The Physics of the Violin

by Lothar Cremer

This major work covers almost all that has been learned about the acoustics of stringed instruments from Helmholtz's 19th-century theoretical elaborations to recent electroacoustic and holographic measurements. Many of the results presented here were uncovered by the author himself (and by his associates and students) over a 20-year period of research on the physics of instruments in the violin family. Lothar Cremer is one of the world's most respected authorities on architectural acoustics and, not incidentally, an avid avocational violinist and violist. The book—which was published in German in 1981—first of all meets the rigorous technical standards of specialists in musical acoustics. But it also serves the needs and interests of two broader makers and players of stringed instruments are expressly addressed, since the implications of the mathematical formulations are fully outlined and explained; and acousticians in general will find that the work represents a textbook illustration of the application of fundamental principles and up-to-date techniques to a specific problem. The first—and longest—of the book's three parts investigates the oscillatory responses of bowed (and plucked) strings. The natural nonlinearities that derive from considerations of string torsion and bending stiffness are deftly handled and concisely modeled. The second part deals with the body of the instrument. Special attention is given to the bridge, which transmits the oscillations of the strings to the wooden body and its air cavity. In this case, linear modeling proves serviceable for the most part—a simplification that would not be possible with lute—like instruments such as the guitar. The radiation of sound from the body into the listener's space, which is treated as an extension of the instrument itself, is the subject of the book's final part.

482 pages, Paperback

First published January 1, 1981

Reviews

[Daniel Pezely · Rating 4 out of 5]

Best suited for physicists who seek mathematical proof of acoustic properties and tactile feedback for aspects that beginning strings players would already understand.

Seemingly practical theories about finger corrosion of strings affecting its mass are outweighed by the practical tendency to replace strings before they break.

Regarding cello soloists performing on a riser or platform: Chapter 14 ends (starting end of p406) noting the value of such platforms might be just tactile feedback to the performer, and if so, let that be reason enough; whereas, a solid smooth surface behind an upright bass has measurable benefits for its acoustic projection.

Only a few items such as those accommodate performers.

That said, the mathematical explanations and validations provided are very thorough if not that practical for a musician or luthier without further extrapolation.

For instance, a physicist or mathematician reduces a problem to idealized components such as an infinitesimal point where a vibrating string crosses the bridge. A mechanical engineer or luthier knows that there are practical consequences to an actual string curving around the top of a carved/planed wood bridge with notches for strings.

While those differences are acknowledged in the book, more context would be welcomed. An additional sentence here and there could have made its information more concrete and practical. Instead, articles on websites for various manufacturers of strings address those details.

I would have loved to read a physicist's insight on André Theunis' article, The Golden Proportions of Cremona (The vibrating string as the basic module), which describes how string length on a Strad mould matches length of interior volume of the resonance chamber and that the upper bout, lower bout and C-bout widths are half its length, inverse Phi and half that, respectively. Unfortunately, no such exploration is given in this book.