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Tuning is for Killjoys

February 3rd, 2021 | 13 min read

By Jeremiah Lawson

More than ever, we need a subversive history of music. We need it both to subvert the staid accounts that misrepresent the past as well as to grasp the subversive quality inherent in these catalytic sounds in our own time. This book aims to provide that alternative narrative. But the goal isn’t to be iconoclastic or controversial. I have no interest in adopting a provocative revisionist pose so I can stand out from the crowd. I simply want to do justice to the subject. I want to tell the story of music as a change agent, as a source of disruption and enchantment in human life.  

I started work on an alternative approach to music history more than twenty-five years ago, but back then I didn’t realize the scope of what I would uncover. My starting point was much simpler than where I ended up. My core belief back then—unchanged today, so many years later—was that music is a force of transformation and empowerment, a catalyst in human life. My curiosity was piqued by the many ways songs had enhanced and altered the lives of individuals throughout history, and especially the great masses of people who don’t get much visibility in surviving accounts.  I didn’t exclude kings and lords, or popes and patrons, from my purview. But I was perhaps even more interested in peasants and plebeians, slaves and bohemians, renegades and outcasts. What did their music sound like? Even better, what did it do?

… My aim is to celebrate music as a source of creation, destruction, and transformation. I affirm songs as a source of artistry, but will also insist on taking them seriously as a social force and conduit of power, even as a kind of technology for societies that lack microchips and spaceships. I want to cast light on the neglected spheres of music that survive outside the realm of power brokers, religious institutions, and social elites, and explore how songs enrich the day-to-day lives of small communities, families, and individuals. Above all, I hope to show how music can topple established hierarchies and rules, subverting tired old conventions and asserting bold new ones.

Ted Gioia’s would-be subversive history of music is the most conventional wisdom an American historian of jazz and blues could have written.  Gioia believes that music is magical and has the power to shake things up and that music, when it taps into what he regards as its shamanistic powers, can heal people and, according to the ancient Greek figure Empedocles, raise the dead.  Gioia has read the history of American popular styles of music pioneered by African Americans as a synecdoche for the history of music the world over and molded the rest of music history to fit that American mythology.

Unfortunately, Gioia misrepresents the past. Some of his misrepresentations may come by the accident of not being nearly as steeped in the history of classical music as he is in the history of American popular music. The most significant failure of his would-be subversive history is taking too pejorative a stance toward the history of tuning systems. He sees the history of music as a dualistic battle between reified concepts such as science vs. magic; notes vs. sound; and Europe vs. Africa almost as though music has no human history in Asia or the Americas.

Whereas instrument builders rely on tuning and temperament systems to make sure you can play the perfect octave, perfect fifth and the perfect fourth on a piano or a guitar, Gioia has a different story about how and why tuning systems were invented. In Chapter 4, “Music History as a Battle Between Magic and Mathematics”, Gioia lays out his case for Pythagoras as the firstborn of repression and suppression as follows:

At a certain point in Western history, music became a quasi-science. Or, to be more precise, those who theorized about music managed to impose a scientific and mathematical framework that would marginalize all other approaches to the subject. We can even assign a name, a location, and a rough date to this revolution. The alleged innovator was Pythagoras of Samos, born around the year 570 BC. The impact of the Pythagorean revolution on the later course of music is still insufficiently understood and appreciated. I believe he is the most important person in the history of music—although his `innovation’ has perhaps done as much harm as good—and I will make a case for that bold claim in the pages ahead. Yet he is often treated as little more than a colorful footnote in cultural history, a charming figure who appears in anecdotes and asides, but not the mainstream narrative of cultural history.

