Thomas’s Mathematical Music

Metaphysics of the Music, part 15

The previous post noted the comparatively spare use Aquinas, unlike earlier theologians such as Augustine or Boethius, made of musical imagery as a metaphor for cosmic harmony. As we shall see, rather, the relevance of Thomas’s views on music for understanding Tolkien, ironically, have more to do with his view of music as exhibiting an exceedingly abstract, almost mathematical kind of existence. In his commentary on Boethius’s De Trinitate, Thomas closely associates music with mathematics on account of the way music derives its first principles from arithmetic and applies these principles to natural things: “In another way, one science is contained under another as subalternated to it. This occurs when in a higher science there is given the reason for what a lower science knows only as a fact. This is how music is contained under arithmetic.” (Commentary on Boethius’s De Trinitate 5.1 ad 5, trans. Maurer). For Aquinas, music represents an “intermediate” between mathematics and natural science, yet he says it bears “a closer affinity to mathematics” since music is more “formal” and thus more separated from matter and motion than is the case in natural science: “music considers sounds, not inasmuch as they are sounds, but inasmuch as they are proportionable according to numbers” (5.3). Behind Thomas’s argument here is his teaching that, although concepts of both mathematics and natural objects involve an act of mental abstraction separating their intelligible principles from the physical, sensible substances in which these principles are actually experienced, mathematics and natural science nevertheless differ in their respective degrees of abstraction (5.1-2). In the case of a mathematical object such as a circle, there is no reference in the concept of a circle to the kind of matter that real (i.e., non-mental) circles are actually made of, since circles can be made out of virtually anything. The case is otherwise with concepts of natural substances such as man, for which the kind of matter the thing is made out of comprises an integral part of the substance’s essence or form. Thus, while the concept of man, like the concept of a circle, is produced by the mind’s abstracting it from the determinate or “signate” matter out of which individual men or circles are actually made, the concept of man nevertheless retains a notional reference to the kind of matter out of which real men are made, namely flesh and bones. To return to the question of music, then, for Thomas, while music as we experience it is of course an inherently physical, sensible, and sensuous phenomenon, in terms of the formal qualities which constitute its sounds as musical sounds, the comparative indifference of music to the particular, material environment, circumstances, or conditions under which it is played makes it similar, in Thomas’s mind, to the heightened degree of mental abstraction involved in mathematics. For Thomas, in short, music is a highly abstract reality that is ultimately concerned with sound, not as sound (i.e., an inherently physical phenomenon), but as a peculiarly mathematical and proportionate kind of sound.


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