When we wrote the first edition of this book, we directed our presenta- tion to the reader with a compelling interest in musical instruments who has "a reasonable grasp of physics and who is not frightened by a little mathematics." We are delighted to find how many such people there are. The opportunity afforded by the preparation of this second edition has allowed us to bring our discussion up to date by including those new insights that have arisen from the work of many dedicated researchers over the past decade. We have also taken the opportunity to revise our presentation of some aspects of the subject to make it more general and, we hope, more immediately accessible. We have, of course, corrected any errors that have come to our attention, and we express our thanks to those friends who pointed out such defects in the early printings of the first edition. We hope that this book will continue to serve as a guide, both to those undertaking research in the field and to those who simply have a deep interest in the subject. June 1991 N.H.F and T.D.R.