From: ficara@panix.com
Date: Thu, 3 Dec 1998 18:14:48 -0600 (CST)
Subject: Math & Music: Good Reading
Don't worry, I don't want to open up this argument again. But Barry
and I, I think, were both trying to say that it in no way belittles
music to say that it is closely related to mathematics.
The other day in a Silicon Valley computer store, I found a
wonderful book that describes the relationship in fascinating detail.
It's from the late 1800s (reprinted in a modern Dover edition for less
than $20), by Hermann Helmholtz: ON THE SENSATIONS OF TONE. It
basically looks at the physical and mathematical bases of music and
then relates those to how things sound to us. Why do ratios of 1:2 (an
octave) and 2:3 (a fifth) sound so good to us? Why is the octave
divided up the way it is and what are other approaches?
Helmholtz was a true generalist, understanding physics and math and
acoustics but also knowing a great deal about music and music theory
-- this book is still used as a text in music theory courses.
To say that music is based in math no more makes something
mechanical out of music than the Parthenon is belittled when you
realize that it is built to precise mathematical ratios.
In his preface to the third edition Helmholtz addresses how
different audiences had received his book: "Those who prefer
mechanical explanations express their regret at my having left any
room in this field for the action of artistic invention and esthetic
inclination ... Other critics with more metaphysical proclivities have
rejected my [work] as too coarsely mechanical. I hope my critics will
excuse me if I conclude from the opposite nature of their objections,
that I have struck out nearly the right path."
One other good book that will help you see the beauty in the arts
and mathematics is Douglas Hofstadter's Pulitzer-winning GOEDEL,
ESCHER, BACH.
Ken
(
geocities.com/stauffer_james)