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# Music and Math

Hey, I need some help from my fellow head-fiers. I'm doing a math project and I need some insight into the world of audio engineers and the like.

How is math applied/used in audio engineering?

I'm only taking intro computer engineering courses, but my teacher has spoken a lot about how analog is converted to digital, and different methods of doing so.. That is mostly on the computer side of things though, not necessarily audio engineers. If I had to guess, I would think that the audio engineers simply convert analog to digital using methods already created by electrical and software engineers.

Sorry for being vague, it's been a while since he's talked about it..
Amazon.com: Science and Music (9780486619644): Sir James H. Jeans: Books

awesome book. i don't know if that'll get you on the track of where you want to go... i'd like to help. if i may ask, what level of school is this for? if college, what is the scope of the class? you can pm if you want.
Aside from the masses of other applications, Fourier series are often used in harmonic analysis to provide functions for waves using infinite series combined with trigonometry: Fourier series - Wikipedia, the free encyclopedia / 5. Harmonic Analysis

You do need a working understanding of calculus & infinite series, though. But if you have that--and maybe some Taylor series under the hood as well--they can be quite easily understood.

Here's a cool java applet to play around with: Fourier Series Applet

How exactly this is used in engineering audio-related products, I do not know.
Fourier Series :
(a1 cos t + b1 sin t) is the fundamental.

(a2 cos 2t + b2 sin 2t) is the second harmonic.

(a3 cos 3t + b3 sin 3t) is the third harmonic, etc.

The distance between notes is 2^(n/12) hz in the well tempered system where n is the number of semitones (eg. 12 semitones is an octave; therefore frequency is doubled. 2^(2/12) will give you a tone, so if we multiple A 440 by 1.1224etc we get 493.88etc) (which results in an change in duration of a particular recorded clip by the same amount).

Not sure how "math is used in the studio", but math and music sure.

There's also a lot of relation to phi Detailed here a little

If I recall correctly, the climax of most songs occurs at 1/phi (0.61803398874989484820458683436564), but dont quote me on this.
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