Arthur H. Benade - Fundamentals of Musical Acoustics: Second, Revised Edition

This book is addressed most directly (though not exclusively) to people having a reasonable playing knowledge of music who would like to learn something of the ways in which music as an art form intertwines itself with our understanding of vibrating objects, with the study of auditory perception, and with the craft of the instrument maker. The focus of the book is on the vibrations of objects and of the air which surrounds them, but the particular manifestations of vibration physics that are chosen for discussion are those which play a significant role in actual music-making. Because music is intended to be heard, we must give considerable attention to the way in which our auditory nervous system functions as it picks out musical patterns from the complex acoustical signals that reach our ears. In the parts of this book dealing with vibration physics and practical music, I shall be quite explicit in telling how and why various phenomena take place. The perception aspects of our subject will be dealt with somewhat differently. I will tell what it is we hear when various kinds of sound are presented to our ears, but will not describe how the vibrations of an eardrum are led through the middle and inner ear to produce a myriad of nerve impulses that travel by many pathways to the central nervous system. Nor will I detail how these impulses come to act upon one another in several ways simultaneously, in a continuous process that can span a number of successive sounds to provide us with recognizable patterns of sensation. In other words, in this part of the subject we will confine ourselves to a description of phenomena, without much concern for the ways in which they come about.

The manner in which each topic is introduced, the order of presentation, and the choice of the topics themselves have all been predominantly influenced by my experience with musicians and instrument makers as we have worked together over the past two decades. Much of the material in this book is of recent origin, a considerable fraction of it being the result of my own observations and calculations, or of my analysis of the recent work of others. While I have tried everywhere to make clear the reasoning behind each assertion and to present examples of the data which support it, it must be understood that the reasons and examples shown here are merely illustrative and constitute only a small part of the basis for my conclusions. Almost everything in this book has had the benefit of extensive rehearsal in both spoken and written form. Over the years I have been blessed with a number of extremely capable students and laboratory guests. The opportunity to sharpen up the various ideas by talking with these people and with interested colleagues in physics and engineering has been immensely valuable. More recently I have had to deal with the expository problems connected with teaching various methods of adjustment to craftsmen or explaining the reasoning behind my activities as I trimmed up someones trumpet, flute, clarinet, oboe, or bassoon. These experiences have added a certain intensity to the more relaxed classroom atmosphere of the courses and lecture series in musical acoustics I have given.

One question that immediately arises in the mind of a prospective reader of a book on acoustics written by a physicist concerns the amount of mathematical knowledge that will be required of him. If you will leaf quickly through the book you will notice that I have rigorously confined myself in the text to the simplest of arithmeticaddition, subtraction, multiplication, and division; a number may occasionally be squared or carry a square root sign. Numerical illustrations of the various calculations are supplied in almost every case, partly as a way to show what is going on and partly as a convenient way to supply ourselves with numbers for later use.