2011 © Hector MacMillan | Terms & Conditions

Honorary Fellow: Association For Scottish Literary Studies

“If we investigate only by physical and chemical means, we can only get physical and chemical answers.”

Sir Alister Hardy, FRS

The question of the Helmholtz resonance as it might relate to the violin-family of instruments first came to my attention around the late 1970's. Experiments then being carried out in Europe and the USA had identified the main cavity-resonance in a 4/4 violin at about 275Hz, a result that went on to find widespread acceptance. Measurements I made at the time, admittedly with very basic electronic equipment, disagreed with this.

As I understood it, the basic 19th century equation stated that the resonant frequency of a cavity, irrespective of shape, is given by Speed of Sound upon 2¹, times the Square Root of the reciprocal of contained volume. Applying this to standard violin-corpus dimensions of approximately 2000cc contained volume, with no correction factors for aperture applied, a predicted resonant frequency of approximately 122Hz results. A small resonant peak [on Sound Level Meter 70db scale] was indeed found, with some difficulty, very close to this calculated frequency.

Puzzlingly, there was another larger peak [SLM 80db scale] at 244 Hz, exactly one octave higher. This higher resonance also proved very difficult to detect because there was a very much larger resonance still, at approximately that commonly-accepted 275Hz figure, which all but swamped it.

Suspecting that Strings and Sound-post might be introducing unhelpful complications, tests were repeated without these. The empty cavity still provided resonance peaks at nominally the same frequencies as the Helmholtz equation had indicated, but with the larger 275Hz resonance now completely absent they were easier to identify.

It would appear that instead of raising the “Helmholtz” resonance by stiffening the cavity walls, as the literature has maintained, the Sound-post introduces an entirely new and stronger resonance [created by mechanical connection between the top and bottom plates] but one which leaves the originals relatively unchanged, if a great deal more difficult to detect. However, at the time, I could find no academic interest willing to investigate further.

I directed most of my work thereafter at attempts to improve the playability of the viola, but ultimately the problems of tuning the Fingerboard led back to that niggling question about the fundamental cavity resonance. A more careful repetition of those earlier tests on the violin was initiated.

To minimise interference with what was being measured these later tests utilised a high-quality earpiece to seal and at the same time inject a sinewave signal at the Tailpin hole, while a Sound Level Meter positioned close to the f-holes measured response. The earlier results were found to have been acceptably accurate

For the various sizes of Viola a rough estimate was made of the contained volume, allowing for the probable effects of linings and blocks, then the calculation made for the expected resonances. Tests were again carried out with the instruments de-strung and no Sound-post fitted.

As had been the case with the violin, the lower of the two detectable resonances [always an octave apart] was seldom more than five percent or so out from the calculated figures, except in the case of fractional-size instruments.

Once again, when the Fingerboard was tuned appropriately, the response across the strings was evened out, with the strings [particularly the A-string] needing considerably less tension to produce a much more sonorous sound.

Whether the two frequencies detected each time are both true resonances or not is unclear, but what is not in doubt is that the basic Helmholtz equation appears to indicate quite accurately the frequency, or an octave relation, to which the Fingerboard should be tuned for optimum response and playability in violins and violas.