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Why Does Classical Music Make You Smarter?

It can take years to learn to hear the song hidden in higher mathematics.

by
David P. Goldman

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April 23, 2013 - 9:10 am


Thirty-six million Chinese kids now study classical piano, not counting string and woodwind players. Chinese parents pay for music lessons not because they expect their offspring to earn a living at the keyboard, but because they believe it will make them smarter at their studies. Are they right? And if so, why?

The intertwined histories of music and mathematics offer a clue. The same faculty of the mind we evoke playfully in music, we put to work analytically in higher mathematics. By higher mathematics, I mean calculus and beyond. Only a tenth of American high school students study calculus, and a considerably smaller fraction really learn the subject. There is quite a difference between learning the rules of Euclidean geometry and the solution of algebraic equations: the notion that the terms of a convergent infinite series sum up to a finite number requires a different kind of thinking than elementary mathematics. The same kind of thinking applies to playing classical music. Don’t look for a mathematical formula to make sense of music: what higher mathematics and classical music have in common is not an algorithm, but a similar demand on the mind. Don’t expect the brain scientists to show just how the neurons flicker any time soon. The best music evokes paradoxes still at the frontiers of mathematics.

In an essay for First Things titled “The Divine Music of Mathematics,” just released from behind the pay wall, I show that the first intimation of higher-order numbers in mathematics in Western thought comes from St. Augustine’s 5th-century treatise on music. Our ability to perceive complex and altered rhythms in poetry and music, the Church father argued, requires “numbers of the intellect” which stand above the ordinary numbers of perception. A red thread connects Augustine’s concept with the discovery of irrational numbers in the 15th century and the invention of calculus in the 17th century. The common thread is the mind’s engagement with the paradox of the infinite. The mathematical issues raised by Augustine and debated through the Renaissance and the 17th-century scientific revolution remain unsolved in some key respects.

The material is inherently difficult, although it’s possible to find simple illustrations of what Augustine means by higher-order number. As I wrote in the First Things piece:

Augustine asserts that some faculty in our minds makes it possible to hear rhythms on a higher order than sense perception or simple memory, through “judgment.” What he meant quite specifically, I think, is the faculty that allows us to hear two fourteeners in the opening of Coleridge’s epic:

It is an ancient Mariner,
And he stoppeth one of three.
“By thy long grey beard and glittering eye,
Now wherefore stopp’st thou me?”

Read by a computer’s text-to-voice program, this will not sound like what Coleridge had in mind. A reader conversant with English poetry intuitively recognizes the two syllables “And he” as a replacement for the expected first syllable in the first iamb of the second line. The reader will pronounce the first three syllables, “And he stoppeth” with equal stress, rather like a three-syllable spondee, or a hemiola (three in place of two) in music. Our “numbers of memory” tell us to expect ballad meter and to reinterpret extra syllables as an expansion of the one expected. The spondees in the second fourteener, moreover, grind against the expected forward motion, emulating the Mariner’s detention of the wedding guest.

Something more than sense perception and logic is required to scan the verse correctly, and that is what Augustine calls “consideration.” As I observed in “Sacred Music, Sacred Time” (November 2009),De Musica employs poetic meter as a laboratory for Augustine’s analysis of time as memory and expectation, and his approach remains robust in the context of modern analysis of metrical complexity in classical music. To perceive the plasticity of musical time in the works of the great Western composers, to be sure, requires a trained ear guided by an educated mind, but the metrical complexity of a Brahms symphony depends on the same faculty of mind we need to hear Coleridge correctly.

It takes years of study, to be sure, to hear the metrical plasticity in Brahms, or to make sense of higher mathematics. But that’s the whole point: The painstaking acquisition of knowledge and technique, and the enhancement of attention span and intuition, are the long-term benefits of classical music study. Humility, patience, and discipline are the virtues that children acquire through long-term commitment. I doubt that blasting your baby with Mozart will do much good. It takes a lot of learning to hear what Mozart is doing, especially because we have lost so much of the musical culture that Mozart took for granted in his audience.

