Same but Sundered: on Mercury, meaning, and metaphor

I’m still reading Planet Narnia, and enjoying every page. Ward begins his chapter on Mercury with these words from C. S. Lewis‘s poem “The Planets”:

Meeting selves, same but sundered.

—Lewis, “The Planets,” lines 17–18

It should come as no surprise that quicksilver (Mercury) is the metal associated with the Roman deity. Mercury is curious in that it can be drawn apart and then rejoined without a trace of that former division. We see this symbolism in the Mercury-associated myth of Castor and Pollux, identical twins who are “same but sundered.”

But what Michael Ward points out that has captured me is the association of Mercury with masterful use of language. Lewis himself noted that Martianus Capella (a name familiar to scholars of the history of music theory) depicts Mercury as the groom of Philologia in De Nuptiis. Philologia, in its original sense broadly meant “love of learning.” But we can’t help but associate it with the more specific derivative, philology, the study of language through the lens of history.

One of the things Lewis does with allusions to Mercury is use him as a metaphor for metaphor—and I doubt you can get much more “meta” than metaphor-izing metaphor. Ward draws on Lewis’s words from The Personal Heresy. Here Lewis is examining a passage from Keat’s poem “Hyperion“:

Tall oaks, branch-charmed by the earnest stars…

John Keats, “Hyperion”

Lewis remarks:

We have all seen the trees with branches stretched up in intense stillness towards the stars. We have imagined or been told of people compelled by magical charms to stand as still as trees. Lay the two side by side and add the word ‘earnest’—which is exactly the point where the sensible image [trees, branches] and the idea of insensible ‘magic’ merge beyond hope of distinction—and the whole, like meeting drops of quicksilver, becomes a single perception.

—Lewis, The Personal Heresy, pp. 20–21, emphasis mine

What Ward points out I find to be so satisfying—that even as Lewis alludes to Mercury via quicksilver, the very form of the sentence reflects (a serendipitously apt word when considering quicksilver) the content of the sentence—”Meeting selves, same but sundered.”

Ward remarks on Lewis’s remark (see how deep the rabbit hole goes?)

This is a deliberately fugal [another word familiar to music theoreticians] sentence, in which the idea of two things becoming one is formally conveyed three times:

1. ‘side…side…add’

2. ‘sensible…insensible…merge’

3. phrastically [sic] in the culmination of (1) and (2) in ‘the whole…like meeting drops…becomes’

Thus, the form and the content of the expression are of the same nature, but of sundered manifestation.

In music, this Mercurial influence might take the form of text painting, in which the words being sung are mirrored in some way by the musical structures that ensconce those words. Or perhaps what Richard Cohn calls “introverted motives” (i.e., musical motives that operate on both a microscopic “surface” level as well as macroscopic “subsurface” level of the music) in his essay “‘This Music Crept by Me upon the Waters’: Introverted Motives in Beethoven’s ‘Tempest’ Sonata” (Engaging Music: Essays in Music Analysis, ed. Deborah Stein, 2005, pp. 226–235). Introverted motives are indeed same but sundered, for they help to unite the piece but operate on different depths of the musical architecture.* It may also be significant that Cohn’s essay analyzes the “Tempest” Sonata, named after Shakespear’s eponymous play. Shakespeare was no stranger to planetary allusions in his works.

This is where metaphor comes in, because Lewis reveled in Spenser and Milton and Dante, writers whose rhetorical mastery of symbols and multiple meanings Lewis seems to have thought unmatched. Lewis saw a threat in reductionists’ attempts to remove what they saw as the superfluous language of metaphor by replacing all those allusions with a single word that could denote the same idea. To borrow, as Ward does, from Owen Barfield, even in trying “to cut away and expose all metaphorical usage,” one does not “escape the curse of Babel.” (The Rediscovery of Meaning and Other Essays, Middletown, CT: Wesleyan University Press, 1997, p. 64). Ward sums it so well, I will end with a quote from him rather than make the attempt myself:

Metaphor rests on the ‘psycho-physical parallelism…’ that characterises the universe, and therefore to deny or to restrict metaphor (the ‘carrying over’ of meaning
from physical units to metaphysical entities) is a mental move similar to a denial of the relationship between material creation and immaterial Creator. To say ‘There is no such thing as Man, there are only men’ [A line uttered by an antagonist in Lewis’s That Hideous Strength] is to resist the imagination’s power of seeing beyond sensory data; it is to stultify that faculty which operates also in the realm of faith.

