Ancient Greek & Neoliberal Harmony Pt. 1: Sophrosyne as Proportion

It seems like the ancient Greeks are actually kinda neoliberal in some ways. In Disagreement, Ranciere calls consensus democracy “the perfect realization” of Plato’s Republic, and, as Shannon Winnubst notes in her great new article in Foucault Studies (which everyone should go read right now), Foucault’s work encourages comparisons between the ancient Greek practices he talks about in, say, Volume 2 of the History of Sexuality, and his lecture courses on neoliberalism. Giving voice to this sense that there’s some relationship between the Greeks and the neoliberals, Winnbust says “it is almost as if, in much too gross historical strokes, we have two bookends standing outside the overlapping milieu of Christianity and modernity: ancient Greece and contemporary neoliberalism” (91). However, as she compellingly argues, the Greeks may be more similar to neoliberals than they are to classical enlightenment liberals, but this doesn’t make them neoliberals. Just because two things are more like one another than either is like a third thing doesn’t mean the two things are identical (I’m no logician, but that feels like an invalid syllogism, right?).

But the Greeks are sort of similar to neoliberals—there’s something there that invites comparison, even if that comparison reveals some pretty fundamental differences.

This is where sound studies and the philosophy of music are really helpful. Greeks and neoliberals both have harmonic political epistemes, while Enlightenment liberals have visual/representational ones. So, the Greeks and the neoliberals are both sonic/harmonic alternatives to Enlightenment visuality. That’s why they initially, at first pass, invite comparison. BUT: Greeks and neoliberals have different understandings of harmony. The Greeks measure harmony geometrically, as a proportion, whereas the neoliberals measure harmony acoustically, as the quality (amplitude) and quantity (frequency) of a signal or sine wave. The sine wave is both sound’s material form and a way to statistically represent probability. So, neoliberal biopolitics—aka the governmentality of statistics—and contemporary acoustics converge in the form of a sine wave, and it is this common denominator that allows for easy transposition between them. If classical liberalism thinks and works in terms of “the gaze,” neoliberalism thinks and works in terms of sine waves. So, understanding acoustics can help us understand material, practical, normalized, creative, and critical functions/properties/possibilities of sine waves. Ultimately, I’m arguing that sound and music studies provide very productive avenues, methods, and resources for theorizing neoliberalism.

I'm breaking this project down into several posts. Here, I limit my discussion to ancient Greek concepts of harmony as proportion. I want to emphasize that I'm not a classicist, Ancient is NOT my area of specialization, and I'm not at all trying to make some sort of scholarly contribution to this area of the history of philosophy. What I AM trying to do is explain the relationship between ancient Greek concepts of musical harmony and their ethical ideal "sophrosyne"...so that we can better understand how the ancient Greek "harmonic" ethos is different than the neoliberal "harmonic" ethos. And honestly, this is far, far more work on ancient Greek philosophy than I ever imagined myself doing. So, you know, ancient people, if I'm missing something or get somethign wrong, let me know! :)

Ancient Greek Harmony

Greeks and neoliberals use harmonic epistemes. Because Foucault’s interest in the Greeks centers on their “orthos logos,” their mechanism for measuring or judging the freedom/truth relationship, I’ll frame my analysis in those terms. Classical liberalism/enlightenment modernity measured truth representationally, with the correspondence theory: confession, as a technology of the self, relies on a correspondence between explicitly expression and inner content. Whereas the classical liberals frame the freedom/truth relationship in terms of the gaze, the Greeks understand it through the concept of moderation or sophrosyne. As Winnubst explains, “the ethical problem of aphrodisia for the Greeks was the ongoing effort ‘to be free in relation to pleasures…to be free of their authority;’ to do so, one must cultivate a particular relation to truth that ‘constituted an essential element of moderation’” (90). So how is moderation (i.e., sophrosyne) a proportional, geometric concept of harmony?

As Helen North explains, “sophrosyne and its cognate forms were…closely identified with the feeling for harmony and restraint which governed every phase of Greek life” (North, 2). Further, North speculates that “the term sophrosyne passed from ethics first to music” (2).[i] Ok, so sophrosyne and harmony are interrelated in ancient Greek thought. I’m assuming that philosophers generally understand what “moderation” means. Here I’m going to focus on what harmony meant in ancient Greek theory.

There’s no one theory of harmony in ancient Greek philosophy—lots of people had lots of different theories about exactly what intervals were consonant and dissonant, about how to divide the octave, fourth, and fifth, etc. While they disagreed about the details, all these theories had the same underlying concept of what harmony was—harmony was a matter of proportion. As A.A. Long explains, ancient Greeks understood harmony as “something balanced, proportional, ratio-like” (207). Or, as Plato says in Timaeus, “the Cosmos was harmonized by proportion and brought into existence” (32c; emphasis mine).

