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, geometria, musica, 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.