Free Republic
Browse · Search
General/Chat
Topics · Post Article

Skip to comments.

Why Does Classical Music Make You Smarter? (The songs are hidden in higher mathematics)
Pajamas Media ^ | 04/24/2013 | David Goldman

Posted on 04/24/2013 10:51:36 AM PDT by SeekAndFind


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.

CLICK ABOVE LINK FOR THE VIDEO

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.

******


TOPICS: Education; Music/Entertainment; Science; Society
KEYWORDS: classicalmusic
Navigation: use the links below to view more comments.
first 1-5051-71 next last

1 posted on 04/24/2013 10:51:36 AM PDT by SeekAndFind
[ Post Reply | Private Reply | View Replies]

To: SeekAndFind; Revolting cat!; Slings and Arrows
What if it's played by Rick Wakeman?


2 posted on 04/24/2013 10:53:24 AM PDT by a fool in paradise (America 2013 - STUCK ON STUPID)
[ Post Reply | Private Reply | To 1 | View Replies]

To: SeekAndFind

Interesting.


3 posted on 04/24/2013 10:54:22 AM PDT by Jane Austen (Boycott the Philadelphia Eagles!)
[ Post Reply | Private Reply | To 1 | View Replies]

To: SeekAndFind

Ahhhhh, Bach!


4 posted on 04/24/2013 10:54:41 AM PDT by dfwgator
[ Post Reply | Private Reply | To 1 | View Replies]

To: SeekAndFind

And, interestingly enough, it is WESTERN Classical Music that is studied.

China has its own Classical Music, but it has a different cadence, a different pattern of rhythm, and different scales than Western Music. The same can be said of Indian Classical Music.

I actually enjoy Eastern music, but in very small doses.

Then it’s Back to Bach for me!


5 posted on 04/24/2013 10:56:23 AM PDT by left that other site ((Ban the ubiquitous and deadly solvent, Di-hydrogen monoxide!!!))
[ Post Reply | Private Reply | To 1 | View Replies]

To: SeekAndFind

Very interesting. I wonder if there’s such thing as a type of music that makes you dumber.


6 posted on 04/24/2013 10:56:42 AM PDT by MNDude (Sorry for typos. Probably written on a smartphone, and I have big clumsy fingers.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: MNDude
I wonder if there’s such thing as a type of music that makes you dumber.

Well I wouldn't exactly call it "music", but I think rap would qualify.

7 posted on 04/24/2013 10:57:47 AM PDT by dfwgator
[ Post Reply | Private Reply | To 6 | View Replies]

To: MNDude

RE: I wonder if there’s such thing as a type of music that makes you dumber.

How about more violent?


8 posted on 04/24/2013 10:58:14 AM PDT by SeekAndFind
[ Post Reply | Private Reply | To 6 | View Replies]

To: dfwgator
Well, THAT'LL get you a girlfriend, Radar ...

/8^)

9 posted on 04/24/2013 10:58:29 AM PDT by knarf (I say things that are true ... I have no proof ... but they're true)
[ Post Reply | Private Reply | To 4 | View Replies]

To: MNDude
I wonder if there’s such thing as a type of music that makes you dumber.

Nonsense! Why, I've listened to metal for years, and I...uh...thingy.

10 posted on 04/24/2013 10:58:38 AM PDT by Billthedrill
[ Post Reply | Private Reply | To 6 | View Replies]

To: SeekAndFind

It’s all about focusing.


11 posted on 04/24/2013 10:59:03 AM PDT by Sacajaweau
[ Post Reply | Private Reply | To 1 | View Replies]

To: knarf

It’ll get you “slaked.”


12 posted on 04/24/2013 10:59:30 AM PDT by dfwgator
[ Post Reply | Private Reply | To 9 | View Replies]

To: Borges; sitetest

ping


13 posted on 04/24/2013 10:59:38 AM PDT by EveningStar ("What color is the sky in your world?" -- Frasier Crane)
[ Post Reply | Private Reply | To 1 | View Replies]

To: MNDude

Hip hop seems to do it.....


14 posted on 04/24/2013 10:59:46 AM PDT by Sacajaweau
[ Post Reply | Private Reply | To 6 | View Replies]

To: MNDude

15 posted on 04/24/2013 11:00:19 AM PDT by stormer
[ Post Reply | Private Reply | To 6 | View Replies]

To: left that other site

16 posted on 04/24/2013 11:04:19 AM PDT by AnAmericanMother (Ministrix of ye Chasse, TTGS Ladies' Auxiliary (recess appointment))
[ Post Reply | Private Reply | To 5 | View Replies]

To: a fool in paradise

Wakeman’s a good keyboard player . . . but the last time I saw him he was nowhere near as good as he used to be. Six Wives was kind of the high point.