Musical Harmony

To be really reductive, the ancient Greeks thought musical harmony was a function of visual-spatial ratios, a measure of the size of the resonating media. For example, pan pipes would be acoustically harmonic if the length and width of the pipes were mathematically proportionate to one another. If the physical size and shape of a resonating substance (wood, a string, etc.) fit a specified system of ideal mathematical ratios (e.g., the golden mean), then the sounds this resonating substance produced would be “harmonic” (or rather, consonantly harmonic). As musicologist Tobias Mathiesen explains, Greek music theory is “an attempt to present all the instruments—flute, reed, and string—as manifesting the mathematical principles of harmonics in the same visual manner” (210; emphasis mine). Acoustic proportion was a function of visual proportion, which was in turn a function of mathematical proportion. The assumption—or ideal—is that visually proportionate instruments should produce acoustically proportionate (in other words, harmonic) sounds…because the same mathematical proportions ought to govern them both.[ii]

For example, the aulos (a double-reeded instrument sort of like the contemporary oboe) was considered a low-prestige instrument and associated with the “unruliness” of femininity (and Dionysus) because its visible and acoustic proportions did not strictly follow ideal mathematical ratios. As Matheisen explains, 

The rough rations between the trupemata [finger holes] and the mouthpiece do correspond to the possible ratios between the pitches produced by those trupemata, but it is clear that any given fingering on the aulos can be used to produce a number of pitches” (Mathiesen 209).[iii]

The aulos is troublesome because it is not adequately proportional: its visible and auditory physical functioning (the intervals or ratios between pitches produced by finger-holes bored in visually/geometrically proportionate ratios) does not truthfully manifest the underlying logos of mathematical harmony/proportion. (This is why the aulos is associated with femininity—both are unruly and immoderate.) Similarly, one’s outward appearance served as evidence of one’s moderate—or immoderate—ethos. As Plato says, “if the fine dispositions that are in the soul and those that agree and accord with them in the form should ever coincide in anyone, with both partaking of the same model, wouldn’t that be the fairest sight for him who is able to see?” (Republic 402d; emphasis mine). Or, as Foucault puts it, sophrosyne’s “hallmark, grounded in truth, was both its regard for an ontological structure and its visibly beautiful shape” (HSv2 89; emphasis mine). Outwardly visible harmony should be the manifestation or expression of inner harmony. As Foucault puts it, “the individual fulfilled himself as an ethical subject by shaping a precisely measured conduct that was plainly visible to all” (HSv2 91). Inner harmony ought to produce outward beauty.

            The exact nature of this relationship between inner and outer harmony was, however, a subject of disagreement among ancient Greek philosophers. Some, like Pythagoras, saw, or rather heard, a direct correspondence between perceived visual/auditory harmony and mathematical harmony. In this view, perceptual harmony was directly proportional to intellectual/mathematical harmony. Plato critques Pythagoras’s theory of harmony because the latter reverses the proper order between material structure and intelligible logic. According to Plato, Pythagoras “put[s] ears before the intelligence” (Repubic 531a), placing disproportionate emphasis on auditory perception, and insufficient emphasis on mathematical proportion (or, “consideration of… numbers” (531c).) The most musical intervals/proportions/ratios are not the ones that sound most consonant, or are most visibly beautiful, but the ones that are the most mathematically and/or philosophically proportionate. In other words, Plato thinks the relationship between visual/auditory proportion and mathematical/philosophical proportion must itself be proportionate, putting greater weight or emphasis on the intellectual than on the perceptual.

In Plato’s Symposium, Socrates functions like an aulos because his visual appearance does not directly correspond to his intellectual harmoniousness. In the same way that auloi can produce visually and acoustically consonant phenomena that are neither directly nor necessarily tied to specific mathematical proportions, Socrates’s visual beauty is not directly proportionate to his intellectual beauty. He is visually dischordant—ugly, mocking and mean, anti-social, etc.—but intellectually harmonious.

