Fletcher on Sethares: TTSS "should be studied by all lecturers i

Dear All,

at the risk of making Bill Sethares blush, here is a recent review
by Neville Fletcher (co-author of "The Physics of Musical
Instruments") of Bill's recent book :

Tuning, Timbre, Spectrum, Scale
by William A. Sethares
Springer-Verlag, London 1998
ISBN 3-540-76173-X
345 pp. plus CD.

(sorry, I left the review reference at home, but can post it if
anyone wants to know - it's in an Australian Journal).

***********BEGIN REVIEW***********

To most people, the 12-note scale of the piano keyboard, and with it
the hierarchy of consonant intervals =BE the octave, fifth, fourth and
third =BE is the basis of all music. Some may be aware that the modern
system of equal temperament, in which all semitone intervals have
precisely the same frequency ratio, is a compromise that sacrifices
the purity of tuning of the consonant intervals (except that of the
octave) for the ability to play equally in all keys, but that is about
where most knowledge stops.

But what is the basis of these musical principles? Take the octave,
for example. Its importance as a concord derives from the fact that
ordinary Western musical instruments have harmonic spectra, in which
the overtone frequencies are integral multiples of that of the
fundamental. If two notes an octave apart (frequency ratio 2:1) are
sounded simultaneously, then many of the overtones coincide and the
result is a pleasant smooth sound, while any mistuning leads to
unpleasant beats and tonal roughness. But what if the individual
notes have inharmonic spectra? A recorded example shows that if the
spectra of the two notes are stretched, then the "octave" must be
similarly stretched to give a concordant sound. It is also possible
to divide either the genuine 2:1 octave or a stretched octave into a
number of equal "semitones" other than 12 =BE both 11-note and 10-note
divisions can sound very pleasant =BE provided that the overtone
spectra of the component notes are adjusted appropriately. And this
is despite the fact that the traditional "concords" have now
disappeared!

Non-Western musical traditions based upon non-harmonic percussion
instruments, such as the gamelan of Indonesia, have faced similar
problems and have developed pleasant-sounding scales with 5 or 7
notes in a slightly stretched octave, but with tunings very different
from simply playing selected notes on a piano.

This excellent book, written by a musically minded electrical
engineer and computer scientist, examines the basis of our whole
concept of melody and harmony and presents compelling recorded
demonstrations using computer-synthesised sounds. The presentation
requires no mathematical background, though the relevant mathematics
and computer programs are given concisely in a series of appendixes
for those who want to follow them further. As well as stretched
octaves, stretched spectra and non-12-tone scales, the author shows
in detail how to construct a synthetic instrument spectrum to match
an arbitrary scale, and conversely how to design a scale to fit a
given instrument spectrum. There is a detailed treatment of the
gamelan, and then, as a virtuoso exercise, he designs a scale and
presents musical examples to match the sounds of a small bell, a
piece of resonant stone, and the pattern of an x-ray diffraction
spectrum! He also shows how a computer can adaptively tune the
notes of a scale so that the result is concordant irrespective of key
changes =BE an aim that is only imperfectly fulfilled by equal
temperament and that leads to disaster in just intonation =BE and
outlines a treatment of music theory for an equal-tempered 10-tone
scale.

The writing throughout is admirably clear and straightforward, the
book production is up to Springer's usual high standards, and the
recorded passages on the CD, which comprise both short examples and
longer compositions in unusual scales on peculiar synthetic
instruments, admirably illustrate the points made in the text. They
also demonstrate that the author is a very competent and persuasive
composer in this new idiom.

This book, which is destined to become a classic, is essential
reading for anyone concerned with computer music, or with the study
of non-Western music. It should be bought and studied by all
lecturers (and read by all students!) in musicology, and should be in
the library of every institution teaching music at an advanced level.
Perceptual psychologists should also include it high on their
reading lists, and I am sure that engineers, mathematicians and
physicists will enjoy it. I found it absorbing reading (and
listening!), and I can recommend it to anyone with an interest in the
fundamental psychological or acoustic basis of music.

Neville Fletcher

********END OF REVIEW QUOTE**************

The last paragraph is 200% right. High praise indeed, and, having
read the book cover-to-cover twice (and more) I've absolutely no
doubt it is deserved.

Thought you'd all like to see this....... Hope you didn't mind me
blowing your 10-ET trumpet Bill !

Patrick O-L