114 Chapter 7
Having used an instrument string to measure the frequency of sound and its laws, Mer-
senne points out that “ if one brought a piece of music from Paris to Constantinople, to
Persia, to China, or elsewhere, along with those who understood the notes, ” they could
perform the piece “ according to the intention of the composer ” because they could adjust
the pitch to the Parisian standard, using his laws to generate the corresponding frequency.^25
Further, the tempo could be specified in universal units, such as beats per resting pulse or
per second by the clock.
These issues of musical time also are connected with Mersenne ’ s reconsiderations of
the clock itself and the means by which it might measure time more accurately. This
forms part of his book on the “ movements of all sorts of bodies, ” on which depends
the problem of vibrating strings. Here, he is much influenced by Galileo, whom his
own activity in this field outstripped on some occasions. In June 1634, he noted that
the frequency of a pendulum is inversely proportional to the square root of its length,
a full year before Galileo found this result. In his Harmonie , Mersenne provides a table
showing this result, noting that physicians might use such a simple pendulum “ to find
out how much faster or slower is the pulse of their patients at different hours and days,
and how much the passions of anger and other hasten or retard it. ” He also noted that
watchmakers could also use this device to improve time-keeping; though the pendulum
watch was not patented by Christiaan Huygens until 1656, with improvements that were
important for it to reach sufficient accuracy for navigation and other precise uses,
Mersenne ’ s insight was an important step.^26
Mersenne ’ s detailed treatment of the mechanics of falling bodies, inclined planes, and
pendulums clearly supports and enables his ensuing deductions about vibrating bodies,
following out Descartes ’ s insight that a vibrating string could be understood as an ensem-
ble of pendulums, one for each point along the string. As Peter Dear puts it, “ Mersenne
accomplished the harmonization of mechanics through the mechanization of music. ”^27 But
Mersenne did not only move in one direction with these deductions, from musical observa-
tions to physical theories. He also moved in the other direction, from the physical proposi-
tions he had established to their musical applications. For instance, he studied the various
sounds made by falling bodies, which vary in pitch depending on the height from which
they fall. From what heights, he asked, ought they be dropped so as to produce any given
consonance or dissonance? He worked out an elaborate table that he mapped into a striking
crisscross circular design, in which the entire musical scale is cross-referenced with the
appropriate falling body ( figure 7.5 ). This construction hovers somewhere between the
conceptual and the observational; it does not seem credible that he has actually heard
the pitches of these “ singing ” bodies with any degree of accuracy as they fell. Mersenne
gives the authority of Aristotle for the general premise that “ a sound is that much higher
if it is made by a faster movement, ” to which he adjoins the Galilean law of freely falling
bodies. From this, Mersenne extrapolates the degrees of velocity reached by two falling
bodies (depending on the height from which they were dropped) and then rather arbitrarily