Does WolframTones use mathematical principles?
In a sense it uses a generalization. Traditional mathematical systems (like arithmetic and geometry) are specific examples in the general universe of formal computational systems. WolframTones uses a broader set, so that in a sense almost every composition is associated with a different possible generalized kind of mathematics. Like traditional mathematics, though, WolframTones is based on using definite abstract systems that have their own “internal logic.” If history had been different, perhaps Pythagoras would have used WolframTones rules instead of mathematics and numbers to describe music.