Most important is the spiritual dimension of classical music: it embodies a teleology. Classical music is a journey to a goal, full of suspense and surprises, but always with a purpose. It is no coincidence that the classical style of Western composition was developed for religious music.

Never before in human history has music been so accessible. A touch-sensitive electric piano with sounds sampled from good acoustic instruments, suitable for a beginning pupil, costs about as much as a video game station. If you want to make your kids smarter, throw out the video games and get them music lessons. Get them involved in youth orchestras where available. Make them sweat. One day they will thank you for it.

******

images courtesy  Stuart Monk /  Nadasazh / Jack.Q / Shutterstock.com

Cross-Posted from Spengler’s Blog

David P. Goldman is the columnist “Spengler” for Asia Times Online; his latest book is How Civilizations Die: (And Why Islam Is Dying Too). He is the Wax Family Fellow at the Middle East Forum.

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Top Rated Comments   
Nonsense.

Just as a skilled carpenter can apply geometry with utmost skill but falter in the geometry classroom, the mathematician may excel at academic geometry but falter on the construction site. Both are exercising the same concepts – challenging concepts – but just in different ways.

immanurl Goldstein has a valid point, there is no reason for classical music to be held as somehow more-refined than that of other genres. (The lives of many of the composers would put modern rock stars to shame, for example.) Fixed-time vs. fluid time? Sounds like you are not that familiar with modern jazz, but I wouldn’t limit it to that – the song that came to my mind was the Allman Brothers’ “Whipping Post.” The song has three-different time signatures in a period of four minutes; I wouldn’t call that fixed.

For that matter, I have seen firsthand classically trained musicians falter at the prospect of playing jazz, swing, and bee-bop. The simple fact is that the subject in question here should not be classical music but music in general. Now, I’m not excusing those who go to concerts and shout “F_ck Yeah!” and get plastered, but I am saying that entire genres should not necessarily be written off because of their audiences. (If you must dismiss a genre, do so on the amount of effort – or lack thereof - that went into its creation.) The role of music we are discussing is its ability to influence intelligence through its requirement of serious dedication and effort to practice it. Any music that requires an equal amount of attention as, say, the first chair violin of Beethoven’s fifth symphony – be it the vocal eccentricities of Billie Holiday, the guitar stylings of Stevie Ray Vaughan, or the piano playing of Floyd Kramer – must be held in the same high regard.
1 year ago
1 year ago Link To Comment
When I go to the symphony, I enjoy the fact that the audience is focused. They are paying absolute attention.

When I go to a rock concert, the crowd is screaming and droning, "F*ck, yeah!" DURING the music, they're stumbling out through the aisles (again: DURING the music) to go get beer, etc.

At the symphony, you don't even applaud between movements. You sit there and quietly wait for the next movement.

Focus. It's all about focus. That's what's needed for everything that gets you highly-scored on an intelligence test.
1 year ago
1 year ago Link To Comment
All Comments   (34)
All Comments   (34)
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1 year ago
1 year ago Link To Comment
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1 year ago
1 year ago Link To Comment
Great post. One microscopic thing:
>A red thread connects Augustine’s concept with the discovery of irrational numbers in the 15th century
Actually, Greeks in the Pythagorean cult were most likely the first to discover irrational numbers, which they called "incommensurable" numbers. This discovery, of course, scandalized them.
1 year ago
1 year ago Link To Comment
"One and one is two..."
1 year ago
1 year ago Link To Comment
Thank you for highlighting your article published in First Things. I felt like I'd just been worked through a grad seminar, without preparing for it. That "prepare a feast, and invite strangers off the street" kind of feeling. Thank you. I want to print it out, check out the music, and read the books you referenced, so I can understand what you just wrote.

