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.

Did Aquinas have an Aesthetic?

In the previous post I cited Leo Spitzer’s comment that Aquinas does not seem to have had “the Augustinian ear for world harmony, ascribing to music a holy character only insofar as it was an element of the liturgy; as an Aristotelian he ‘reflects’ the world as it is, rather than attempting to re-create it by forging it together into a unit.” If so, the alleged tone-deafness of St. Thomas in matters of metaphysics might be related to the general absence of an explicit aesthetics in Thomas’s thought. John Milbank, for example, observes on the one hand that “[j]ust because there was no aesthetics in Aquinas’s theological philosophy, the aesthetic is therein everywhere present,” while on the other hand suggesting that “the latency of fundamental beauty in Aquinas meant that it was also for him a blind spot: one could even say that Aquinas probably supposed his own theology to have more to do with abstract reason than was really the case. This blindness invited a later rationalistic reduction by nominalism and neo-scholasticism of the Patristic legacy in which he stood, and to resist this one indeed requires a more explicit aesthetics, conjoined to a more explicit poetics…” (Milbank, “Scholasticism, Modernism, and Modernity,” 670). Related to this is Francesca Aran Murphy’s observation that, unlike Franciscans such as St. Bonaventure, none of the Dominican scholastics, including Albert the Great and St. Thomas, ever explicitly listed beauty as a transcendental and therefore convertible property of being. On the other hand, Murphy points out that, “whilst both Albert and Thomas say little of beauty in the main body of their writings, they both succumb to its lure in their respective Commentaries on The Divine Names of Pseudo-Dionysus. In these texts, each of these writers speaks of the universal extent of beauty, and names God as its first cause. In The Divine Names, Dionysius defines the beautiful as one of the sources of being” (Murphy, Christ the Form of Beauty: A Study in Theology and Literature, 213). Also, as Milbank is concerned to show, Thomas’s aesthetic vision, however blurred by his intellectualism, was to his credit at least sufficiently clear to inspire, through the work of Jacques Maritain, the “more explicit poetics” of twentieth-century Catholic artists and writers such as David Jones, G.K. Chesterton, Flannery O’Connor, and J.R.R. Tolkien.

Aquinas’s “Tin Ear” for the Music of the Spheres

Metaphysics of the Music, part 14

Against the metaphysically tragic interpretation of Tolkien’s creation-myth—according to which, first, it is the Ainur’s Music that creates the rest of the world and, second, the Music therefore represents an authentic form of being in comparison to which all later permutations of creation are so many disparagable accretions—my claim is that Tolkien’s music imagery both presupposes and self-consciously portrays the kind of Christian, creational, and consequently much more positive metaphysics he shares, for example, with St. Thomas Aquinas. To this end, there are three aspects of Thomas’s thought I want to develop in the posts to follow: the first is Thomas’s own occasional remarks on the nature of music; the second consists in select elements of Thomas’s theory of beauty or aesthetics in general; and the third concerns the broader metaphysical “existentialism” and realism involved in Thomas’s aesthetics. At each of these three levels, as I hope to show, Thomas has an important contribution to make where the proper interpretation of the metaphysics of Tolkien’s music imagery is concerned.

Unlike Tolkien, the music imagery of Augustine, Boethius, and the whole musica universalis tradition actually seems to have made very little impression on St. Thomas’s metaphysical imagination: fire and light we certainly find in his philosophy of being (examples of Pseudo-Dionysius’s influence), but there is very little music. Commenting on this lacuna, Leo Spitzer remarks how Thomas does not seem to have had “the Augustinian ear for world harmony, ascribing to music a holy character only insofar as it was an element of the liturgy; as an Aristotelian he ‘reflects’ the world as it is, rather than attempting to re-create it by forging it together into a unit” (Spitzer, Classical and Christian Ideas of World Harmony, 74). As we shall see, accordingly, Thomas’s ultimate significance for understanding the metaphysics of Tolkien’s musical imagery will lie in quite a different direction. Thomas’s personal interest in music, such as it was, was informed by his direct experience with sacred music as part of his religious devotion and duties as a priest, a subject he addresses in ST 2-2.91, “Of taking the divine name for the purpose of invoking by means of praise” (on this passage, see Eco, The Aesthetics of Thomas Aquinas, 131-2). More than this, Thomas’s education and general cultural milieu would have required of him a particular familiarity with Boethius’s De Institutione and Augustine’s De Musica (Eco 131). His command of some of the more technical and mathematical details of the latter work in particular, for example, are on display in his commentary on Aristotle’s De anima (Bullough, “St. Thomas and Music,” 14, 19-21). (Thomas F. O’Meara, incidentally, has also made the observation in his study of Aquinas’s “cultural milieu” of thirteenth-century Paris that it was only the century prior that polyphony had been introduced and developed in Gothic music, whose “rhythmical motion of independent parts,” together with the Gothic illustrated window and the Scholastic Summa, constitutes a third example of the period’s “love of plurality ordered.” O’Meara, “Paris as a Cultural Milieu of Thomas Aquinas’s Thought,” 709.) And while Thomas does not seem to have had much use in his cosmology or metaphysics for the Pythagorean notion of a musical world harmony, as his treatment of divine power in the Summa indicates, neither was he completely insensible to the notion’s explanatory force. While expanding on how the universe cannot be improved given the order already bestowed upon it by God, Thomas gives the following argument strongly reminiscent of what I pointed out in Augustine earlier: “For if any one thing were bettered, the proportion of order would be destroyed, just as if one string were stretched more than it ought to be, the melody of the harp would be destroyed” (ST 1.25.6 ad 3).