_____

*Fractals and the Mandelbrot set also come to mind as structures that could be thought of as Mercurial.

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Grammatica, Dialectica, Rhetorica: in which the three roads meet in music theory pedagogy

[The following are some thoughts I’ve been mulling over ever since my earlier post on the liberal arts.

UPDATE: The revised version of this essay has now been published in Engaging Students: Essays in Music Pedagogy. You can read it here.]

A great deal of the national conversation on education has centered on the avant-garde and the use of technology in the classroom. While many of these ideas have merit, I find myself increasingly intrigued by the notion of combining new ideas with old ones—very old ones. I am referring to the trivium, that relic of medieval university curriculum to which we don’t give much traction any more, even in liberal arts institutions. And on the face of it, why would we? Grammar, logic, rhetoric: these are great for giving a speech, but most of us don’t do that. Music belongs to the quadrivium, after all. But every field of study has its grammar, logic, and rhetoric, if we think of these words in more general terms.

Grammatica

  • grammar |ˈgramər| noun
  • the whole system and structure of a language or of languages in general, usually taken as consisting of syntax and morphology
  • ORIGIN late Middle English: from Old French gramaire, via Latin from Greek grammatikē (tekhnē) ‘(art) of letters,’ from gramma, grammat- ‘letter of the alphabet, thing written.’ *

What do students normally think of as music theory? Probably what we in the discipline would only consider the “nuts and bolts.” Constructs like scales, intervals, and time signatures are these nuts and bolts, a kind of musical grammar. But so often my students have thought music theory is the identification of such things, that in labeling the Roman numerals or identifying the tone row they are “doing theory.” For a long time as an undergraduate, I thought that analysis was being able to account for every note in the score and classify it. I fear most students make that mistake, believing that information alone will get them through the gauntlet of the undergraduate music theory curriculum. And perhaps I am to blame for failing to dissuade them of that delusion. If the assignments I hand out and the exams I proctor are entirely focused on getting students to identify, define, and label musical data, then I can hardly blame them for thinking that’s all there is. Medieval scholars knew, as do we, that one may understand what a nail and hammer are, but knowing neither builds the house, nor makes it a particularly solid house. This brings us to dialectic.

 

Dialectica

  • dialectic |ˌdīəˈlektik| noun
  • the art of investigating or discussing the truth of opinions.
  • ORIGIN late Middle English: from Old French dialectique or Latin dialectica, from Greek dialektikē (tekhnē) ‘(art) of debate,’ from dialegesthai ‘converse with.’ *

Once we know what the materials are and what they do, how are they put together to form something we recognize as a house? What underlying logic makes sense of an assemblage of wood and nails? The second member of the trivium, dialectic (logic), helps us arrange information (the nuts and bolts) into meaningful patterns, so dialectic here does not mean merely syllogizing to win an argument. It is particularly relevant to music theory, which as a study is predicated on the belief that there is an internal logic to the way music unfolds. When a new way of unfolding (in the colloquial sense, not the Schenkerian) is invented, music theorists work to unlock that logic. The cadential second inversion triad is so called because it logically flows to the dominant just before a cadence. Some students get this; they are the ones who can transfer a concept learned in one example and apply it to a new one.

It is music’s logic that underlies all of Peter Schickele’s musical humor. Imagine listening to P.D.Q. Bach’s Short-Tempered Clavier as a student versed only in the music’s grammar. Although we could identify the blues scale used in the D major prelude, we would miss the joke of such a phenomenon occurring in a piece supposedly written in the early eighteenth century. A student might pick up on the fact that something sounded amiss, but may not know why.

I, as a teacher, have a responsibility to draw students’ attention to the underlying dialectic. For this reason, I frequently differentiate between the way a particular musical phenomenon might appear “in the wild” as opposed to “in the zoo.” I want my students to understand that under the controlled laboratory conditions of the classroom, we tend to see clear, obvious examples. I want to balance that out by giving them “field experience,” where they may have to sort out a number of factors that muddy the waters. At this stage, they should know how to wield a hammer and how to put a house together (i.e., put up the walls before the roof).

