source file: m1413.txt Date: Tue, 12 May 1998 12:40:46 +0000 Subject: Fletcher on Sethares: TTSS "should be studied by all lecturers i From: "Patrick Ozzard-Low" 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