source file: m1569.txt
Date: Fri, 30 Oct 1998 17:42:07 -0500

Subject: Polansky's consonance funtions

From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>

>Mathematically, i work a lot with my students (and use in my
>own composition work) some variant of the tenney HD function, which is
very
>similar to the Euler function and the barlow function 

There are two major problems with these definions. First, as they are
defined over rectangular rather than triangular lattices, they make (for
example) the minor third and major seventh equal in consonance, which
does not accord well with experience or practice. Second, they suffer
from the same problem as Lucy's definition, in that a distant point in
the lattice can be a very good approximation of a consonant interval
from, and so clearly more consonant than many closer points in the
lattice to, a given origin.