The Dream of Oresme 27
Table 2.1
Oresme ’ s diagram.
1 2 4 8 16 32
3 6 12 24 48
9 18 36
27 54 108
81
243
729possibilities, Oresme may be indicating implicit speculations about as yet unused “ har-
monic ” possibilities. Less speculatively, his diagram indicates a nascent interest in pure
combinatorics (the array of all possible products of a certain form, here powers of 2 and
3), as well as the possibility of visualizing them in such an array.
Oresme approvingly quotes Cassiodorus ’ s sentiment (by then a commonplace) that
human ears are too gross to perceive these celestial ratios, which also govern earthly music.
Yet, along with Boethius and so many ancient authors, Oresme nonetheless goes on to
consider even an inaudible “ music ” of the spheres as crucial to the cosmos. In so doing,
he shows the continuing availability of music as the meeting ground between the supra-
sensual world of mathematics and the perceptible evidence provided by astronomy.
In fact, Oresme deploys music to solve a long-standing astronomical problem. In geo-
centric cosmology, there remained the question of which musical pitches should be
assigned to the various heavenly spheres. In particular, does the “ highest ” sphere, that of
the fixed stars, correspond to the lowest or the highest pitch of the celestial system, even
assuming (as Oresme does, following Aristotle) that no audible sound results? Even though
these spheres produce no sound grossly audible to our ears, Oresme still applies the
musical language of relative pitch to describe the various possibilities. He uses the spheres ’
decoupling from ordinary processes of sound production to consider new possibilities of
“ musical ” cosmology.
If, he asks, the sphere of the fixed stars were in diurnal revolution, as required by the
geocentric view, then what musical pitch should be associated with it? Oresme notes that,
according to many accounts, this rapid revolution of a huge and massive structure is often