The very fact that Pythagoras is lumped together with other `pre-Socratic’ thinkers is sadly revealing. He is remembered for what he preceded, rather than for what he actually did. In truth, we should pay far more attention to what happened before Pythagoras emerged on the scene, what I might call the pre-pre-Socratic era, rather than defining his contribution by what happened afterward. Greek culture before his arrival revered what we call nowadays Orphic thought (named after Orpheus, the mythical musician, but almost always considered a historical personage in those distant days), and believed songs possessed powerful magic. The rise of Pythagorean music theory, circa 500 BC, changed all that by conceptualizing music as a rational science of sounds that could be described in mathematical terms. Today there’s a lot of talk about algorithms in music—with every aspect, from composition to curation, reduced to rules and formulas—but the very first algorithm entered Western music with this philosophical rupture that happened more than 2,000 years ago.

Pythagoras’s attempt to define and constrain musical sounds by the use of numbers and ratios continues to shape how we conceptualize and perform songs in the current day, and even now we distinguish between melody and noise. Music, as it is taught in every university and conservatory in the world today, is explicitly Pythagorean in its methods and assumptions. And even when musical styles emerged from the African diaspora that challenged this paradigm, threatening to topple it with notes that didn’t belong to scales and rhythms that defied conventional metric thinking, the algorithmic mindset prevailed, somehow managing to codify non-Pythagorean performance styles that would seem to resist codification.  Even today, I see the Pythagorean spirit as the implicit philosophy undergirding the advances of digital music—the ultimate reduction of song to mathematics—and technologies such as synthesizers, drum machines, Auto-Tune, and the dynamic range compression of current-day recordings.  Music: A Subversive History, pages 48-49

And this new system has proven surprisingly resilient in the face of all sorts of challenges. By the time we get to Augustine, who wrote a treatise on music in the late fourth century AD, the reduction of music to mathematics is all but complete. He even uses the Latin word numeri (or “numbers”) to refer to rhythm. The pulse of music is now a matter of counting, and the forward motion of a performance a type of calculation. And that’s how matters remained until the African diaspora disrupted this complacent view in the twentieth century. Ibid. page 50

Any system that started circa 500 BC can’t be a “new” system.

When has music never involved counting? Let me put this in practical terms, how can you describe the difference between Scott Joplin’s “The Great Crush Collision March” and “Bethena (A Concert Waltz)” without making any reference to numbers? You can’t describe the difference between 4/4 and 3/4 time signatures in music without using numbers. You can’t even talk about the difference between a perfect fourth and a perfect fifth (“Here Comes the Bride” and the “Star Wars” theme song respectively) without making reference to number. The claim that the African diaspora disrupted “this complacent view” depends on a presumption that “this complacent view” as Gioia describes it has ever prevailed in Western music. Pythagorean ideas about music are neither new nor nearly as prevalent as Gioia would have us believe.

Now, in one sense, Ted Gioia’s claim that African diaspora music untuned the cosmos as perceived by Western intellectuals indebted to the Pythagorean tradition is accurate. Ancient philosophers working within the post-Pythagorean Western traditions did believe it was important for earthly, human music to be some kind of reflection of a cosmic harmony that consisted of numbers whose perfect ratios might be beyond the ken of mortal ears.  This was summed up well by Daniel K. L. Chua decades ago:

The very fact that tuning seems such a marginal if not an irrelevant explanation of music’s meaning today testifies to a disenchanted world. Tuning, for the ancients, was a magical formula; its numbers tempered the cosmos. If music was ever absolute then this was the only time in history that music was genuinely absolute music. It harmonized everything. What the Romantics discovered as absolute music was a mere shadow of what Pythagoras formulated two thousand years earlier, for the absolute music he bequeathed to humanity was not so much a music to be composed as a music that composed the world.

In Plato’s account of creation, music tunes the cosmos according to the Pythagorean ratios of 2:1, 3:2, 4:3, and 9:8, and scales the human soul to the same proportions. This enabled the inaudible sounds of the heavens to vibrate within the earthly soul, and, conversely, for the audible tones of human music to reflect the celestial spheres, so that heaven and earth could be harmonized within the unity of a well-tuned scale. This scale came to be pictured as a monochord … [see here] … that connected the stars to the earth like a long piece of string that vibrated the structure of the universe (plate 1). Its geometric and astral mathematics represented the binding order of an immutable and crystalline world. So music, as the invisible and inaudible harmony of the spheres, imposed a unity over creation, linking everything along that entire chain of being.  … Thus music was not simply an object in a magical world, but the rational agent of enchantment. Pages 14-15

If that’s the case, however, then Ted Gioia’s dualism between the math/science of Pythagoras vs the magic of an Empedocles or a healing shaman dissolves. If the Pythagoras of legend used music and song to heal and to change the moods of angry drunks then the difference between Ted Gioia’s “science” and “magic” might have little to do with actually Pythagorean ideas about music.