 

Rhetorica

  • rhetoric |ˈretərik| noun
  • the art of effective or persuasive speaking or writing, esp. the use of figures of speech and other compositional techniques.
  • ORIGIN Middle English: from Old French rethorique, via Latin from Greek rhētorikē (tekhnē) ‘(art) of rhetoric,’ from rhētōr ‘rhetor.’ *

Is the house well designed? Can we look at its structure and appreciate the architect’s gift for form and function, light and darkness, line and space? Can we design and build our own house? Rhetoric is the skillful employment of grammar and dialectic. In music theory it equips students to evaluate and draw out some significance to their analysis. Ultimately, it isn’t the labels that make me a musician; nor is it understanding the logic of musical mechanics. The rhetoric of music involves not only its technical correctness but also its artfulness.

Compare a student’s attempt at writing a fugue to one of Bach’s, and one can immediately see that even if the technical specifications are correct, the student’s composition will lack the rhetorical elegance of Bach’s. This is why composition projects can fill such a vital role in a student’s music theory education. Such projects push students beyond simply identifying musical events and toward creating technically, musically satisfying solutions. We start with part-writing exercises, which tend to lean more toward dialectic than rhetoric. But then students can try harmonizing a preexisting melody, then writing their own melodies and harmonizing them. Over the span of multiple classes, students are led into rhetorical thinking.

Writing analytical prose can accomplish similar rhetorical goals, provided we encourage students to avoid the onerous “play-by-play.” We do students a disservice if we wait until their final year or two before asking them to write analytical prose of any substantial length. Early attempts need not be long; even in the first year of study, a paragraph or two may be a good place to start.

The Place Where Three Roads Meet

  • trivium |ˈtrivēəm| noun
  • an introductory curriculum at a medieval university involving the study of grammar, logic, and rhetoric.
  • ORIGIN early 19th cent.: from Latin, literally ‘place where three roads meet,’ from tri- ‘three’ + via ‘road.’ *

I have already implied that these three echelons of pedagogy are somewhat artificial because they can exist simultaneously. Indeed, I think the ideal curriculum would entail each class progressing from grammar to dialectic to rhetoric. On a larger scale the school term would begin with heavy emphasis on grammar, gradually lean more on dialectic as the term continued, and finally end with greater practice in rhetoric—rather like a compound form. The music major curriculum should be an overall progression from grammar to dialectic to rhetoric. I think this is the assumed direction of many music departments, but I am unaware of many that intentionally communicate this to students.

One may note the rough similarity between this schema and that of Bloom’s Taxonomy. Bloom essentially subdivides each part of the trivium into two subcategories (grammar = knowledge and comprehension; dialectic = application and analysis; rhetoric = synthesis and creation). But the goal is the same—progression from fundamental knowledge to understanding how it is assembled and eventually to value judgements and creation of new ideas—from engagement with music that is shallow to deep. I don’t want my students to splash in the kiddie pool and think it’s the ocean.

The philosophy of the trivium blends well with that of the inverted classroom. The lecture, often freighted with music’s grammar, leaves little time for in-depth analysis or evaluation. The traditional lecture, like textbook reading, is essentially an info dump that, when moved outside of class, frees the class period for higher levels of cognition and musicality. For my part, I want students to graduate beyond the sterility of pedagogical examples to the organic, sometimes gritty, mysteries of real music as soon and as much as possible. What better way than to disseminate the basic information in pre-recorded lectures and model for them how music theory can enhance their listening experiences, performance decisions, compositions, and appreciation for those of others.

*New Oxford American Dictionary 3rd edition © 2010 by Oxford University Press, Inc.

This work is copyright 2013 Enoch Jacobus and licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.

Bioshock: In which we reflect on human nature and video games as art

Can video games be art? Notable film critic Roger Ebert, in his words, “was a fool” for declaring that video games can never be so. He hasn’t changed his opinion so much as realized that he shouldn’t have commented at all. Roger Ebert wields a far more eloquent pen than I do, and his comments have been debated back and forth since at least 2005 [But for highlights of the juicy gossip, check out the oldest reference I could find (27 Novemeber 2005), a recap (16 April 2010), Ebert’s caveat (1 July 2010) and more via the Wikipedia page on “Video Games as an Art Form“] so I’m not particularly interested in writing a polemic against what he freely admits is an opinion, nor in debating the nature or definition of art (which will never be agreed upon). I’m interested in talking about Bioshock.

