116 Chapter 7
takes the ratios of these speeds to represent the musical ratio that they would sound at that
terminal velocity. He does not correct for air resistance or any other factor that would
indicate the kind of experiment he elsewhere insists on; this whole proposition seems a
jeu d ’ esprit , an imaginary return from physics back to the spirit of music from which it
had emerged. Though allegedly staged on Earth, its pattern of deduction is much closer
to that which Kepler (and Mersenne) had used to examine the harmonic relations between
the planets. In that sense, Mersenne is trying to bring back to Earth what he had learned
in the heavens.
Above all, Mersenne ’ s musical motivations led him to investigate the physics of sound.
Descartes had noted overtones at the octave, fifth, and third; Mersenne noticed other
petits sons , “ little sounds ” that could be heard from a single string a second octave higher
and, above that, the note a major third higher still ( figure 7.6 ). Their successive ratios of
string lengths fall along the series of the first five integers. He noted that “ it is necessary
to find complete silence to perceive them, although this is not necessary when one has a
trained ear. ” These overtones were overlooked because musicians “ are so anticipating and
preoccupied with the natural tones of the string that there is (it seems) no place in their
ordinary senses or imagination to receive the idea or species of these small, delicate
sounds. ” He notes that it is easier to hear them played by a bass viol in the silence of the
night, details that suggest the range of his experiments. Despite the difficulty of producing
and distinguishing these sounds from the fundamental tone (or the habitual sound of the
string in the player ’ s ear), “ I have had no difficulty and I have met many musicians who
hear them as well as I and undoubtedly ever one hears them when they lend the necessary
attention. ”^28 Though the petits sons had been there all along, Mersenne was the first to
hear so many of them because of his extraordinary attention to every detail of musical
experience and instrumentation. As precedents he mentions only Aristotle, not Descartes,
though Mersenne knew of Descartes ’ s Compendium. Even so, Mersenne went much
further than Descartes precisely because of his far greater interest in the fine details of
music. Where Descartes barely commented on the extra tones, Mersenne verified his
observations “ very exactly more than a hundred times, on the viol and on a theorbo, as
well as on two monochords, ” in order to exclude the possibility “ that these different tones
do not come from other strings that are on the instruments and that tremble without beingFigure 7.6
The fundamental pitch (C) and the first four overtones ( petits sons ) above it, corresponding to integral ratios, as
observed by Mersenne.