Creation as Decay in the Music of the Ainur

Metaphysics of the Music, part 10

It is in similar, metaphysically tragic terms that Bradford Eden, in his Boethian interpretation of Tolkien, understands the relationship between the Ainur’s Music and the subsequent phases of creation. As we saw earlier, Boethius recognizes three specific kinds of music: cosmic, human or vocal, and instrumental. In Eden’s hands, however, Boethius’s threefold classification becomes also a Neoplatonic progression, or rather digression, from highest to lowest, and the pattern around which the entire subsequent history of Middle-earth is allegedly structured:

The gradations of music’s power in Middle-earth from its appearance in the first page of The Silmarillion all the way down to the Fourth Age in The Lord of the Rings reflects a Neoplatonic hierarchy of being, from the highest form of music, universal or comic [sic] music, down to human/vocal music, and then down to instrumental music. This chain of musical being also embodies the diminution of cosmic love/harmony that ends with the most material and literal, in the instruments of Man. (Eden, “The ‘Music of the Spheres’,” 192)

Again, according to Eden the pattern in Tolkien’s creation-story is a pattern of metaphysical corruption or dilution of being, a “diminution of cosmic love/harmony that ends with the most material and literal.” Pressing the point further, Eden writes:

There may be an unconscious decay of cosmological theory written into The Silmarillion that can only be detected by one who is knowledgeable about the entire mythological reality that is Middle-earth. Each theoretical step taken away from the “Great Music,” which set everything into motion, is a slow descent away from “the divine.” This is a strong thread throughout the writings of Plato and Aristotle, that each gradation and division of music away from the “pure” or “universal” results in a type of gradual descent downward in spirit and soul…. Elves and Men are farther away in both time and space from the “music of the spheres” and closer to the third and lower type of music in the Third Age. (190-1)

On this Platonic reading of Tolkien, each subsequent stage of his creation-account and subsequent mythical history involves a necessary “decay,” a “descent downward” or falling away from the “pure” and “divine” origins of the Music of the Ainur, so that physical reality itself finally emerges, as it does for Plotinus, as a veritable metaphysical catastrophe or accident, necessary yet regrettable.

Boethius, Music of the Spheres, and the Music of the Ainur

Metaphysics of the Music, part 6

The next influential Christian thinker after Augustine to turn his attention to the significance of music, in terms of both its own principles as a science and as a metaphor for cosmic harmony, is the sixth-century Boethius, whose views on music Bradford Lee Eden has compared at some length with Tolkien’s narrative (Eden, “The ‘Music of the Spheres’: Relationships between Tolkien’s The Silmarillion and Medieval Cosmological and Religious Theory,” 183-193). Possibly the most influential treatise ever written on the subject of music, it was through Boethius’s De institutione musica that classical musical theory was primarily transmitted to the Middle Ages and Renaissance (Godwin, The Harmony of the Spheres: A Sourcebook of the Pythagorean Tradition in Music, 86). Toward the beginning of his treatise, Boethius distinguishes three kinds of music: cosmic (musica mundana, or “music of the spheres”), human (musica humana, the music of the human body and soul), and instrumental (musica instrumentalis) (Boethius, Fundamentals of Music, 1.2, trans. Bower. See also Godwin, The Harmony of the Spheres, 86). The three primary examples of the cosmic music distinguished by Boethius include the movement of the heavenly bodies, the combination of the physical elements, and the changing of the seasons. Of the heavenly bodies, for example, Boethius thinks it impossible that “so swift a heavenly machine moves on a mute and silent course” and “that such extremely fast motion of such large bodies should produce absolutely no sound…,” and in a later chapter Boethius even correlates each of the planetary spheres with the various standard musical strings (“the hypate meson is assigned to Saturn, whereas the parhypate is like the orbit of Jupitor,” etc.) (Boethius, Fundamentals of Music, 1.27).