In The Aesthetics of Music Roger Scruton pointed out that the Pythagorean cosmology of the ancient Greeks, which was the prevalent Western conception of music, was abandoned between the sixteenth and seventeenth centuries.  Kyle Gann’s recent book The Arithmetic of Listening has spelled out why and how–the discovery of the overtone series in the seventeenth century made it less necessary to rely on Pythagorean postulates about melodic and harmonic intervals being tuned by the purest and simplest number ratios available. Prior to discovery of the overtone series, Pythagorean ratios were the only baseline even for people who wanted to tune by ear. Gann’s history had debunked Gioia’s history on Pythagoras and the ancient Greeks on music five weeks before Gioia’s book hit the market.

Where Gann’s work dispelled myths Gioia promoted about Pythagoras, I take issue with Gioia on Augustine. Augustine’s De Musica was written around 386 to 391 AD, largely prior to his Christian conversion.  We can’t hold it against Augustine that he worked with the prevailing scientific and cosmological ideas available to him in the 4th century AD. That’s bad history and bad historiography.

We shouldn’t take Gioia’s word for it that Augustine reduced music to numbers and counting. He should have quotes from Augustine to prove the claim. Gioia never quotes Augustine. Worse yet, in his glib take on Augustine, Ted Gioia neglects to mention that Augustine never finished the treatise. Any history, subversive or not, should get these basic things done.

How do I know Augustine never finished De Musica?

But if these six books On Music are only a fragment of a projected cycle on the liberal arts, they are, also, only a fragment of a larger treatise on music. They are, in the words of Augustine `only such as pertain to that part called Rhythm.’ Much later, in writing to Bishop Memorius, he speaks of having written six books on Rhythm and of having intended to write six more on Melody (de melo). As we shall see, this intended part would have been a treatise on Harmonics.

It is necessary, for the understanding of these books on Rhythm, to know what the ancients meant by music, by rhythm, and by melody. It is true St. Augustine tells us that, of these six books, the first five on rhythm and meter are trivial and childish, but this is a rhetorical statement to introduce us to the more serious business of the sixth book on the hierarchy of numbers as constitutive of the soul, the universe, and the angels. … Pages 153-154

I’m quoting from the same edition of Augustine mentioned in Gioia’s bibliography. Gioia could have made a case that Augustine did something worse than reduce music to numbers and counting; he could have pointed out there’s nothing in the treatise a Western reader of our time and place would even recognize as music showing up in the treatise!

Yet Augustine called it De Musica so, however pedantic and boring the treatise gets, we know that he’s building toward a musical definition. Unlike Gioia, I’m going to quote Augustine. He defined what music was in a way that lets a reader know this won’t be about melody or harmony (yet). In the excerpts that follow, “M” refers to “master” and “D” to “disciple.”


M. Music is the science of mensurating well. Doesn’t it seem so to you?

D. It might seem so, if it were clear to me what mensuration is.

M. Don’t let this disturb you, that, as you just said, in all things made, music included, measure must be observed, and yet that this is called mensuration in music.   …

M. For you to understand that mensuration can regard music alone, while measure, from which the word is derived, can also be in other things. In the same way diction is properly attributed to orators, although anyone who speaks says something, and diction gets its name from saying.  …

M. Then, mensuration is not improperly called a certain skill in moving, or at any rate that by which something is made to move well. For we can’t say anything moves well unless it keeps its measure. …

M. Music is the science of moving well. But that is because whatever moves and keeps harmoniously the measuring of times and intervals can already be said to move well.  For it is already pleasing, and for this reason is already properly called mensuration. Yet it is possible for this harmony and measuring to please when they shouldn’t.  For example, if one should sing sweetly and dance gracefully, wishing there-by to be gay when the occasion demanded gravity, such a person would in no way be using harmonious mensuration well. In other words, that person uses ill or improperly the motion at one time called good because of its harmony. And so it is one thing to mensurate, and another to mensurate well.

