Dayton Clarence Miller. The Science of Musical Sounds, New-York. Mac Millan C°. 1922.

Dayton Clarence Miller. Study of Musical Sounds.

D. C. Miller’s book—[the name of its author is widely known thanks to his experiments with the “ether wind”]—on musical acoustics was written in 1915 and constitutes an exposition of lectures delivered

in the Lowther Institute of Popular Lectures. The second edition, 1922, was reprinted almost without changes and, although during the war the author carried out a number of important military-acoustical investigations, he did not include them in the new edition of his book.

The interest in technical and musical acoustics that is now being widely manifested makes it necessary to dwell in a few words on Miller’s book, all the more since the chief value of the book consists in the numerous drawings, graphs, and illustrations, which can be used by Russian readers without waiting for the book to be translated into Russian.

Having set forth in Chapters I and II the general foundations of experimental acoustics, in Chapter III the author presents his method of recording sound curves by means of an apparatus he calls the “Phonodeik”; this apparatus is provided with a thin (0.01 mm) glass membrane, set into vibration by the incident sound waves. Miller’s apparatus differs little in principle from those used earlier, but it possesses great sensitivity and makes it possible to record sounds up to 10000 cycles/sec.

Chapter IV of the book is devoted to methods of harmonic analysis of curves and contains a description of various types of harmonic analyzers; it should be noted how much labor and inventiveness was expended on the construction of harmonic analyzers that make it possible to speed up many times the painstaking work of analyzing curves.

Chapter V, the most important from a fundamental standpoint, explains how to take into account the distortions introduced into the curve of a sound recording by the resonant properties of the horn, the membrane, and the mirror system. Miller calibrates his instrument for the strength of sound at various frequencies from 100 to 4000 cycles/sec by means of a set of 61 standard (closed) pipes of identical “subjective” loudness. This calibration proved to be the most difficult part of the task and would have required, in the author’s words, “the work of one investigator for 8 hours a day over the course of 3½ years.” The use of a set of pipes of identical subjective loudness naturally introduces an element dependent on the sensitivity of the ear, and since the ear is comparatively very little sensitive in the region of low tones, all of Miller’s analyses underestimate too much the energy of the low part of the spectrum, as was noted by later investigators.

In Chapter VI are given the results of an investigation of the sound of the following musical instruments: tuning fork, flute, violin, clarinet, oboe, horn, piano, voice. The results of all the analyses are presented in the form of graphs giving the energy of the individual harmonics (overtones) of the sound. Such sound, or more precisely timbral, “spectra,” first applied by Miller, are now in common use.

Chapters VII and VIII set forth the question of the analysis and synthesis of vowels. Numerous and very detailed analyses of the sound of vowels at different pitches, pronounced by various male and female voices, in different languages, made it possible fully to clarify the question of the position of the “formants” of all the principal vowels and of the transitional sounds between them, and fully confirmed Helmholtz’s views. The author’s experiments on the reproduction of vowels by means of sets of organ pipes are very interesting.

It is extremely regrettable that throughout the entire book the author makes a theoretical error, assuming that the strength of a sound is proportional to the product \(n^2 A^2\), where \(n\) is the frequency and \(A\) the amplitude of the curve recorded by the membrane; this relation is correct only if by \(A\) one understands the amplitude of oscillation of the air particles. If, however, \(A\) is the amplitude of the recorded curve, then the strength of the sound is proportional only to \(A^2\), without the factor \(n^2\), as is easily seen from the fundamental equations given by Rayleigh. Fortunately, the results of the final analyses do not contain this error, since the introduced correction factor (p. 164), inversely proportional to the square of the frequency, compensates for the erroneous multiplication by \(n^2\).

The book is impeccably produced and contains 188 illustrations and a detailed bibliographic index. Price—about 4 dollars.

S. Rzhevkin.