Unfortunately the math involved with music doesn't really help us enjoy it any more.

Pythagoras discovered that if you stop a string to half it's length it will sound it's octave, and if you stop it to a third of it's length it will sound a fifth.

But we usually use the equally tempered scale which is slightly different. It is a convenient piece of mechanical jiggery pokery that allows us to play in different keys on the same instrument.The mathematics is fairly simple. Again if you stop the string to half it's length you will get the octave.

But this time instead of dividing the string into it's natural musical divisions we divide it in such a manner that the ratio between the lengths of one fret and the next is the same. Now by didving the string into twelve steps this way we need to look for a number which multiplied by itself twelve times will give twice the length. The number that does this is the twelfth root of two. Now the fifth is about 1.33484 which is just a little over a third. This is what makes some notes and chords sound a little off.