As video games go, Bioshock isn’t exactly old, nor is it particularly new. In an industry constantly obsessing over the next big thing, Bioshock is the middle child— it was a really cute kid, but we’ve kind of forgotten about it in our enthusing over the newest darling baby. I played it again recently and found myself transported, dare I say, “enraptured,” in ways few games have been able to achieve. It is typically categorized as a First-Person Shooter (FPS), which it certainly is. But it transcends the genre is ways the Call of Duty franchise never has. The former, I submit, is art; the latter, entertainment. These two need not be mutually exclusive (art-ertainment? ent-art-tainment?). Video games developers gotta eat too.

Bioshock is not easily explained, as evidenced by a quick Google search of “How to Explain Bioshock.” But I can tell you that it has probably exposed more young people to deep philosophical thought on society, politics, art, free will, and human nature than books will. It’s sad, but in all likelihood, true. What’s more, these young people are so moved by these ideas that they turn to the internet to find out more about what they just experienced, why it moved them, and if others shared a similar experience. They are producing fan fiction, and pages devoted to Bioshock-inspired art. (Of course, this begs the question, “Is it art?” but that’s a recursive discussion.)

The game amalgamates numerous influences: sc-fi horror, Ayn Rand’s objectivism, Art Deco, Cole Porter. When the game was released in 2007, it fueled and added new dimensions to my interest in the history, popular music, technologies, and philosophies of the first half of the 20th century. Indeed, a lot of the “punk” sub-genres (steampunk, dieselpunk, gearpunk, atompunk, etc.) have this effect on their participants. In many ways, it draws on into the spirit of the era, if not the actual historical facts. Bioshock straddles the grittier dieselpunk and shiny decopunk sub-genres.

To be sure, the game is creepy. Really creepy. I couldn’t play it at night. So why did I play it at all? Especially since I already knew about the mid-plot twist and the ending? My brain answers that it’s because it was a richly intellectually experience, and that’s true. But my heart answers that it was a catharsis, and I suppose that is also true. Isn’t that what art does? Ebert’s own criteria for what art should do seems like affirmation to me: “[T]he real question is, do we as consumers become more or less complex, thoughtful, insightful, witty, empathetic, intelligent, philosophical (and so on) by experiencing them? Something may be excellent as itself, and yet be ultimately worthless.” (Source)

“ALL GOOD THINGS OF THIS EARTH FLOW INTO THE CITY”

Here is the set-up. In 1919 a young man, soon to be known as Andrew Ryan, flees Russia, realizing that his people have merely traded the lies of the Czar for the lies of the Bolsheviks. He emigrates to the United States, following so many others in the hope that a free society would let him prosper. America was better, but Ryan saw in the New Deal programs of the 30s a threat to that freedom. He came to despise any form of socialism for its parasitic effects. Further disillusion came from the government’s attempts to nationalize some of his land, as well as its use of atomic weapons to end WWII.

Ryan, fearing atomic war and government interference, poured his wealth into the building of a secret utopia he called Rapture (which as one reviewer has noticed can have multiple, telling nuances: in modern usage “a feeling of intense pleasure or joy,” but in a more archaic sense “seizing and carrying off,” from which the word rape comes). Rapture is a city beneath the waves, built on the sea bed of the Atlantic, “a city where the artist would not fear the censor, where the scientist would not be bound by petty morality, where the great would not be constrained by the small!” With such promises, Ryan lures the cream of the world’s crop to his underwater city (rapturing them, as it were).

Ryan’s vision is one free from government interference and religious morality. Consequently, artistic expression becomes increasingly sadistic, creating tableaux vivants by casting living people in plaster. The scientific community, free from the constraints of ethics, experiment on living humans. They create plasmids, elixirs that splice the human genome, giving users the ability to cast ice, electricity, and other forces from their hands.

This genetic manipulation is made possible by the discovery of a secretion of sea slugs dubbed ADAM (the catalyst that activates it is called EVE). But Adam is addictive. And it has some other minor side effects—like excrescent growths and insanity. Anything in the name of science, right? The denizens of Rapture keep on, believing they can perfect the formulae and evolve beyond the defects. No one stopped to consider that that might not b the real problem. As Brigid Tenenbaum, one of Rapture’s few sane survivors, says:

ADAM improved every aspect of man, except his character.