17 posted on 04/24/2013 11:06:17 AM PDT by AnAmericanMother (Ministrix of ye Chasse, TTGS Ladies' Auxiliary (recess appointment))
[ Post Reply | Private Reply | To 2 | View Replies]

To: SeekAndFind
Why Does Classical Music Make You Smarter?

It allows you get a better Handel on your studies.

18 posted on 04/24/2013 11:07:42 AM PDT by Ken H
[ Post Reply | Private Reply | To 1 | View Replies]

To: left that other site

Some of the Indian Classical Music out there is purely divine.

It uses similar scales as Western Classical Music, but has a much older history, and often, more complex melodies.


19 posted on 04/24/2013 11:07:42 AM PDT by James C. Bennett (An Australian.)
[ Post Reply | Private Reply | To 5 | View Replies]

To: MNDude
Very interesting. I wonder if there’s such thing as a type of music that makes you dumber.

After four years of careful study I think that the songs that makes you the dumbest are (in order) Hail Columbia and Hail to the Chief.

20 posted on 04/24/2013 11:07:43 AM PDT by KarlInOhio (Choose one: the yellow and black flag of the Tea Party or the white flag of the Republican Party.)
[ Post Reply | Private Reply | To 6 | View Replies]

To: SeekAndFind

>>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. <<

I just saw one in Frys for $35 — I almost bought it.

I played trumpet and still play flute. Playing a musical instrument can be a very relaxing and fun thing to do. If you do play you know what I mean. If not it is almost impossible to explain how good making music makes you feel.


21 posted on 04/24/2013 11:08:19 AM PDT by freedumb2003 (LBJ declared war on poverty and lost. Barack Obama declared war on prosperity and won. /csmusaret)
[ Post Reply | Private Reply | To 1 | View Replies]

To: SeekAndFind
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.

I believe this is factually incorrect. Pythagoras had all sorts of ideas about the relationship between music, the universe and higher thought.

He died around 500 BC, about 1000 years before Augustine.

22 posted on 04/24/2013 11:08:30 AM PDT by Sherman Logan
[ Post Reply | Private Reply | To 1 | View Replies]

To: SeekAndFind
Where the math is really obvious is in the late medieval and early Renaissance music.

DuFay, Ockeghem, and Dunstable seem to have spent most of their spare time squeezing mathematical puzzles into their music.

23 posted on 04/24/2013 11:09:12 AM PDT by AnAmericanMother (Ministrix of ye Chasse, TTGS Ladies' Auxiliary (recess appointment))
[ Post Reply | Private Reply | To 1 | View Replies]

To: dfwgator; stylecouncilor
Ahhhhh, Bach!

Now that's funny.

s, ping....

24 posted on 04/24/2013 11:09:46 AM PDT by onedoug
[ Post Reply | Private Reply | To 4 | View Replies]

To: SeekAndFind

Nice keys.


25 posted on 04/24/2013 11:10:34 AM PDT by grobdriver
[ Post Reply | Private Reply | To 1 | View Replies]

To: James C. Bennett
My daughter studied Indian Classical music in college.

One of their assignments was to go to local concerts. She heard through a friend that a sitar player at one concert announced to his fellow musicians back stage: "There's a little American girl in the front row counting tala!"

26 posted on 04/24/2013 11:13:03 AM PDT by AnAmericanMother (Ministrix of ye Chasse, TTGS Ladies' Auxiliary (recess appointment))
[ Post Reply | Private Reply | To 19 | View Replies]

To: SeekAndFind

Learn the circle of fifths and modulation, the moveable do system for scales and memorize key signatures and you’ve already learned enough to build chords, figure out any scale in any key and if you combine it with the time signatures, learn to read music and you’re almost 90% there.

That doesn’t mean you’ll be Beethoven but it does give you enough to understand why some sounds sound great and some really sound horrible and if you’re really really lucky, you’ll have been born with perfect pitch, if not, you can learn relative pitch so you can tell the difference between the sound of E and F#.

There’s a guy who supposedly has a system to teach anyone perfect pitch, reviews were pretty bad for his system. I had the first tape and it boiled down to listening to different note’s timbres but just listening to different chords and notes will give you plenty of information.


