PRINTED BY BALLANTYNE, HANSON AND CO. [The rights of translation and of reproduction are reserved.] PREFACE. THE present treatise neither pretends to nor aims at giving a complete description or demonstration of the phenomena of Sound, or of the history and laws of Music. Those who wish to study these subjects thoroughly, whether from their scientific or artistic aspect, must have recourse to special works and special study. Following the example given by Helmholtz in his now classical book, "Die Lehre von den Tonempfindungen," I have tried to bring together in a plain and simple form two subjects which have hitherto been treated of separately. The student of physics did not go much into the study of musical arguments, and our artists do not suf ficiently understand the very important bearing that the laws of sound have upon many musical questions. Science has latterly made notable progress in this respect. She has come to regard the history of the development of Music from a single point of view, and is on the road to furnish a larger and firmer basis to musical criticism. To expound briefly the fundamental principles of such a science, and to point out its most important applications, has been the object and scope of this treatise. I hope, therefore, that it will be received with some interest both by lovers of science and by lovers of art. PIETRO BLASERNA. April 1875. CONTENTS. 1. Periodic movements, vibration-2. Sonorous vibration.-3. Vibration of a bell-4. Vibration of a tuning-fork, graphic method-5. Vibration of a string-6. Of plates and mem- PAGE 1. Transmission of sound-2. Propagation in air-3. In water 1. Characteristics of sound, and difference between musical sound and noise-2. Loudness of sound, and the various 1. Measure of the number of vibrations; the graphic method- 2. Cagniard de la Tour's siren-3. Pitch of sounds; limit of audible sounds, of musical sounds and of the human 1. Musical sounds-2. Law of simple ratio-3. Unison, inter ference-4. Beats-5. Their explanation-6. Resultant notes-7. Octaves and other harmonics-8. Consonant chords and their limits-9. The major fifth, fourth, sixth, 1. Helmholtz's double siren-2. Application of the law of simple |