Musical acoustics in the age of Vitruvius

Musical Times, Spring 2005 by Maconie, Robin

As if to confirm this, Vitruvius goes on to summarise Aristoxenus's classification of the Greek modes. Why is this important? Vitruvius is not a musician and does not claim to be one, saying only that he is including a section on the modes for the sake of completeness. In doing so, however, he is also telling the reader that designing for public speaking involves musical considerations.

THE enhancement of speech melody is further addressed in a chapter on amphitheatre design. Modern recording studio and concert hall architecture is designed to provide equivalent enhancement to all degrees of the musical scale, in keeping with our Western musical heritage of equal temperament, unhindered modulation, and latterly 12-note and electronic music. Such freedom of movement of a fundamental tone is specific to advanced written music of European origin, and in any case creates problems for the acoustic design of public buildings. What we can learn from the Greek system of modes is of a system of pitch priorities allowing for certain notes being fixed, and others (characterising the particular mode of expression) being variable. Under such a convention the job of the architect is to respect the interval proportions of the priority fixed pitches forming a tetrachord that remains constant for every situation. Vitruvius also discusses the use of jar resonators to enhance alternate pitches. The four fixed pitches are identified approximately in modern notation as A and B below middle-C, and D and E above.12

We can show that the wavelengths associated with these pitches are also related to standard human dimensions. The pitch A = 440Hz, a wavelength of around 30 inches, is equivalent to the unit length of a Roman pace (passus); the adjacent B to a wavelength of about 26 inches, perhaps related to the shorter step length of an average Roman adult female. Elsewhere Vitruvius specifies the dimensions of the seating in an amphitheatre as 'not less than a foot and a palm in height, nor more than a foot and six fingers,' and the depth of the terraced seating 'not more than two and a half feet, nor less than two feet.'13 Since a Roman foot, defined as one-sixth of a man's height (of approximately 5' 6'') is about 11 inches, these Vitruvian measures correspond to betweeni3 and 15 inches in height (i.e., half a passus), and 22-27 inches in depth. From an acoustical viewpoint it is the depth of seating that is responsible for reinforcing the tonality of a speaking voice, since the cascade of periodic reflections from the risers of stepped seating of equal depth reinforces pitches of the wavelength represented by the depth of the seating, which for seating of 22-inch depth is about E, and for 27 inches B (a 10:9 tone), in general agreement with Aristoxenus.14 So when Vitruvius declares 'There can be no consonances either in the case of the notes of stringed instruments or of the singing voice, between two intervals, or between three or six or seven; but, as written above, it is only the harmonics of the fourth, the fifth, and so on up to the double octave ',15 he is not talking about consonances as between a voice and accompanying lyre or harp, but of room-assisted resonance as it affects the voice or assists the voice accompaniment of a stringed instrument, and he is also saying that assisted resonances are limited to those intervals that would normally correspond to the proportionate wavelengths of a room for length and breadth, or to intervals in the ratio 4:3, 3:2, 2:1, 8:3, 3:1, 4:1.