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Musical acoustics in the age of Vitruvius

Musical Times, Spring 2005 by Maconie, Robin

ACOUSTIC AND MUSICAL IMAGERY play a distinct if forgotten role in myth and legend. The name 'Jack' in a nursery tale, for example, can be a clue to a story told with the aid of a plucked string instrument, an allusion echoed in the name of the plucking mechanism of a harpsichord. Both 'Jack and the beanstalk' and the rhyme 'Jack and Jill' can be understood in this way, as stories related to the resonances of stretched strings, to be told with the aid of a musical instrument, a harp in the former case, a single string (monochord, guitar, fiddle, lute) in the latter.1 Other examples of traditional lore with a musical subtext include Zeno's paradox of Achilles and the tortoise,2 and the biblical account of Samson slaying the lion and its body being colonised by a swarm of bees, a variant of which is given by Virgil in Georgia II.3 Studies of harmonic relations between strings of similar length but differing weight and tension, or of different length but similar weight and tension, are reflected in philosophical and doctrinal issues as weighty as the dynamics of the solar system,4 the organisation of the ideal state,5 and the sacrament of the eucharist.5

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Acoustics and musical considerations also play a hidden role in classical architecture. Despite extensive and explicit documented indications of the correspondence of structural proportions and musical ratios in historic religious, civic, and domestic buildings, almost no attention has been given in the literature to the practical and philosophical implications of proportioning an interior in accordance with the modes of vibration of a stretched string (or air column, say of a trombone). In Rudolf Wittkower's magisterial Architecture in the age of humanism, to take just one example, the author discusses the theoretical and cultural antecedents to musical proportioning in the architecture of Palladio, a figure of crucial importance in the history of urban design, without once considering that musical ratios are of any more than aesthetic significance.7 In an era lacking universal standards of measurement, architects and builders alike worked to a system of proportion, and employed musical devices such as the tromba marina to ensure that the ratios of length to breadth to height were in harmony with one another.8 These were instruments designed to be fine-tuned to the longest dimension of a rectangular room, by adjusting the pitch to a point where the direct and reflected sound combined to produce a distinctly brighter and louder tone. This harmony of tone and dimension occurs when the fundamental wavelength of the tone (the distance between successive pressure peaks) conforms exactly with the distance between opposing walls, or to a unit fraction of it, an effect sometimes called the eigentone. Having established a 'fundamental' equivalent to length by assisted resonance of a standard tone of fixed pitch, the builder is then able to derive exact width and height ratios from harmonics of the same wavelength, expressed as string tension or trombone tube length (slide position). This is not as difficult as it sounds, since the basic structure needed to arrive at an accurate measurement, i.e. to adjust the distance between two walls to a separation at which an audible reinforcement of a wavelength is produced, only requires a fixed wall (preferably in the open), a flat paved surface, and an adjustable wall, consisting of a few courses of loose bricks, at the approximate distance required. It is fine-tuned measurement, a little like surveying today with a laser interferometer. Suppose the desired length to width ratio is 4:3, for instance, the tromba marina having been tuned to the longer wavelength, moves into position between the fixed and movable walls, plays its third harmonic to set the new wavelength, and the loose bricks are moved back or forward until a ringing tone is heard. The new measure can then be recorded as a knot in a guideline.

THE ten books on architecture written in the first century by Marcus Vitruvius Pollio summarise the precepts of town planning, civic engineering, and the design and construction of public and private accommodations in ancient Greece and Rome. Vitruvius inspired the classical revival in European building design and his study remains essential reading for students of architecture and architectural history today.9 He was a practical professional rather than a philosopher. What he has to say about music and acoustics can tell us about the realities of musical thinking in classical times, simply because the design of cities and buildings expresses the real priorities of living, as distinct from the kind of aesthetic or moral pronouncements encountered in Plato on the implications of applying music for entertainment purposes or the enhancement of poetic meaning.

The bulk of Vitruvius's remarks on acoustics relate to public building and amphitheatre design. Voice projection is a major consideration. In a larger building where a speaker has to be audible over a considerable area, audibility (locating the source) is as much a factor in design as intelligibility (being able to understand what is said). Audibility relates to the unimpeded and assisted transmission of sound from a distant source to the listener, and is the architect's main concern; intelligibility on the other hand relates to the contribution of structural resonances and reflections to the diffusion of a near or distant signal, and involves a knowledge of building materials and construction. Both audibility and intelligibility involve a partnership between the speaker and the built environment. A speaker learns to speak more loudly and evenly for the voice to carry a greater distance, and to articulate more distinctly in order that the words spoken may remain clearly audible in every particular.

Musical acoustics in the age of Vitruvius

Musical Times, Spring 2005 by Maconie, Robin

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