Mathematics and harmony

 

In Wednesday’s post I said I was surprised to find that I hadn’t shared Dryden’s “Song for St. Cecilia’s Day” before. I’ve just come across a post I started writing early last summer and never posted, and I mentioned the poem there. It’s only a fragment, and I don’t remember where I’d planned to go with the post, but I’m going to share it anyway.

 

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My friend Esther and I have been reading the classic Introduction to Arithmetic by Nicomachus of Gerasa, who lived about a century after Christ. In the last chapter of the book he discusses the relationship between numbers which he calls, following Pythagoras, Plato, and Aristotle, the harmonic proportion.

Harmony is a three dimensional number and “is most useful for all progress in music and in the theory of the nature of the universe.”

The ancient philosophers, and the medievals after them, believed that the motion of the cosmos was musical in nature.

In his discussion, he uses the word “diapason,” which I learned from John Dryden’s poem, “A Song for St. Cecilia’s Day, 1687.” Here is the first stanza:

From harmony, from Heav’nly harmony

               This universal frame began.

       When Nature underneath a heap

               Of jarring atoms lay,

       And could not heave her head,

The tuneful voice was heard from high,

               Arise ye more than dead.

Then cold, and hot, and moist, and dry,

       In order to their stations leap,

               And music’s pow’r obey.

From harmony, from Heav’nly harmony

               This universal frame began:

               From harmony to harmony

Through all the compass of the notes it ran,

       The diapason closing full in man.

 

In C.S. Lewis’s creation myth in The Magician’s Nephew, Aslan sings Narnia into existence. J.R.R. Tolkien’s creation myth in The Silmarillion is part of this tradition, too: Eru Iluvatar’s creates the Ainur from his own thoughts, and their songs after Iluvitar’s pattern bring everything else into existence.

Lewis’s version, being written for children, is the simpler, more straightforward one—everything in Narnia is made by Aslan. But Tolkien’s is an image not only of God the creator, but of Man, made in his image, acting as sub-creator, following the pattern of order, harmony, beauty.

From Harmony this universal frame began*

Boethius playing the monochord
Anonymous,
Cambridge, University Library
Public Domain
Link

“Pythagoras and his followers devoted a great deal of attention to acoustical and musical phenomena. They regarded consonances—especially of a fourth, fifth, and octave—as models of that harmony, conceived of as an accord or equilibrium of different elements, which they equated with the human soul or with the ordering principle of the universe. The assignment of the numerical ratios that are at the basis of musical concordances was for the Pythagoreans the starting point for discovering the laws which governed both the feelings of the soul and the movements of the universe. They arrived at these results experimentally, through the monochord, whose invention was attributed to Pythagoras himself.”

 ~Music in Greek and Roman Culture, by Giovanni Comotti (tr. Rosaria V. Munson)

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*I just realized I’ve never shared John Dryden’s “Song for St. Cecilia’s Day” here, which is a horrible oversight. Do read it—it’s so beautiful and fairly sums up the medieval understanding of how the order of the entire cosmos is a musical relationship.

Sorry about the unexpected hiatus

Violin Daughter had her senior recital last weekend, so my Minnesota daughter flew in at the beginning of last week, then my mom flew at the end of the week, then Minnesota daughter flew back home at the beginning of this week and my mom flies back tomorrow afternoon. So, no blog post this week, either.

As a consolation, here are a couple of recordings from the recital. This first one is the Meditation from the opera Thaïs by Jules Massenet, accompanied by her former music teacher.

This next one is the 4th movement from JS Bach's Partita in D minor. When we were discussing whether to hold her recital in the parish house where there is a grand piano (she also played two piano pieces, a Rachmaninoff and a Debussy) or the sanctuary of our 250 year old church building, she said she needed the acoustics of the sanctuary, "Because that Bach piece is LIT."

Out of the mouths of babes

Once when my sister, Anne Marie, was two or three years old, we were out driving when a particularly low quality song came on the radio. When it was over, she remarked, “That song isn’t real. Somebody just made it up.”

Naturally I DID NOT LAUGH when she said it, even though I laugh every time I remember or retell it.

But I have remembered it and retold it regularly, not just because it was funny, but because I think there’s real truth in there.

I was reminded of it again this morning while reading Stratford Caldecott’s Beauty for Truth’s Sake. In his chapter on music he quotes the English composer John Tavener, who says that, “all music already exists. When God created the world he created everything. It’s up to us as artists to find the music.”

He goes on to say:

Music just is. It exists. If you have ears to hear, you’ll hear it! . . . I believe we are incarnated in the image of God in this world in order for us to re-find that heavenly celestial music from which we have been seperated. Our whole life is a continuing return to the “source.”

(p. 96)