In a footnote, the translator pointed out, “It is impossible to render modulari by ‘to modulate’ because ‘modulate’ in English has a technical musical meaning … “. Music is regarded as a science, but a science of measurement that was still an art.  Even if Gioia had quoted this passage his take on Augustine is still pejorative.

The distinction between reason and non-reason for things being done turns out to be one of the linchpins in Augustine’s definition of what even qualifies as art but it is a foundation, not the telos of the art:

M. But don’t you think art is a sort of reason, and those who use art use reason? Or do you think otherwise?

D. It seems so.

M. Therefore, whoever cannot use reason does not use art.

M. … But if all imitation is art, and all art reason, all imitation is reason. But an irrational animal does not use reason; therefore, it does not possess an art. But it is capable of imitation; therefore art is not imitation. …

M. Then tell me, which is to be considered dearer, what is contained in our intellect or what is accidentally attributed to us by the judgment of an ignorant people?

D. No one doubts the first is far above all others, even those things which are not to be thought ours.

M. And so you don’t deny, do you, all science is contained in the intellect?

D. Who does?

M. And, therefore, music is in the intellect.

D. That seems to follow from its definition.

The mind has to understand something is being expressed before the heart to have a feeling about it. That’s not reducing music to number. Why is number significant? What is the meaning of measurement?

M. … And it is now time you learn how important this thing is, because the unity you love can be effected in ordered things by that alone whose name in Greek is analogia and which some of our writers have called proportion.

Now by Book II Augustine finally starts getting into the nuts and bolts of Latin poetry. We need to see from Augustine’s work whether he’s really reduced music to number or if his discussion of poetic rhythm is really working toward a larger point.

D. I now understand, and I agree a certain combination of feet can be made in which it is fixed just how many feet the progression is to be, before it starts over again. …

M. Then, since it’s proper for things distinct from each other to be distinguished by names, it’s well to learn the first kind of combination is called rhythm by the Greeks; the second, meter. In Latin they could be called, the first, number (numerus); the second, measure (mensio or mensura). …

M. … And so all meter is rhythm, but not all rhythm is meter.


M. … For reason certainly teaches some meters are established as immobile, that is, where nothing should be changed, as in this one we have just talked about; others as mobile, where one may substitute certain feet for others …

But, with regard to the composition of meters, it is enough at present to see diverse meters can be joined together so long as they agree with respect to beat.

Putting this in contemporary musical terms, if you’re going to play in 4/4 you need eight eighth notes, not nine. If you have nine eighth notes as your recurring musical pattern the meter stops being 4/4 and becomes 9/8. If you have seven eighth notes you’ve got 7/8. The difference between these meters can be as vivid as the differences between the music of Duke Ellington, Dave Brubeck, and Sergei Prokofiev. Augustine was describing the differences between poetic rhythms and meters in a way comparable to what I have just described as the differences between musical time signatures in more modern music. We can’t talk about these meters without making reference to numbers. The number doesn’t “reduce” the music to something subhuman, numbers let us define the naturel of the “flow” of the music and poetry. To lay down a groove you have to keep time, and that requires counting.

If Ted Gioia’s Music: A Subversive History were your only source of information about Augustine in general and his treatise De Musica in particular, you’d never learn any of what I’ve just discussed. Gioia’s would-be subversive history attempts to pass off the entire history of tuning instruments in the Western tradition as a conspiracy to suppress magic and impose totalitarian rule on the masses. That Gioia has made such a hash of Augustine makes it hard not to consider the likelihood that his would-be subversive history will turn out to be wrong on other issues.