source file: m1568.txt
Date: 29 Oct 98 16:34:21 EST

Subject: Re: TUNING digest 1567

From: Larry.Polansky@Dartmouth.EDU (Larry Polansky)

--- You wrote:


Can anyone offer a comprehensive mathematical explanation of consonance?


Robin

--- end of quote ---

I teach this topic a lot in my classes, robin, and there are some good
resources. historically, tenney's History of Consonance and Dissonance is a
good reference. 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 (these are explained
pretty well in Chalmer's "Divisions...".). we've done some fun things here in
seminars with plotting the different functions over common intervals, and so
on, and it turns out that they're all pretty similar (low primes vs. few
exponents is the basic idea), but have some interesting differences as well.


these are not cognitive functions, exactly, which would need to use the
critical band and a heck of a lot of other things (including timbre, context,
temporal displacement, memory, etc etc etc)... they are something more like
very concise cognitively informed musical similarity functions (if that makes
any sense)


lp