            To someone who, like Pythagoreans or Alcibiades in the Symposium, thought the relationship between visible and intellectual harmony was a “mutual exchange of beauty for beauty” (218a), Socrates seems very disharmonious. This is why Alcibiades, in his praise of Socrates at the end of the Symposium, compares Socrates to an aulos/ανλονς (215b). But the joke is, as ever with Socrates, on us, that is, on those who think he really is like a flute or flute-player.  For Plato, visual beauty ought to be accorded les import than intellectual beauty—that’s the Symposium’s main argument, after all. Socrates might not be visibly beautiful in equal proportion to his intellectual beauty, but he is visibly beautiful in proper, mathematical, harmonic proportion to his intellectual beauty. Which is to say: Socrates accords greater import and attention to intellectual beauty, because that is its proper place and function. Ironically, his initial aulos-like qualities are evidence that he’s more like a well-tempered stringed instrument (e.g., a kithara). His mind is significantly more harmonious than his body…and that’s what makes him more proportionate than anyone else, “gold” (and more proportionate, like the guardians) rather than just “bronze” (less proportionate, like the plebs) (Symposium 219a). Socrates seems like an aulos only to those who do not recognize the true and proper relationship between visible/perceptual and intellectual harmony.[iv] 

            So “proportion” is a ratio that is representable both visually/perceptually and mathematically; metatheoretically, the relationship between perceptual and mathematical proportion is itself proportionate. The Greeks visualized mathematical ratios in geometric terms. As Plato states in the Republic, “A man experienced in geometry would…grasp the truth about equals, doubles, or any other proportion” (530a). Mathiesen includes to diagrams that clearly show how Greeks thought sonic harmony was a function of geometric ratios.

[this is Mathiesen's diagram]

Because I’m a theorist and not a trained mathematician, and because even the Greeks widely and wildly disagreed about the specific methods for mathematically calculating ideally harmonic ratios, I’m not going to go too deeply into the calculations. I do, however, want to convey a general sense of the proportionality. Distilling centuries of often inconsistent and conflicting mathematical accounts of musical harmony to their common denominator, Mathiesen explains:

The story of Pythagoras’s discovery of the harmonic ratios is told and retold by many writers, Greek and Latin, with certain variations, but its essence lies in the application of four numbers—12, 9, 8, and 6—to produce the Pythagorean ‘harmonia.’ Nichomachus’s version has Pythagoras first detecting the consonant intervals of the octave, fifth, and fourth…” (399)

When instruments were visually/materially organized by mathematically proportional ratios, they would produce the musical intervals of the octave, fifth, and fourth. For example, when you fret or put your finger down on a monochord (basically, a single string over a resonator, like a one-stringed guitar) so that the string is divided on a 1:1 ratio, the interval between the two pitches is an octave; at a 3:2 (12:8 or 9:6) ratio (the golden mean), the interval between the two pitches is a fifth. This is just one simple example; the ancient Geek music theorists bickered about the mathematical derivation of musical harmony with the same nitpicky vehemence that hipster music fans exhibit when discussing the nuances of their favorite sub-sub-subgenre. I do not want to get sidetracked by going into those details. But the proliferation of accounts is itself evidence of the centrality of mathematical proportion to ancient Greek concepts of musical harmony.[v]

Ethical/Political Harmony

Classicists have established that an “analogy between musical and ethical harmony” (A.A. Long 203) was widespread in ancient Greek philosophy, from the pre-Socratics like Heraclitus and Pythagoras, to the Stoics. An explicit and widely-read example of this analogy appears in Plato’s Republic. Here, he argues that “we’ll never be musical—either in ourselves or those whom we say we must educate to be guardians—before we recognize the forms of moderation” (402c). He says musicality requires moderation,[vi] and equates madness and licentiousness to unmusicality.[vii] For example, he compares poor musical harmonization to gluttony.[viii] If moderation or sophrosyne is understood as a type of musicality, how exactly is moderation/sophrosyne proportional?

Foucault, in his chapter on sophrosyne in HSv2, uses the language of “proportion” to describe the Greek’s concept of moderation/sophrosyne as virile self-mastery:

the point where the relationship with oneself would become isomorphic with the relationship of domination, hierarchy, and authority that one expected, as a man, a free man, to establish over his inferiors; and it was this prior condition of ‘ethical virility’ that provided one with the right sense of proportion for the exercise of ‘sexual virility,’ according to a model of ‘social virility.’ (HSv2 83).