Although it is with the classical idea of the “music of the spheres” that commentators have most often compared the Music of the Ainur, it is worth noting that the Ainulindalë itself does not in fact ever refer to the heavenly bodies, nor are they elsewhere in Tolkien’s mythology ever described as producing any kind of sound or music. Of greater relevance to the Ainulindalë, therefore, it would seem, are Boethius’s second and third examples of cosmic music, namely the harmony of the elements and seasons. Of the former, for example, Boethius asks: “If a certain harmony did not join the diversities and opposing forces of the four elements, how would it be possible that they could unite in one mass and contrivance?” (Boethius, Fundamentals of Music, 1.2). Similarly, in the Ainulindalë it is in a state of Boethian harmony that the four elements first appear to the Ainur in the Vision:

And they observed the winds and the air, and the matters of which Arda was made, of iron and stone and silver and gold and many substance: but of all these water they most greatly praised. And it is said by the Eldar that in water there lives yet the echo of the Music of the Ainur more than in any substance else that is in this Earth; and many of the Children of Ilúvatar hearken still unsated to the voices of the Sea, and yet know not for what they listen. (Silmarillion 19)

As for his third category of cosmic music, Boethius compares the “consonance” of the four seasons with the attunement of lower and higher strings of an instrument, so that “the whole corpus of pitches is coherent and harmonious with itself”: “For what winter confines, spring releases, summer heats, and autumn ripens, and the seasons in turn either bring forth their own fruit or give aid to others in bringing forth their own” (Ibid.1.2). In a comparable expression found in the Ainulindalë of the accord between seasons and weather patterns, upset only by the disruptions of Melkor, Ilúvatar informs the Valar Ulmo:

‘Behold the snow, and the cunning work of frost! Melkor hath devised heats and fire without restraint, and hath not dried up thy desire nor utterly quelled the music of the sea. Behold rather the height and glory of the clouds, and the everchanging mists; and listen to the fall of rain upon the Earth! And in these clouds thou art drawn nearer to Manwë, they friend, whom thou lovest.’

            Then Ulmo answered: ‘Truly, Water is become now fairer than my heart imagined, neither had my secret thought conceived the snowflake, nor in all my music was contained the falling of the rain. I will seek Manwë, that he and I may make melodies for ever to they delight!’ (Silmarillion 19)

The Metaphysics of the Music of the Ainur

Tolkien’s Metaphysics of the Music, part 1

This post marks the beginning of a new series on Tolkien’s “metaphysics of the Music.” At the center of Tolkien’s creation-story, the Ainulindalë, is the eponymous “Music of the Ainur,” the beautiful, cosmic composition sung by the angelic host together with the Creator before the creation of the world, and the pattern according to which the history of the world later unfolds. In previous posts I’ve considered the Ainur’s Music as a dramatization of Tolkien’s Thomistic theology of sub-creative possibility, according to which the human art of sub-creation, no less than the divine art of creation, has as its dignified task the “interpretation” and “imitation” of the divine mind and essence. In this series of posts, by contrast, my interest is in the Music in its own right and in the significance this particular image holds for Tolkien’s general, Thomistic philosophy of being.

I will begin my argument, thus, with a survey of the musica universalis tradition of such eminent thinkers as Pythagoras, Plato, Augustine, and Boethius, to which many commentators have traced the historical origins of the music imagery in the Ainulindalë. Yet despite the attention it has received, the precise metaphysical meaning of the Ainur’s Music has often been missed, when it has not been outright misunderstood. For in addition to the prevalent interpretation of the Ainur and their Music as the true or at least proximate “creators” of the world (a position I have critiqued previously), there has been a marked tendency in the Tolkien literature to read his creation-drama and the Music of the Ainur in particular in terms of the emanationist logic of Neoplatonic philosophy. On this understanding, later stages of the creation-process and world-history are seen as metaphysically inferior to, and thus a “tragic” falling away from, the supposedly more authentic, divine, and pure reality represented by the primeval Music. In contrast to this metaphysically tragic reading of the Ainulindalë, I will give some attention to some of the salient themes of the comparatively “comic” metaphysics and aesthetics of creation articulated by St. Thomas Aquinas, and in light of which I will offer my own analysis and interpretation of, first, the Music of the Ainur, but second, its more often neglected yet equally important counterpart, the Vision of the Ainur. My ultimate purpose is to show that, through his combined images of the Music and Vision of the Ainur, Tolkien on the one hand provides the world with a beautiful yet mythical, ideal pattern that, on the other hand, and consistent with his Thomistic, existential realism, finds itself “eucatastrophically” surpassed when the world is finally blessed by the Creator with its own, mind-alluring because mind-independent being.

Boethian omnipotence: The Power to do the Good

Theology of the Possible

Apropos my post yesterday applying Aquinas’s Augustinian privation theory of evil to his theology of the possible is the following passage from William Courtenay discussing Boethius’s Neoplatonic conflation of divine power with divine goodness:

One further text undoubtedly influenced eleventh-century thinking about capacity and volition as well as the problem of God’s inability to do evil. In the fourth book of The Consolation of Philosophy, Boethius developed his own rationale for why “supreme goodness cannot do evil.” Admitting the seemingly larger range of action open to mankind, who can do both good and evil, in contrast to God, who can only do the good, Boethius made a virtue of necessity. Only the good is worth doing. The ability to do evil is the ability to do nothing, since evil is nonbeing and nothing. And since omnipotence is a divine attribute, its meaning is determined by the range of divine action, which is only toward the good. Consequently, omnipotence is defined as power to do the good, not the power to do anything. (Courtenay, Capacity and Volition, 30-1)