Descartes’s Musical Apprenticeship 97
This amazing letter ends with a larger consideration of the nature of sound that seems
to look from the contemporary theory of “ pulses ” of air set in motion by a vibrating body
toward a more general theory of waves. Descartes notes that the vibrations that strike the
ear are not those that engender the sound: he compares the process to the horizontally
spreading circles caused by a stone dropped in water, “ though the stone goes straight
down. ” This was not, to be sure, an original observation; Cohen judges that it remained
within the “ pulse ” theory of sound, which did not truly become a wave theory until a
century later when it developed into a mathematical theory of longitudinal waves of com-
pression and rarefaction.^31 But the question of the nature of sound was, for Descartes and
Mersenne, alive and connected to the musical and physical issues they were struggling
to resolve.
This intense exchange of letters at the end of 1629 was by no means the end of their
correspondence on these matters. Thirteen other letters remain from 1630 to 1634, spaced
more widely, bearing witness to Descartes ’ s interest in music in connection with other
issues in natural philosophy, especially the vibrating string and falling weights in and out
of a vacuum. Yet on April 15, 1630, Descartes wrote that “ in fact I cannot distinguish
between a fifth and an octave, ” though it is hard to take seriously his assertion that he is
really so tone deaf as not to know a fifth from an octave, when he has written so clearly
on just that difference. 32 He goes on to make an astute contrast between the recognition
of intervals heard out of context with the perception of intervals “ when they are placed in
a concert of music. ” His further remarks seem to admit knowing the very intervals he had
just claimed he could not distinguish.
In a letter of October 1631, Descartes theorizes thatsound is nothing else than a certain vibration [ tremblement ] of the air, that comes to tickle our ears
and that the turns and returns of this vibration are more sudden as the sound is higher [in pitch]; so
that, two sounds being an octave from each other, the deeper only vibrates the air one time while
the higher vibrates just twice, and likewise with the other consonances. Thus one must suppose that
when two sounds strike the air at the same time, they are that much more concordant when their
vibrations recommence more often with each other and when they cause less inequality in the whole
body of the air.^33The standard theory of “ pulses ” of two pitches that coincide more or less completely when
received at the ear here seems to shift toward a concept of frequency (as we now call it),
which considers the element of time with respect to the vibration itself. At this point,
Descartes wrote in the margin that “ I abuse here the word ‘ vibration ’ that I take for each
of the blows or little shakes that move the body that vibrates. ” His marginal note shows
his hesitation about how exactly to describe the state of the vibrating air , as opposed to
the vibrating body that caused the sound or the vibrating ear receiving it. This problem
continued to be the central issue on which rested the mathematical theory of waves and
vibrations, and hence the whole mechanical theory of continuous media. The vibrating