[microsound] book review: Fractals in Music

[Josh Ronsen <joshronsen@xxxxxxxxx>]

BOOK REVIEW
"Fractals in Music: Introductory Mathematics for
Musical Analysis" by Charles Madden
The book's title is misleading: little is mentioned
about fractals, geometric structures in which large
elements mirror smaller elements, and nothing is
specifically mentioned about musical works which use
fractal-like structures, like John Cage's proportional
rhythmic frameworks in the 1940s, or David Clarke
Little's computer music in the 1990s. Most of the book
is painfully dull, explaining how to use simple
statistics (mean, standard deviation, etc.) to analyze
melodies of some disparate examples: Xenakis' "Etona"
(based on random organization), Schubert, a Gregorian
chant, and melodies derived from white noise, brown
noise and pink noise. Over half the book is spent
picking through these examples, mathematically
determining how "random," each piece is, which is a
particularly boring thing to work through, and even
more particularly useless. Madden never writes about
how this information can be used, how this relates to
fractals, or how any of this could be applied to music
that is not a single voice of chromatic pitches. And
in his examples, he doesnít examine a fractal melody
to see how "random" that would be, or how random
different fractal melodies would be. A middle chapter
of the book goes through examples of composers using
the Fibonacci number series (1, 1, 2, 3, 5, 8, 11,
etc), whose ratios of successive pairs approach the
Greek "Golden Ratio" of 0.618. Much of this is spent
counting measures to see if there is a significant
musical moment at this point in pieces by Varese,
Gershwin, Schoenberg, Bartok, and Stockhausen.
Varese's "Hyperprism" is one bar off from having a
major development at the Golden Mean point!
Ultimately, we learn that this is an extremely dull
concept to contemplate. And in a piece that lasts 200
measures, what noticeable difference is there if there
is a change at measure 123 or 130? The human mind
couldn't notice an audible difference between the two.
All this said, the first two chapters are worthwhile
reading, providing an overview of Chaos Theory (in
which fractals play a useful part) and the natural
harmonic and equal-temperament tunings. A more
interesting piece on the use of fractals in music is
Rolf Wallin's "Fractal Music - Red Herring or Promised
Land?" written 10 years earlier.
http://www.notam02.no/~rolfwa/Fractalarticle.html

-Josh Ronsen
in Austin, Texas


		
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