: Re: good/bad scales

I pointed out in a recent tuning-math posting that you need to go to
51 notes to fill out the 11-limit diamond epimorphically. For the
7-limit diamond, it would be 18 notes, which is in Joe's range, so I'd
better hop to it and find some examples.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> <>Hi Gene!
> Could you define epimorphic again.

Suppose you have a JI scale, numbered in order of interval size above
the unison, so that the unison is 0, and going to n-1, where n is the
number of scale elements in an octave. Then it is epimorphic with val
h if h(s[i]) = i, where s[i] is the ith scale element.