The aesthetic traditions from which the violin's design evolved have roots that can be traced back to some of the earliest expressions of our civilization. In Ancient Greece, the idea of harmony signified the joining together of separate elements into a unified whole, and it was given a simultaneously musical and mathematical treatment by Pythagoras and his followers in the sixth century B.C. They found the simple ratios that describe the relationships between the lengths of vibrating strings and the consonant musical intervals, and these they held as evidence of a deep and simple mathematical harmony underlying the complexities of nature. 150 years later, Plato, in the Timaeus describes the architect of the world bringing order out of chaos by dividing it up and laying out the heavens and the earth in proportion, according to these musical ratios; and the planets were sent humming in their spheres in accordance with the musical geometry of this cosmic harmony. (See also the short essay "...On the Pythagorean Tradition" in the "Reflections..." section.)

 

In our own day, while we have divorced our aesthetic sense from that grand vision of an all embracing harmony, the Pythagorean legacy stills lives on in our mathematical sciences. For the modern luthier, the discipline of acoustical physics has supplanted the older ideal of musical proportion as a way of understanding our work. Today some luthiers yet try to capture the soul or character of an instrument in number -- the equations expressing the simple relationships between mass, stiffness, and dimension that determine its resonant frequencies and tonal response.

The beginnings of the basic layout are seen in the picture to the left. The centring circles are located by successive golden section divisions of the line segment forming the centre line of the body of the instrument. As can be seen, these are then used to establish the layout of the four corners, as well as the f-holes, providing a simple and integrative scheme for the basic elements of the instrument's design.

In my own work, I like to refer to the metaphor of the traditional musical geometry in the design of my instruments not so much in expectation of acoustical performance -- that depends more on other factors -- but more as an appeal to the imagination. I try to compose my designs (within my acoustic parameters) as I would a piece of music, with an eye to utilizing these traditional methods and proportions, laying out the arcs of the instruments' outline with compass and straightedge (or now, their electronic equivalents)-- sculpting with music -- trying to capture in my mind's ear an echo of that primordial harmony.

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