Die Lehre von den Tonempfindungen

Abstract

THIS work traces the connection between physical and physiological acoustics, on the one hand, and the general principles and practice of music, on the other. Professor Helmholtz's qualifications for taking up this subject are unique. In each branch of science involved in the inquiry he has a reputation at least equal to that of any specialist in that branch. In the combination of eminently original mathematical power and consummate skill in physical and physiological research with the technical knowledge of a trained musician, he stands absolutely alone. It need therefore surprise no one that the volume before us, the first edition of which was published in 1862 as the fruit of eight years' work, has practically revolutionised the subject with which it deals. He begins by completely clearing up the nature of the quality (timbre) of musical sounds. He fixes his reader's attention on the harmonics which previous observers had recognised as accompanying a fundamental note. These, he shows, are no isolated phenomena, but invariable concomitants of nearly all musical sounds. In fact, what appears to be a simple note of any assigned instrument, is really a composite sound consisting of a number of different tones, all, however, members of a series connected together by a simple law. The quality of the sound depends on the relative intensities in which these partial-tones are present in the whole mass of sound (Klang) heard. Helmholtz illustrates his theory by determining the relative intensities of the audible partial-tones produced by the principal kinds of musical instruments, and also those corresponding to the different vowel-sounds of the human voice. He has also invented an apparatus by which the most important members of the complete series of partial-tones corresponding to a fundamental tone can be sounded with any assigned relative intensities, and which is capable of producing a tolerably close imitation of many sounds differing widely from each other in quality. These investigations occupy the first part of the work. Die Lehre von den Tonempfindungen, von H. Helmholtz. (Braunschweig: F. Vieweg. London: Williams and Norgate. 3rd edition. 1870.)