To be moderate was to understand and implement proportion across one’s dealings; one’s desires had to be proportionate (e.g., to one’s responsibilities), one’s authority had to be proportionate (to one’s social position), and one’s desires and authority had to be proportional to one another. Only one who is successfully ruled by proportion may rule others and maintain a proportionate society. Or, think of it this way: “moderation implied that the logos be placed in a position of supremacy in the human being and that it was able to subdue the desires and regulate behavior” (Foucault HSv2 86)—the proportionate man was one whose “logos” was more powerful and more extensive than his desires. Or, the moderate man was one who maintained the correct balance between logos and desires. If “to rule one’s pleasures and to bring them under the authority of the logos formed one and the same enterprise” (Foucault HSv2 86), this logos was proportion. It was proportional because reason had dominion over desire and corporeality—everything was in its appropriate position in a hierarchical relationship.[ix]

Foucault’s understanding of proportion is consistent with Plato’s (and also, interestingly, with Ranciere’s reading of Plato in Disagreement). For Plato, a harmonious city was one in which “Each man does one thing” (Republic 397e), and there is a “proper order for each of the things that are” (Gorgias506d); when each thing follows its own proper logos, the whole will be harmonic, consonant, balanced, well-ordered, etc.[x] For example, the mind and the body each have specific functions, and the moderate man is one who maintains a “harmonious adjustment” (Republic 411e) of soul and body, that is, an overall balance between the two by keeping each in its proper place.[xi] In the moderate man, “his whole soul—brought to its best by acquiring moderation and justice accompanied by prudence…in proportion as soul is more honorable than body” (Republic 591b; emphasis mine). This is what Plato is talking about in Republic 410c, where he states that “guardians,” or the rulers of the city, “…should possess both natures…And must they not be harmoniously adjusted to one another?” “Of course.” “And the soul of the man thus attuned is sober and brave?” (emphasis mine). Moderation means giving the soul a greater proportion of dominion or authority over one’s life than the body. Sophrosyne is a practice of harmonious attunement because it is a matter of respecting proportional distributions.

Sophroysne was a manifestation of the same harmonic logic that governed the rest of the universe—music, the planets, mathematics, etc.[xii] Just as there were various systems for calculating the most ideally harmonic systems of ratios/proportions, this harmony-moderation connection was made in a variety of ways. According to A.A. Long, “Aristotle observes (Top. IV.3 123a37) that symphonia [loosely, “consonance”] may be predicated of ‘moderation’ (sophrosyne) but such a usage is metaphor since strictly all symphonia pertains to sounds” (203). Drawing a more macro-level analogy or isomorphism, “the Stoics envisaged a virtuous character as directly analogous to a harmonic system” (Long 218). Working with smaller-scale comparisons, “Ptolemy and Aristides Quintilianus…se[t] up correspondences between specific virtues and harmonic intervals” (Long 215). Though Foucault does not explicitly connect harmony with proportion, he does use musical language to describe Plato’s concept of sophrosyne:

in the individual who is sophron, it is reason that commands and prescribes, in consonance with the structure of the human being: ‘it is fitting that the reasonable part should rule,’ Socrates says…and he proceeds to define the sophron as the man in whom the different parts of the soul are in agreement and harmony, when the part that commands and the part that obeys are at one in their recognition that it is proper for reason to rule and that they should not contend for its authority” (HSv2 87).

Importantly, Foucault connects sophrosyne with a proportional concept of harmony: something is consonant when its component parts are all in their proper, assigned place. This “harmonization” is the “structural” and “ontological” relationship that Foucault attributes to the ancient Greeks and contrasts to the “epistemological” notion of truth operative in, say, the imperative to confess.[xiii]

Sophrosyne is attunement to truth: harmony is produced when “reason rules.” Often, for the ancient Greeks, reason itself was harmonic—the logos was a mathematical system of proportions. As A.A. Long notes, “orthos logos, in Greek philosophical usage quite generally, connotes the presence, application or realization of determinacy, proportionality, exactitude of quantitative or numerical order” (207). The geometric/mathematical ratios are the orthos logos or true reason that determine what is moderate and what isn’t. So, virtue meant bringing one’s life, or the city, in accordance with the logos of harmonic proportion. Conversely, an unjust city is a disharmonious one: for example, Plato argues that “oligarchy would contain this one mistake that is of such proportions” (Republic 551d; emphasis mine). The logos is a structure or instrument for producing a well-ordered, harmonic body, be it an instrument, a human being, or a polity. à

It is clear that metaphorical and/or literal concepts of musical harmony as proportion served as the measure or model for moderation/sophrysune.[xiv] Moderation/sophorysune, in turn, was a model for “subjectivity” (or rather, self-relation—the “subject” is somewhat of an anachronism in this context), political and social relationality, and for epistemology. So, we can say that ancient Greek theories of self-relation, political relation, and epistemology are grounded in a proportional theory of musical harmony. Neoliberal theories of subjectivity, politics, and knowledge are grounded in a different theory of musical harmony, one modeled on the sine wave. For the ancient Greeks, sophrosyne could link freedom and truth because both “freedom” (self-mastery) and “truth” (beauty/harmony/mathematical logic/orthos logos) were understood proportionally; for neoliberals, the competitive market can link freedom and truth because both “freedom” (optimalization) and “truth” (success) are understood “acoustically” as sine waves.

