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.