Descartes’s Musical Apprenticeship 91
he finds the simpler lines of the rete more “ satisfying to the sense ” than the complex design
of the mater because the rete is more distinctly perceivable. The man who would go on
to advocate “ clear and distinct ideas ” uses an astronomical instrument to illustrate the
aesthetics of melodies.^10
Sense can perceive an object “ more easily ... when the difference of the parts is smaller ”
and “ when there is greater proportion between them. ” These proportions “ must be arith-
metic, not geometric, the reason being that in the former there is less to perceive, as all
the differences are the same throughout, ” such as in figure 6.2. By comparison with the
simple progression of an arithmetic proportion (in his example, 2, 3, 4), a geometric pro-
portion involves a middle term whose relation to its neighbors is harder to discern, such
as dividing an octave 2:4 in half at its geometric mean 8. Though Descartes accepts thatFigure 6.1
An astrolabe from the workshop of Jean Fusoris (Paris, ca. 1400) in the Collection of Historical Scientific Instru-
ments, Harvard University. The rete is the inset metal structure with curved lines, showing the mater and plate
underneath; the straight rule rotates to measure distances on the instrument.