Mersenne’s Universal Harmony 111
Mersenne also emphasizes that the investigations of sound and light mutually clarify
each other, so that the study of sound is the royal road to understanding nature as a whole.
Ever since his visits with Descartes and Beeckman in the Netherlands in 1628 – 29, he had
considered light, like sound, to be a purely corporeal phenomenon. This required a certain
adjustment in reading the divine poetry of scripture so as not to conflict with these scien-
tific insights. In that spirit, Mersenne interprets sacred scripture to present the study of
universal harmony as the key to human excellence, whose understanding of nature culmi-
nates in personal and religious perfection.^16
Writing in the aftermath of Galileo ’ s pioneering work, and by comparison with it, one
might think of Mersenne as derivative or as essentially a reporter, not an originator of
discoveries. Yet Mersenne reached certain insights well before Galileo. As he presents
his work in Harmonie Universelle , he connects these insights within his overarching
musical context. Though he was rarely, if ever, truly original in the sense of initiating a
new question or line of investigation, Mersenne was able to use his extraordinary persis-
tence and awareness of the history of prior developments to extend them still further. Some
of these have an obvious musical origin and importance, such as his demonstration that
pitch is proportional to frequency and hence musical intervals are ratios of frequencies of
vibration. Though G. B. Benedetti, Vincenzo Galilei, and Beeckman had already estab-
lished the fundamental argument underlying this general proposition, Mersenne showed
how to count the slow vibrations of very long strings against “ a heartbeat, or a very slow
and lazy pulse ” he takes as measuring a second of time.^17 In so doing, he gives an experi-
mental and observable actuality to this proposition, in accord with his principled prefer-
ence for deeds over words. Mersenne ’ s musical-physical experimentation gave the first
absolute measurement of the frequency of a vibrating body, which Galileo had thought to
be impossible because the rapidity of audible vibrations blurs them together so that they
cannot be counted by sight.
Mersenne solved this problem by using a string 17 ½ feet long, “ a lute or viol string
of the size one mounts on racquets, ” alluding to the vogue of tennis that also touched
Descartes, though this Gargantuan string is “ made from a dozen sheep ’ s intestines. ”^18
Essentially, Mersenne magnified a musical string to the point where its vibrations are
commensurate with human sense capabilities. Stretched under a weight of half a pound,
his string vibrates at two cycles per second, just countable because its cyclical “ turns
and returns ” have been sufficiently slowed. Then Mersenne increases the weight on the
string: under two pounds, it vibrates four cycles per second; under eight pounds, eight
cycles per second. Though he does not make this explicit, these observations depend on
his musical awareness, for these specific cases correspond to successively higher octaves
above the lowest tone, as given by the series of ratios of frequencies 2:4:8 given by the
ratio of weights ½ :2:8. One infers that he adjusted the weight upward and listened for
the octaves (and perhaps also noted the characteristically doubled visual wave-form of
the string).