Thank you for inviting us to your feast.
1 year ago
1 year ago Link To Comment
I'm leaning toward the cultivation of a good work ethic as the true link between music study and subsequent endeavors. Also, music, science, and the language of science, math, all have to do with patterns. In science, we disentangle and discover the patterns. In music we create the patterns. Sure, music will help adapt the mind to detecting patterns.
1 year ago
1 year ago Link To Comment
You've been riding this hobbyhorse for a while; time to get off. Chinese success has little to do with music, and everything to do with the social limitations, Confucian tradition, the narrow track available for social advancement, and the parental push made especially acute by the one-child policy. Widespread musical study --whatever its arguable benefits-- is an effect, not a cause, and owes as much to the drive for consumer spending as it does to the drive for success.
1 year ago
1 year ago Link To Comment
seconded
i'm tired of this "china envy"
most of these kids would be incapable of playing an instrument without the sheet music in front of them
skilled mimicry with a profound work ethic centered around pleasing the nearest authority figure imho
1 year ago
1 year ago Link To Comment
No. It doesn't "make" you smarter. Sorry, all you numbskulls out there. Rather, smart people -- people who read, people who ponder, people who pursue art -- are attracted to classical music. Lesser minds are attracted to, uh, just off the top of my head, Beyonce, or that half-wit spouse of hers, or WHATever. Little minds love that sort of crap. Me? I love Rachmaninov -- his symphonies, his preludes, his dances, his concertos. And I love the Dandy Warhols! What can I say, those guys rock. Check out Horse Pills. Kick it. But anyway ... What's the question?
1 year ago
1 year ago Link To Comment
I shared a cabin at music camp with three trombonists. There is something about wind instruments that counteracts the beneficial effects of music study---perhaps brain damage due to hypoxia. All the trombonists, oboists and French hornists I've met had the symptoms.
1 year ago
1 year ago Link To Comment
Hey! I resemble that remark! Should I hit the "abuse" button? :)

Or take it seriously?

Let's try the latter:

If I understand correctly, what you're saying is that bone players, oboists, and French horn players, considered as species, don't show the signs of increased intelligence that you're touting as the result of musical study.

I'm skeptical that musical study makes anyone more intelligent. But let's assume for the sake of argument that it does.

This being the case, most trombonists and horn players hardly ever see sixteenth notes or sophisticated melodic passages until they're at the college level. Band-music composers labor under the conviction that neither trombone players nor horn players at the high school level can play anything more sophisticated than ooom-pahs or offbeats. Same is true of tuba players. There are precious few musical solos in the concert band literature for trombone and French horn. When finally immersed in orchestral literature, French horn players have found something to live for. But (if musical quality of life is defined as having solos) trombonists still get short shrift. Most composers put trombonists behind a glass that says, "Break in case of bombastic necessity". Then we get to play soli passages at fortissimo volume. Soli is close to solo, but it's not the same.

But concert band literature has already done most of the damage in high and junior high school. Clarinets and flutes and trumpers and saxes are all over the place, note-wise, while trombones, French horns, and tubas are treated like red-headed stepchildren. For years, I've been saying that if you're a lower-brass player, you get about half of the quality of a music education that the reeds and trumpets get. Now, I think it may not even be that good.

Music educators must agree with you that the students on lower-brass instruments are dumber.

I don't know why oboe is on your list. Oboists are not dull-witted. They just live in a little solipsistic universe that presumes all music is nothing but a prelude to an oboe solo. They know their own parts very well but hardly ever listen to the whole piece. ;)
1 year ago
1 year ago Link To Comment
The author says "the first intimation of higher-order numbers in mathematics in Western thought comes from St. Augustine’s 5th-century treatise on music." That is not so. Long before St. Augustine, Pythagoras elaborated the connection between music and higher mathematics.
1 year ago
1 year ago Link To Comment
Pythagoras knew about the harmonic series. That is elementary mathematics. The idea of a igher order of number is stated clearly in Augustine, and takes us to Leibniz' calculus and Cantor's transfinites. Read the linked essay fro First Things.
1 year ago
1 year ago Link To Comment
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