One of the function of the brain is to predict the future. Neurons and brain systems are rewarded for correct predictions and punished for incorrect ones.

The main theory of the paper was that music is pleasant because it's repetitive nature and simple patterns makes it easy for the brain to predict, thus there is a lot of reward to extract from it. They focused on modern trance music and ethnic african drumming, both which feature very long very repetitive sequences, which reward the brain so much that they can induce a trance like state.

Not any random combination of physical objects is a musical instrument (yes, avantgarde music exists, ...) The sax is built the way it is because it generates a sound spectrum with harmonic relations between the frequencies (integer ratios, ...). Those who originally built the sax didn't use math to design it, but it so happens that the result respects certain mathematical ratios, because those ratios are highly predictable and pleasant to the brain.