27 posted on 04/24/2013 11:19:49 AM PDT by Lx (Do you like it, do you like it. Scott? I call it Mr. and Mrs. Tennerman chili.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: SeekAndFind

Classical music and math: 1901 Fruitgum Company”

Ev’ry time I try to prove I love you,
1,2,3, Red Light, You stop me,.
Baby you ain’t right to stop me.


28 posted on 04/24/2013 11:20:55 AM PDT by USMCPOP (Father of LCpl. Karl Linn, KIA 1/26/2005 Al Haqlaniyah, Iraq)
[ Post Reply | Private Reply | To 1 | View Replies]

To: left that other site

Is it micro-tonal? Western music has twelve notes to an octave while some eastern music has twenty four or more. It’s really weird to hear if you’re used to Western music.

Playing a sitar is pretty interesting but soon it starts to sound the same. What was that guy’s name, Ravi Shankar??? He used to play for hours; I don’t see how he could stand it.


29 posted on 04/24/2013 11:23:50 AM PDT by Lx (Do you like it, do you like it. Scott? I call it Mr. and Mrs. Tennerman chili.)
[ Post Reply | Private Reply | To 5 | View Replies]

To: AnAmericanMother

Was he still playing with the knives?


30 posted on 04/24/2013 11:24:31 AM PDT by Lx (Do you like it, do you like it. Scott? I call it Mr. and Mrs. Tennerman chili.)
[ Post Reply | Private Reply | To 17 | View Replies]

To: USMCPOP

Very interesting!

I consider myself a musician. I love math. I’ve accomplished a bit of things in my life as far as business and I even played collegiate sports (golf). Out of all the things in my life I only found mystery in math and music.

I constantly push my kids towards math and tell them that “everything can be solved with math”. I likewise would love to push them towards music but do not push them to the level I do with math.

With all that I have done in life music seems to be the most difficult thing I have ever undertaken.


31 posted on 04/24/2013 11:32:27 AM PDT by METARZAN
[ Post Reply | Private Reply | To 28 | View Replies]

To: SeekAndFind

Too much sax and violins for me.


32 posted on 04/24/2013 11:34:31 AM PDT by Walmartian (I'm their leader. Which way did they go?)
[ Post Reply | Private Reply | To 1 | View Replies]

To: MNDude
Very interesting. I wonder if there’s such thing as a type of music that makes you dumber.

Like the tuneless howling of the Imam from a minaret?

33 posted on 04/24/2013 11:41:24 AM PDT by Ice Cube
[ Post Reply | Private Reply | To 6 | View Replies]

To: SeekAndFind
http://www.weeklystandard.com/print/articles/irish-setter-dad_555534.html?page=2

P.J. O'Rourke's response to the old Yale perfessor Amy Chua who wrote "The battle Hymn of the Tiger Mother". Very funny.

OTOH, I find that classical music is a favorite of mine, back to childhood. It does have the power to reach inside you and pull out emotions and a higher thought process.

34 posted on 04/24/2013 11:41:43 AM PDT by texas booster (Join FreeRepublic's Folding@Home team (Team # 36120) Cure Alzheimer's!)
[ Post Reply | Private Reply | To 1 | View Replies]

To: EveningStar; .30Carbine; 1cewolf; 1rudeboy; 31R1O; ADemocratNoMore; afraidfortherepublic; ...

Dear EveningStar,

Thanks for the ping! Very interesting article!

Classical Music Ping List ping!

If you want on or off this list, let me know via FR e-mail.

Thanks,

sitetest


35 posted on 04/24/2013 11:43:36 AM PDT by sitetest (If Roe is not overturned, no unborn child will ever be protected in law.)
[ Post Reply | Private Reply | To 13 | View Replies]

To: Ice Cube
Like the tuneless howling of the Imam from a minaret?

That would be Kor-rap music.

36 posted on 04/24/2013 11:44:12 AM PDT by N. Theknow (Kennedys=Can't drive, can't ski, can't fly, can't skipper a boat, but they know what's best for you.)
[ Post Reply | Private Reply | To 33 | View Replies]

To: SeekAndFind

The horses appear to appreciate it . . . and I’m constantly battling with people who think horses should listen to country/western.


