Contemplation, Euclid, and Music

euclidI am not contemplative by nature. Those who know me realize how true that statement is.

Yet, at this past weekend’s conference in Louisville, Kentucky entitled The Fruitful Garden, an inspiring group of Classical educators caused me mightily to wish that I could be more contemplative in my life.

Whenever I hear talks by certain of my colleagues (as an example, Martin Cothran), I want to suit up and hit the battlefield, charging ahead with the mission of renewing the magnificent standards that once characterized education in this country.

But when my ear absorbs talks by other colleagues—Christopher Perrin and Andrew Kern spring to mind—my normally wound-up self slows. My forward motion rests and I want to reflect. That feeling is fabulous.

So believe it or not, Saturday night, after the close of the conference, I found myself perusing the text of The Elements, Euclid’s classic work on geometry and mathematics. Written around 300 B.C. it overflows with the freshness of ideas formulated yesterday.

But why would I be consulting Euclid, you ask? Blame that on Andrew Kern who, in his plenary address, referred to Euclid’s first definition:

A point is that which has no part.

These few words, he said, led him to a contemplation that lasted nearly five years. Ultimately, that contemplation brought forth a life-changing revelation. I was intrigued.

Backing up, though, why was Kern talking about geometry? The conference was focused on the seven Liberal Arts: the mastery of grammar, logic, rhetoric (the trivium), followed by the study of arithmetic, geometry, astronomy, and music (the quadrivium). These are the real liberal arts, as opposed to the trendy “subjects” that pass for the Liberal Arts today on many college campuses.

Looking at the opening of The Elements, I scratched my chin and thought, “When, oh when, Carol, has such a sentence brought you to that level of revelation?” The answer is: never or, at least, never from Euclid. To be honest, I doubt I have contemplated any single sentence for five years (unless it be Scriptural).

But driving away from Louisville on Sunday morning, watching the clouds illuminated by the rising sun, something did smack into my thought. It isn’t words I contemplate, but melodies. Melodies, harmonies, rhythms, and the elements of music. But above all, melody.

Melody is our first grammar. We sing before we can speak. Our first melody is our cry at birth. Our dearest melody is our cry for “Mama.” Melody pours from the human heart.

Of all of the melodies I have ever contemplated, the most powerful one comes from Beethoven’s concerto for Violin, Opus 61, written in 1806 during what we call Beethoven’s Middle Period. I have spent decades reflecting upon this work, and particularly a single melody. And yes, it once brought me the same kind of life-changing experience Kern described with Euclid’s first definition.

The experience stemmed not from the beauty of the melody, per se, but rather how Beethoven offers it to us. Despite being sorely tempted to walk you step-by-step through the piece, I’ll save that for another day—perhaps a Friday Performance Pick. Instead, let me say that Beethoven crafted this movement with a subtle, powerful design, overflowing with waves of the expected and unexpected to tantalize his listeners.

At least, it tantalizes his listeners today! But for various reasons, this violin concerto didn’t catch on in 1806. So, rather than waste his considerable effort, he took the score and turned it into a concerto for piano and orchestra.

Today one rarely hears that version. And that’s as it should be. While interesting and beautifully crafted, it doesn’t begin to express the power of the original violin concerto. Nor does it rival his five major piano concerti, even under the fingers of the best pianist.

Still, let me return to the melody I mentioned—this gentle, ravishing, almost heroic theme that for years has permeated my mind. It first appears in the opening statement of the orchestra, and returns next in what we designate as “the second theme” area—a section defined by a change in harmonies. But every time the solo violinist is about to play it throughout the body of the piece, Beethoven snatches it away, giving it to other instruments in the orchestra. The woodwinds or strings embrace it. The soloist is allowed to decorate it. But it is never his own to play.

Finally, after the cadenza—the part of a concerto where the soloist has free reign to improvise—as the movement is about to end, Beethoven delicately drops the melody into the violinist’s fingers. Hushed, yet exuberant, it soars over the gentle punctuations of the orchestra, as if the heavens opened up and God’s grace shined down on a small piece of wood known as a violin.

At least that’s how it sounded the day I finally “got” it. After years of studying this piece, I suddenly was awed by the power of Beethoven’s design. I cognitively and emotionally grasped a higher glory expressed by this final presentation of the theme. My inner ear exploded. My heart was filled with joy.

Euclid’s definitions have exploded the consciousness of seekers since the times of Ancient Greece. Similarly, the masterful control of melodies, harmonies, and rhythms by genial composers like Beethoven cause listeners to gasp in awe. Their musical designs bring wonder. And that wonder invites us into a deeper exploration of music and the Liberal Arts—a timeless, gratifying journey open to all.

Painting: Cifrondi, Euclid (17th Century)