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[i] North, Helen, Classical Philology 1948

[ii] For example, Mathiesen discusses Nchomachus’s theory of “‘ruling proportion’, in which two middle terms form various ratios with the extremes and the product of the means is equal to the product of the extremes. This proportion is represented by 12:9:8:6, which embraces geometric proportion (12:8::9:6), harmonic proportion (12:8:6), and arithmetic proportion (12:9:6), as well as the whole-tone ratio, 9:8, the common measure of musical rations and the difference between the fifth and the fourth” (400-01).

[iii] There’s A LOT to say about the queerness and unruliness of Alcibiades in Plato’s Symposium, its connection to the re-introduction of the “flute girls,” and the unruliness of the aulos. Basically: if sophrosyne is being a man in relationship to oneself, being “harmonically proportionate,” then the aulos is not harmonically proportionate, so it is feminized and immoderate, sort of the way Xanthippe is represented in the Phaedo…But that’s a tangent to be explored elsewhere. Unless somebody’s already written on that, which would be awesome. (Judith Periano…?

[iv] “if you chose to listen to Scorates’ discourses you would feel them at first to be quite ridiculous; on the outside they are clothed with such absurd words and phrases—all, of course, the hide of a mocking satyr…so that anyone inexpert and thoughtless might laugh his speeches into scorn. But when these are opened, and you obtain a fresh view of them by getting inside, first of all you will discover they are the only speeches which have any sense in them; and secondly, that none are so divine, so rich in images of virtue…” (Symposium 221e-222a).

[v] As Alan Bloom points out in his translation of Republic, rhythim is also proportional: “the various meters are compounded of feet based on three basic proportions: the 2.2 or equal…; the 3.2…; and the 2/1…The four forms of sound are apparently the notes of the tetrachord…” (453n48)

[vi] “Is the naturally right kind of love to love in a moderate and musical way what’s orderly and fine?” (Republic 403a)

[vii] Being “mad or akin to licentiousness” is “unmusical” (403 b-c).

[viii] Plato says: “likening such food [attic cakes] and such a way of life as a whole to melodies and songs written in the panharmonic mode and with all rhythms” (404d). Panharmonic modes don’t sufficiently distinguish among and prioritize more- and less-harmonic intervals. You might compare them to a Western chromatic scale, which includes all 12 tones in an octave, not just the 8 tones in a major or minor scale.

[ix] The theory of the divided line is a hierarchical order grounded in a metaphorics of proportion. For example, the intelligible gets a bigger proportion of space on the line because it is more “real” than the visible: “take these four affections arising in the soul in relation to the four segments: intellection in relation to the highest one, and thought in relation to the second; to the third assign trust, and to the last imagination. Arrange them in proportion, and believe that as the segments to which they correspond participate in truth, so they participate in clarity” (611d)

[x] Thus, as Plato argues in Republic, “for all well-governed peoples there is a work assigned to each man in the city which he must perform” (Republic 406c). A harmonic city is one in which the gold souls do gold things, when silver ones do silver things, and so on. Those who are “mixed,” who do more than one thing and have more than one role, have no place in Plato’s ideal city because they would disrupt its harmonious attunement. As Plato says, “he doesn’t harmonize with our regime because there’s no double man among us, nor a manifold one, since each man does one thing” (Republic 397e).

[xi] As Judith Periano explains, “the music taken in by the physical senses recalibrates the harmony of the soul through a metaphysical mimesis that tunes the soul to the cosmic scale (rather than to a physical body) so that the soul can supervise the physical body and the body’s instincts in an ideal, essentially acetic self-practice” (33) à music orders the soul, and puts the soul in charge of the body (ie soul in harmony w body)

[xii] “This famous Pythagorean ‘harmonia’…provides a perfect paradigm for music as an embodiment of rational numerical order and, by extension, universal order” (Matheisen 363)

[xiii] “The relation to truth was a structural, instrumental, and ontological condition for establishing the individual as a moderate subject leading a life of moderation; it was not an epistemological condition enabling the individual to recognize himself in his singularity as a desiring subject and to purify himself of the desire that was thus brought to light” (HSv2 89).

[xiv] We have frequently asserted² that there are housed within us in three regions three kinds of soul, and that each of these has its own motions; so now likewise we must repeat, as briefly as possible, that the kind which remains in idleness and stays with its own motions; in repose necessarily becomes weakest, whereas the kind which exercises itself becomes strongest; [90a] wherefore care must be taken that they have their motions relatively to one another in due proportion. (Timaeus 89e-90a).