“NO GODS OR KINGS. ONLY MAN”: humanism

You will have notice the eye-popping visuals that rely heavily on the art deco movement, with its incorporation of a noble and heroic take on the human form that seems almost Hellenistic in scope. Let’s compare some of Bioshock‘s statuary with some real-world, Art-Deco counterparts:

Real: Oscar statuette

Bioshock: Descent in the Bathysphere.

Real: Statues at the Hoover Dam, designed, I believe, by Oskar J.W. Hansen.

Bioshock: Welcome to Rapture. Opportunity Awaits.

Real: Central train station, Helsinki, Finland

Bioshock: bust of Andrew Ryan

Real: The famous likeness of the titan Atlas at Rockefeller Plaza

Bioshock: Atlas holds up the world.

Oskar J.W. Hansen was the sculptor responsible for the statuary and and bas relief sculptures at the Hoover Dam. He wanted his work to express “the immutable calm of intellectual resolution, and the enormous power of trained physical strength, equally enthroned in placid triumph of scientific accomplishment.” (Source) Sound familiar? This echoes the first words of Andrew Ryan we see in the game: “No gods or kings. Only man.”

After disembarking from the bathysphere shown in the clip above, what the player discovers is neither a utopia nor even a haven for mankind. I’ve seen sci-fi explore the science-gone-amuck angle before, but I’ve never experienced it so viscerally. The player is thrust into a horrifying environment in which self-inflilcted genetic mutation has driven the world’s once best and brightest to madness or death. At every glance, irony stares back. You may have noticed Django Reinhardt’s 1949 rendition of “Somewhere Beyond the Sea” in that last video. Here’s the whole thing.

If nothing else, this game has introduced or reignited a younger generation’s interest in music from the era. A quick iTunes search reveals that this particular version of the song has become immensely popular, with downloads funneled through searches for Bioshock’s music. The licensed music used in the game certainly serves to place Rapture in an historical context, but it also serves a narrative function, poignantly providing ironic commentary on the location or information just received. It’s use is summed up well by William Gibbons.

“SOMEBODY’S GOTTA SCRUB THE TOILETS”: class inequality

So why did Ryan’s utopian vision end in madness? The short answer is greed, hubris, and hypocrisy. How do you keep a construction project the size of a city at the bottom of the ocean a secret? You take all the manual laborers who built it and you forbid them from leaving once they’re done working. Ryan’s vision for a society of brilliant visionaries, thinkers, was like any society. As antagonist Frank Fontaine says, These sad saps. They come to Rapture thinking they’re gonna be captains of industry, but they all forget that somebody’s gotta scrub the toilets.” Consequently, Fontaine manipulates the disenfranchised to undermine Ryan’s authority, instigating a civil war unknown to anyone on the surface.

A key, yet silent, narrative element of Bioshock is the experience the player has first of the sprawling, luxurious Olympus Heights apartments that housed elite citizens (the veritable “gods” of the Rapture), followed soon after by wretched, cramped, lower-class accommodations in the Artemis Suites. (For more on the used of Greek mythology, read on.)

Here’s a fan-made video depicting some of the events leading up to the 1958 New Year’s Eve Riots that became the death knell for Rapture.

“IT IS ONLY WHEN WE STRUGGLE IN OUR OWN INTEREST THAT THE CHAIN PULLS SOCIETY IN THE RIGHT DIRECTION”: philosophy

Ayn Rand’s objectivism holds up human reason and self-interest as necessary and virtuous in the pursuit of human progress. Andrew Ryan, in his audio logs found throughout the game, echoes this philosophy: “I believe in no God, no invisible man in the sky. But there is something more powerful than each of us, a combination of our efforts, a Great Chain of industry that unites us. But it is only when we struggle in our own interest that the chain pulls society in the right direction. The chain is too powerful and too mysterious for any government to guide. Any man who tells you different either has his hand in your pocket, or a pistol to your neck.”

