Musimathics.
The Mathematical Foundations of Music,
Vol. 1
by Gareth Loy
The MIT Press, Cambridge, MA, 2006
608 pp., illus. 263 b/w. Trade, $50
ISBN: 0-262-12282-0.
Reviewed by Stefaan Van Ryssen
Hogeschool Gent
Jan Delvinlaan 115, 9000 Gent, Belgium
stefaan.vanryssen@hogent.be
There are numerous
books on the mathematical foundations
of music, and most of them follow more
or less the same line: from the early
musing of the Greek mathematicians who
tried to explain the scale in terms of
ratio's between integers, through the
physical aspects of music (frequency,
duration, loudness, timbre) and the basics
of organology or the way artifacts are
made to sound to the perception of music.
Musimathics is no exception to this
except maybe that from time to time the
author lets something of his personal
life shimmer through the otherwise dry
and almost monotonous text. (I liked his
story of a test he did with the pitch
of a wine bottle.)
What makes this book exceptional, however,
is the attempt Loy makes to gradually
build a mathematical, or rather algorithmical
foundation of composition. Using a programming
language of his own conception, and giving
numerous examples of pieces of code, he
turns the activity of composing upside
down and inside out. He shows how underlying
rules and structures are implicit in any
composers work (here of course using
Western models and assumptions, but the
exercise could be done for any musical
tradition) and how choice, aesthetics
and the desire to please, distract, shock
or infuriate overlay these basic foundations.
Divine inspiration lies on top of a lot
of concrete layers.
There are, however, some questions to
be answered. I am sure Loy has good reasons
to think that a lengthy treatment of the
historical evolution of the theory of
harmony and scales from the Greeks through
medieval times till the 'well tempered'
keyboard has some relevance for composers
today, but I for my part am not convinced
it does. It might be interesting for encyclopaedic
purposes, but is it really necessary to
use more then 50 pages to go through all
this? Wouldn't it have been enough to
outline the problem, describe the most
important historical solutions, and treat
some of the most interesting ones (like
Harry Partch's system) a bit more in depth?
A second problem I have is with his treatment
of the physical aspects of music. A lot
of pages are spent on basic physical concepts
and laws. Sure enough, it is necessary
to know what they are if one wants to
understand how instruments work and what
acoustics is all about. But as soon as
things get really interesting and maths
and physics are getting really important,
Loy skips the issue and refers to the
second volume "where we will further develop
this in detail". It is very frustrating
for the reader to take on a cartload of
theoretical baggage and, then, having
to wait to use it just when the fun begins
in the next volume.
In the same vein, Loy's treatment of the
algorithmic underpinnings of composition
is very promising. But where does it all
lead? Lengthy digressions on neural networks
or referencing systems in computer programs
may be unavoidable, but at least one would
like to know what the ultimate goal would
be.
To sum it up: There is something for everyone
in this book. It is clear and well written
at times, with humour and insight, but
it is only one of a pair of legs. As a
devoted biped I certainly hope the second
volume will be published soon; otherwise,
the foundations of music are prone to
topple over.