37 posted on 04/24/2013 11:45:58 AM PDT by 1rudeboy
[ Post Reply | Private Reply | To 1 | View Replies]

To: SeekAndFind

38 posted on 04/24/2013 11:47:30 AM PDT by Pharmboy (Democrats lie because they must.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: SeekAndFind

She has lovely but small...hands.

39 posted on 04/24/2013 11:51:08 AM PDT by Pharmboy (Democrats lie because they must.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: a fool in paradise

Well, then Telemann about it!


40 posted on 04/24/2013 11:51:36 AM PDT by Revolting cat! (Bad things are wrong! Ice cream is delicious!)
[ Post Reply | Private Reply | To 2 | View Replies]

To: Pharmboy
She has lovely but small...hands

All Chinese... hands look the same.

41 posted on 04/24/2013 11:52:35 AM PDT by Revolting cat! (Bad things are wrong! Ice cream is delicious!)
[ Post Reply | Private Reply | To 39 | View Replies]

To: SeekAndFind

East..if you’re listening to classical music, then you obviously can’t be listening to rap, or hard rock..or whatever garbage is out there.


42 posted on 04/24/2013 11:52:47 AM PDT by ken5050 (My tagline has mysteriously vanished...)
[ Post Reply | Private Reply | To 8 | View Replies]

To: MNDude

Ghetto rap.


43 posted on 04/24/2013 11:55:05 AM PDT by stephenjohnbanker
[ Post Reply | Private Reply | To 6 | View Replies]

To: MNDude

“Progressive” rock.


44 posted on 04/24/2013 11:55:45 AM PDT by Revolting cat! (Bad things are wrong! Ice cream is delicious!)
[ Post Reply | Private Reply | To 6 | View Replies]

To: Sherman Logan

You’re right in a way. It was not necessarily Pythagoras, but one of the thinkers “of the school of Puthagoras”—that is, people he hung with, colleagues and students—who were considering these issues around 500 BC. Lacking any concept of science as we understand it, they looked for patterns in the observable world as a guide to the principles by which the universe was made. They observed the way a harp strong produces sound as its length is divided, and from there extrapolated our ability to perceive the resultant tones to a general perception of beauty. But this is a far cry from the higher math developed by Liebnitz and Newton and their successors.


45 posted on 04/24/2013 11:56:08 AM PDT by ottbmare (The OTTB Mare--now a Marine Mom)
[ Post Reply | Private Reply | To 22 | View Replies]

To: freedumb2003
If you do play you know what I mean. If not it is almost impossible to explain how good making music makes you feel.

Agreed. I've been playing guitar for well over 50 years. I have a great collection, newest being a Gibson Hummingbird.

Whenever crap starts bothering me beyond my ability, I just pick one up and play....always helps me to clear my mind.

FMCDH(BITS)

46 posted on 04/24/2013 11:56:48 AM PDT by nothingnew (I fear for my Republic due to marxist influence in our government. Open eyes/see)
[ Post Reply | Private Reply | To 21 | View Replies]

To: Ken H

” Why Does Classical Music Make You Smarter?

It allows you get a better Handel on your studies. “

And Chopin wood makes you stronger....


47 posted on 04/24/2013 11:57:02 AM PDT by stephenjohnbanker
[ Post Reply | Private Reply | To 18 | View Replies]

To: stephenjohnbanker

You gotta stop Haydn yer feelings.


48 posted on 04/24/2013 12:00:57 PM PDT by Billthedrill
[ Post Reply | Private Reply | To 47 | View Replies]

To: MNDude

‘a type of music that makes you dumber’ - how about really bad worship music?


49 posted on 04/24/2013 12:02:05 PM PDT by bboop (does not suffer fools gladly)
[ Post Reply | Private Reply | To 6 | View Replies]

To: Billthedrill
Nonsense! Why, I've listened to metal for years, and I...uh...thingy. Makes me think of "The Houseplant Song" by Jars of Clay. "if it's syncopated rhythm your soul is gonna rot........."
50 posted on 04/24/2013 12:02:07 PM PDT by showme_the_Glory (ILLEGAL: prohibited by law. ALIEN: Owing political allegiance to another country or government)
[ Post Reply | Private Reply | To 10 | View Replies]


Navigation: use the links below to view more comments.
first 1-5051-71 next last

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.

Free Republic
Browse · Search
General/Chat
Topics · Post Article

FreeRepublic, LLC, PO BOX 9771, FRESNO, CA 93794
FreeRepublic.com is powered by software copyright 2000-2008 John Robinson