Music and mathematics: how are they related?

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my main question: is there some mathematical formula that leads to a great song? be it a beat, melody, etc. what is the mathematical difference between dissonance and connosance? we know that listening to classical music at a young age results in high math scores. but why?
i have listened to compositions by such artists as daniel cummerow.(those who applied mathematical algorithms to making music). and i can say without a doubt that none of these artists will be on the top hits anytime soon. so what mathematical formula creates a great song? what makes a melody catchy?
 
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Pythagorean
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my main question: is there some mathematical formula that leads to a great song?
no, there's musical theory which is a set of "rules" that lead to palatable music.

be it a beat, melody, etc. what is the mathematical difference between dissonance and connosance?
A good metric of dissonance and consonance is the distance between the notes involved. The closer they are, the more dissonant. But this isn't an absolute rule. Mainly, the notes need to be integer fractions of each other to be more "connonant". (Google the harmonic series in terms of music).

Examples of consonant combinations are the unison, the octave, the fifth. See how they place in the harmonic series (for instance, an octave is twice the frequency of the fundamental).

we know that listening to classical music at a young age results in high math scores. but why?
I'm pretty sure there's no significant correlation. It may just be a marketing technique for the Baby Mozart people, or correlates found may have just come from the fact that more intelligent people listen to classical music and also happen to pass intelligence genes to their kids.

I play instruments for my baby to show her cause n' effect, but it's interactive (I let her play with the instruments as best she can).

so what mathematical formula creates a great song? what makes a melody catchy?
The most popular set of chords in Western music is the I-IV-V. This is likely because of their integer relationship in frequency. (Also, I is to IV as V is to I so there's a hierarchy there).

Some examples of I-IV-V are:

A, D, E
E, A, B
G, C, D
C, F, G
 
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http://www.maths.abdn.ac.uk/~bensondj/html/music.pdf

If math is what you want, don't say you didn't ask for it.:smile:

It has much theory on symmetries and consonance as well as general signals and waves.
wow, that is music as only an electrical engineer could love it. kudos.

and that circle of fifths stuff is familiar. i ran into it while googling after seeing the http://boingboing.net/2009/08/01/bobby-mcferrin-hacks.html" [Broken]. the idea i found was that the structure of the cochlea itself has something to do with it, but i got a little lazy about it when confronted with checking the math.
 
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