A lot of people claim that music is just math and I don't understand why. Is there any facts behind this claim? It angers me when people make this claim and when I ask them to explain, even when they can't they don't see they are wrong.
[Math] What relation does music have to math
music-theorynumber theory
Related Solutions
It sounds like you really want to read Benson's Music: a Mathematical Offering (freely available at the link). I'm not completely sure what you're asking, but if it's anything like "why is it natural to think about music in terms of sine waves," this question is addressed right in the introduction:
...what's so special about sine waves anyway, that we consider them to be the "pure" sound of a given frequency? Could we take some other periodically varying wave and define it to be the pure sound of this frequency?
The answer to this has to do with the way the human ear works. First, the mathematical property of a pure sine wave that's relevant is that it is the general solution to the second order differential equation for simple harmonic motion. Any object that is subject to a returning force proportional to its displacement from a given location vibrates as a sine wave. The frequency is determined by the constant of proportionality. The basilar membrane inside the cochlea in the ear is elastic, so any given point can be described by this second order differential equation, with a constant of proportionality that depends on the location along the membrane.
The result is that the ear acts as a harmonic analyser [emphasis added]. If an incoming sound can be represented as a sum of certain sine waves, then the corresponding points on the basilar membrane will vibrate, and that will be translated into a stimulus sent to the brain.
Not a "proof" but a very interesting property that makes the diatonic scale unique. Summarizing from http://andrewduncan.net/cmt/ :
Diatonic scale (and its complementary, pentatonic scale) has the highest "entropy" (in other words, "variety") among all possible 7-note (or 5-note) scales (there are 66 of them). Therefore, the diatonic scale is the most rich in content 7-note scale which makes it a fertile ground for melodic ideas.
Neither 5 or 7 have common factors with 12 therefore it's not possible to distribute notes uniformly as it is with 6. Distributing 6 notes gives us the whole-tone scale {C, D, E, F♯, G♯, A♯, C} which is highly regular, has no tonality and creates a blurred, indistinct effect and thus, not very "useful".
Best Answer
There are many mathematical aspects of music, but there also many non-mathematical aspects that are inherently cultural.
As an example of a "math aspect", take a look at harmonics: we like hearing sounds that produce the "same" frequencies, and these are just integer multiples of the basic frequency that is being played. Another example would be that of equal temperament, which creates a semi-optimal distance between notes, such that the possible harmonies are maximized.
That being said, the actual number of tones in an octave as well as the choice of scale are completely culture dependent - Western ears are used to 12 tone octaves and certain scales but not others, in what seems to be a rather arbitrary choice. So I think it's fair to say that music is definitely not "just math" - it's very strongly tied to the culture we were brought up in rather than to some mathematical formula.