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.