Moving the Immovable 45
Box 3.2
(continued)Josquin ’ s final Phrygian cadence recapitulates the extraordinary arc of the whole motet by
moving from a Dorian harmony (D – F – A) four measures from the end via a penultimate
Aeolian harmony (A – C – E) to the final, extended Phrygian chord (E – B) ( ♪ sound example
3.4c):vertical rise eventually gave way to its natural fall. With this in mind, Josquin ’ s feat exceeds
the ancient example of Philoxenus, going beyond the natural (and pagan) to show the even
greater force of divine grace.
The implications of Aristotle ’ s analysis extended beyond musical examples. Oresme had
used Aristotle ’ s categories in formulating his new mathematics of change.^10 In 1624,
Francis Bacon epitomized “ all violent motion ” by a moistened finger rubbing a glass ’ s
rim to excite its ringing, which he found similar to the chiming of a bell or the plucking
of a string. This “ motion of liberty, i.e. from compression to relaxation, ” Bacon considered
“ the chief root of all mechanical operations, ” transforming nature itself through the artful
redirection of “ violence. ”^11 Medieval alchemists theorized the possibility of elemental
transmutation in terms of Aristotle ’ s concept of an undifferentiated “ prime matter ” that is