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.

The Ballad of the White Horse

For many years in our home school I read G.K. Chesterton's poem "The Ballad of the White Horse" to my kids during the month of October. This is the story of Alfred the Great's struggle against the pagan invaders in the late 800s. I chose this month for our annual reading because Alfred's feast day is the 26th of October.

After all my kids graduated, I missed the annual read-aloud, so a couple of years ago I hosted a series of Zoom calls and read the poem aloud to whoever showed up. Before each reading I gave a little bit of historical or literary context to aid the understanding of my listeners.

Each book takes around fifteen minutes to read aloud, so it's perfect for Morning Time. I usually started reading early in the month and read two or three books a week so we'd finish ahead of the feast day, but some years we didn't manage to start till later in the month. It's all good -- just DO read (or listen to) this wonderful tale!

Here's the whole playlist.

Check out my "Alfred the Great" tag for more posts on the history of Alfred, excerpts from the poem, suggestions for keeping the Church's liturgical calendar, and ideas for related things to add to your Morning Time.