Unless I’m much mistaken, the developers intended to show the fallacies of this philosophy by looking at what a society becomes when there are no checks and balances on one’s selfish ambition. Almost everything I’ve read about Bioshock mentions Ayn Rand’s didactic novel, Atlas Shrugged (1957), which forms the philosophical inspiration for the game. The game probably sparked curiosity in the book, as it did me. But Bioshock came out in 2007. In 2008, the United States (and the world) experienced a severe economic downturn. Spawning a January 2009 article in the Wall Street Journal entitled “Atlas Shrugged: From Fiction to Fact in 52 Years.” But the recent films have also contributed to renewed interest in Rand’s ideas. Regardless of the side of the aisle one happens to prefer, the fact remains that Bioshock, almost presciently, brought objectivism to the attention of a wider audience before it seemed to matter to so many people.

“APHRODITE IS WALKING THE HALLS”: mythology

Bioshock is rife with allusions to Greek mythology, often dripping with hidden meaning and irony.

The airplane flight that begins the game is Apollo Air Flight DF-0301, named for the god typically associated with the sun, but interestingly was also the god of music, poetic inspiration, prophecy, medicine, and pastoral life. The plane crash in some ways foreshadows the wreckage Rapture’s inspiring purpose has become.

One of Rapture’s economic centers, Poseidon Plaza, named after the god of the sea (and earthquakes).

Artemis Suites, a working-class residence attached to Apollo Square, named after the goddess of the hunt and, ironically, protector of young girls.

Arcadia is an undersea park and oxygen generator, named after a mountainous district in the Peloponnese of southern Greece. In poetic fantasy it represents a pastoral paradise, and in Greek mythology it is the home of Pan. This area of the game features the Saturnine cult, named after Saturn (Cronus), who ate his own children. Very telling.

Rapture’s power production facility,Hephaestus, named for the crippled god of fire and of craftsmen.

This in-game protest poster sports Atlas, “defender of the people,” the pseudonym of taken on by Andrew Ryan’s opposition during the Rapture Civil War. It is, of course, obliquely referring to Ayn Rand’s “Who is John Galt?” from Atlas Shrugged.

Hestia Chambers houses Fontaine’s Home for the Poor and the Little Sisters Orphanage, ironically named for the goddess of hearth, home, and family.

Mercury Suites, the most affluent homes in Olympus Heights, are named after the god who was patron of both merchants and thieves. Hmm.

Point Prometheus houses the facilities where plasmids were developed. Like their namesake, the scientists here though they were bring mankind the very power of the gods. And for their meddling, they were punished.

Other references include: the cosmetic surgeon, Dr. Steinman, and his obsession with Aphrodite, goddess of beauty; Neptune‘s Bounty, Rapture’s fishery; Siren Alley, Rapture’s red-light district, named after the mythological mermaids whose singing lured sailors to their deaths; Plaza Hedone, a subsection of Siren Alley rife with old, illicit plasmid facilities; Persephone, Rapture’s “correctional facility” that is suspended over a chasm, named for the woman carried off by Hades and made queen of the underworld;

Of course, the over-arching symbolism of Atlantis is not lost on me. A city of paradise beneath the waves, brought to its knees by cataclysm. Indeed, Atlantis has historically been linked to the idea of utopia, such as in Francis Bacon‘s New Atlantis and Thomas More‘s Utopia. In 1882 Ignatius L. Donnelly published Atlantis: the Antediluvian World, in which he confessed to believe that the Garden of Eden was in Atlantis (remember ADAM and EVE?). It, along with Atlantis, he said, were destroyed by the Great Flood of Genesis chs. 6–9, linking the ideas of Atlantis’ destruction with retribution for sin.

“THE END IS NIGH”

So, this turned out to be a much longer post than I had envisioned. I began working on it 21 February, and have intermittently worked on it until now, so I will end here. I will say, though, that the visual and audio elements are so important to the experience of Bioshock. You can visit the Rapture City Archives for images of posters, sighs, banners, and more. Garry Schyman’s moody scores for Bioshock and Bioshock 2 can be heard at his website. The licensed songs from the 30s, 40s, and 50s can be found on iTunes or via YouTube. I look forward to the release of Bioshock: Infinite on 26 March.

Musings on Musica Universalis: in which we consider the quadrivium

The Seven Liberal Arts

Music is a science of melos [complete musical complex of melody, rhythm, and text] . . . But we define it more fully in accordance with our thesis: ‘knowledge of the seemly in bodies and motions.’

