Why Aren't Vibrations and Acoustics More Helpful In Designing Musical Instruments? by Mark French

Almost everyone who knows anything about musical instruments has heard about the mystique surrounding Stradivarius violins. Stories about the creation and the life of million dollar Strads are now the stuff of movies, legend and urban myth. Perhaps it is an inseparable part of the American psyche that we love to rate things and are always interested in the one, single best of just about anything. Talk to a Harley-Davison fanatic if you want to do a little field work on this topic. Anyway, conventional wisdom has it that Strads are the best violins ever, whatever that means. Not surprisingly, there have been many attempts to analyze the sound and the construction of these instruments to see what makes them so good. Very good technical people have applied pretty much every tool available to the problem. These tools include CAT scans to precisely define the geometry and scanning laser vibrometers to measure the structural response. The results, however, have been inconclusive.

The problem might be thought of as having two separate components. The first is describing exactly what features of the sound makes these instruments so wonderful (and they clearly are wonderful, whatever that means). This is a purely descriptive task and would seem to be a textbook application of psychoacoustics. The second part of the problem is to describe the structural features of the instruments responsible for the sound.

Experimental results hint at some of the causes of the wonderful tone of these instruments, but I know of no clear, accepted explanation. The literature is full of papers about how minor differences in the finish are important and how the instruments need to be conditioned by exposure to sound. There are also all kinds of speculations about kinds of wood and how it was conditioned before construction. It seems that, for every authoritative statement, one can find an opposing, but equally authoritative statement. My guess is that our tools are still far too crude for the task at hand. It is possible that the test equipment is still not sensitive enough, but I suspect, rather, that our analysis methods are more the problem. A couple areas for improvement come to mind:

1 - Many people have done modal analysis on violins. The general result is that at higher frequencies, the modal density is so high as to make interpretation a near hopeless task. It would seem that linear modal analysis may not be the tool for the job. Does that mean non-linear analysis is required? I hope not, but maybe. Maybe there is a different, but still simple way of looking at the structural data. After all, modal analysis assumes we are measuring the answer to a set of 2nd order linear differential equations. Yet, we know those equations are only an approximation.

2 - Psychoacoustics is still a young field and I think there is definite room for improvement in our suite of metrics. There are lots of cool buttons in psychoacoustic software packages, but I suspect that we have a long way to go in really understanding what they all mean

3 - Our methods for analyzing acoustic-structure interactions are still not developed enough for the task. I know of no finite element model good enough to clearly represent the higher modes of a violin or any other stringed instrument. Then, there is the problem of the computing power needed to do a BEM analysis of the instrument that would be valid at higher frequencies. It gets out of hand pretty quickly.

I want to be clear that these observations are not a comment on the technical abilities of the people who have worked on the problem. Problems worthy of attack show their worth by fighting back. This is one of the great ones; it is the intersection of physics, physiology and psychology. It will certainly be a thrill when somebody finally figures out the answer, but part of me will still be sorry that the mystery is no longer. Dunnwald, H.; "A Procedure for the Objective Estimation of the Tone Quality of Violins", Acustica, Vol. 58, No. 3, August 1985, pp162-9

Fletcher, Neville and Rossing, Thomas, "The Physics of Musical Instruments", Springer-Verlag

Hutchins, C.M.; "The Air and Wood Modes of the Violin", Journal of the Audio Engineering Society, Vol. 46, No. 9, Sept. 1998, pp751-65

Jansson, E.V.; "Admittance Measurements of 25 High Quality Violins", Acustica, Vol. 83, No. 2, March-April 1997, pp337-41

Rossing, Thomas, Moore, Richard and Wheeler, Paul, "The Science of Sound", Addison Wesley