How does music relate to math?

intervals and wavelengths

The physics of sound has a lot to do with integer ratios and approximation. And the rudiments of music involve a lot of subdividing into two and subdividing into three.

Other than that, the people who make a fuss about music and math being related really want to sound deep and philosophical but don’t know much about what they’re talking about.

Strings and air tubes have harmonic frequencies. That is, when you vibrate them at just the right frequency, you set up standing waves with nodes and anti-nodes in particular places. When a bunch of these harmonic frequencies are played at the same time at different phase angles, we think it sounds pretty.

Pattern recognition! Or something.

There is an essential problem when it comes to music that is mathematical in nature. You want to divide an octave (a frequency doubling, the most basic musical interval) into an equal number of steps (not too few, not too many) that are equally spaced to make things convenient for keyed instruments without the ability to make continuous changes in pitch. On the other hand you want the notes to have some basic frequency ratios that sound pleasing to the ear (minor third: 6/5, major third: 5/4, perfect fifth: 3/2, etc.). These two goals are at fundamental odds with one another. Modern music has chosen the former in this compromise with the chromatic scale being twelve equal divisions of the octave, and hence no intervals other than octaves or multiples of an octave are rational (the perfect fifths are quite close though).

(For any scheme that divides the octave into a number of equal steps the frequency ratio of any given note over its lower immediate neighbor will be the n-th root of two where n is the number of steps. It turns out out can’t build nice ratios of n-th roots of two as they are always irrational.)

I love that song!

Ahh… BoC = Boards of Canada

Not really related to the physics and mathematics of music but I thought that it was interesting the way Tool fit the Fibonacci Sequence into their song Lateralus. Sorry no link, I’m on my iPhone.

So I go over to YouTube and try ‘just intonation’ and this is the first hit. I have to wonder if they are exaggerating the dissonance of the the chords played without their system though (it’s a commercial after all I think) but it provides a good illustration.

there seem to be quite a few books about this on amazon although i don’t know if they’ll word things in a simple way. i’ve never thought about a linkage between the 2. good question

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although conor oberst doesn’t seem to think theyr’e related: and it will be more like a song, and less like it’s mathhhh

intervals and wavelengths, redux

I know it’s recommended that one should play classical music for infants because it helps activate and develop neural connections in the same region of the brain which are most actice when one is engaged in mathamatical problem solving.

One song + one song = Two songs

Then it gets a bit more complicated from there.

To be very precise: equal temperament, see my question

http://www.fluther.com/disc/40336/what-do-earworms-and-the-number-10594630943592952645618252949463417-have-in-common/

Here’s an interesting article on ‘The Correlation Between Music and Math: A Neurobiology Perspective’:

http://serendip.brynmawr.edu/exchange/node/1869

Check out Battles theyre considered a math rock band.

@uberbatman: I got to see them at Bumbershoot last year (or maybe the year before)? They’re very fun to watch do their thing, too.

damn you cyndyh <envy> :P