—Aristides Quintilianus, On Music (1.4), trans. Thomas J. Mathiesen

The quadrivium has been on my mind the last few months, although I didn’t know it. “What’s that?” you say. “What sweet wine are you squeezing from your mind grapes now—this quadrilater-wha?”

Quadrivium is Latin for “the four ways” [from quad(r): “four” and via:”way/road/path”], and it consisted of arithmetica, geometriamusica, and astronomia. Coupled with the trivium [grammatica, dialectica (logic), and rethorica (rhetoric)], it formed the seven liberal arts, which were preparatory for the serious study of philosophy and theology.

In our modern understanding of these subject, music might seem to be the odd one out (à la Sesame Street’s “One of These Things Is Not Like the Others“). After all, it’s an art, right? It’s all emotional and subjective and open to debate. Not like science, the immutable pillar of our society, based on facts and empirical evidence. The term music here is problematic, which comes from the same root that gave us the word muse, a word we associate with creative process in general. Indeed this word was often associated with the Greek word for art: tekhnikos, a word the modern reader would be more likely to align with “technical” fields like the sciences and mathematics. But back in the day, they weren’t so concerned with studying the practice of music (what we would consider musical study) as how musical relationships, like mathematical, geometric, and celestial relationships divulged the universe’s underlying order. This is where that whole “harmony of the spheres” idea came from.

There has been no shortage of recent scholarship connecting music with mathematics (the Society for Mathematics and Computation in Music even publishes the Journal of Mathematics and Music and hosts a biennial conference). Transformational theory borrows heavily from algebra; musical set theory borrows from mathematical set theory. Furthermore, there have been neato connections made that directly link geometry to pitch, like Chladni figures and cymatics (a nice introduction to both can be seen here).

What’s remarkable is how . . . remarkable . . . we find these connections to be. It’s not unusual for modern man to dismiss the cultural, social, educational, religious, or philosophical bent of an earlier age. But Boethius was seeing these connections in the 6th century, and he was just realizing the ideas Plato had in The Republic! Before Plato, the Pythagoreans certainly toyed with the idea, although more in the creepy-secretive way than in the public-education way. But the underlying principle, in whatever form it took, seems to be that “everything is connected.”

We live in an age that likes to divide things up. Some call it pigeonholing, others putting people in a box. We don’t just have “science” any more; we have geology, astronomy, physics, biology, etc. Do we even have categories as broad as “biology” any more; we have neurobiology, botany, zoology, microbiology, and on an on. I’m not just a professional in the fine arts; I’m a musician . . . a music theorist . . . specializing in transformational theory . . . specifically geometric conceptions of harmonic space. Also, I like bacon, but enough about me.

I get it—division into categories helps us process information. How Aristotelian of us! But what happens when an idea straddles the line between, say, sculpture and dance, or between technology and biology. Well, then you need to know something about both. Truth be told, theoretical physicists have been trying to come up with a “theory of everything” for a while now (albeit in a very different sense).

So, to the five of you who will read this (or perhaps I’ve given myself too much credit), expect a few more posts on this topic as I roll ideas around for what I hope will be a fruitful research project. And what better place than in service to this blog’s “mission,” or, at the very least, excuse for existence—the intersection of seemingly disparate ideas, somewhere between theology and physics, music and metaphysics, geometry and philosophy.

A Glamorous Education: in which John Gardner muses on the allure of sentence structure

Honey and Locusts

I’m currently enjoying Sir Ken Robinson’s book Out of Our Minds: Learning to Be Creative quite a bit. Robinson is one of the world’s leading experts on creativity and education. If you missed it when I posted it a few months ago, be sure to watch his excellent video, Do Schools Kill Creativity?

One of the many things I’ve learned so far reading this book is an etymological lesson on a modern word with origins I would not have guessed… a lesson I now happily pass on to you!

During the Middle Ages, when very few Western Europeans possessed any sort of education at all, the first schools that began appearing were known as schola grammatica — Grammar Schools. These schools focused primarily on teaching grammar, particularly Latin grammar. As a result, students of grammar (or, as it was rendered in Ye Olde English, gramarye or glomerye) became revered by…

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