In the century after Oresme ’ s imaginary debate between Arithmetic and Geometry, their
sisters Music and Astronomy returned to the question whether a seemingly immovable
center could somehow move. That center could be the Earth or the mode of a musical
composition, both generally assumed to be unchanging. Because each celestial sphere was
associated with a mode, a change of mode suggests motion between spheres. As innovative
musical compositions used unprecedented changes of mode, the immovable musical center
began to move. In the following decades, the new astronomy put forward the theory of a
moving Earth. Other musical considerations moved Vincenzo Galilei to prefer heliocen-
trism decades before the controversy came to a head. More generally, harmony became a
crucial term in the debates about Copernican astronomy.
Through the fifteenth century, writers on music struggled with disturbing contradictions
between the ancient authorities about the exact ordering of the celestial spheres. For
instance, in his Liber de arte contrapuncti ( Book on the Art of Counterpoint , ca. 1476),
Johannes Tinctoris expressed considerable frustration:
I cannot pass over in silence the opinion of numerous philosophers among them Plato and Pythagoras
and their successors Cicero, Macrobius, Boethius, and our Isidore [of Seville], that the spheres of
the stars revolve under the guidance of harmonic modulation, that is, by the consonance of various
concords. But when, as Boethius relates, some declare that Saturn moves with the deepest sound
and that, as we pass by stages through the remaining planets, the moon moves with the highest,
while others, conversely, ascribe the deepest sound to the moon and the highest to the sphere of the
fixed stars, I put faith in neither opinion. Rather I unshakably credit Aristotle and his commentator,
along with our more recent philosophers, who most manifestly prove that in the heavens there is
neither actual nor potential sound.^1
This fundamental disagreement led Tinctoris to join Aristotle in rejecting celestial sounds,
but other writers generally opted for one or the other of the ancient alternatives. Thus,
Giorgio Valla in 1501 followed Boethius and assigned the sun the mese , the “ middle ” note
of the Greek gamut ( figure 3.1a ), whereas Franchino Gaffurius in 1596 followed Cicero
and assigned it the lychanos hypaton , the “ highest ” note ( figure 3.1b ).^2 Yet both versions
associated the sun with the Dorian mode (see figure 3.4 ), considered the first or primal
3 Moving the Immovable
