Is algebraic sound synthesis possible? [closed]

Question

Lets say you have an normal song with two layers, one instrumental and another of just vocals. Now lets say you also have just the instrumental layer. Is it possible to "subtract" the instrumentals and obtain the pure vocals? Is there going to be loss? How would I go about performing this specific type of subtractive synthesis?

Answer 1

Yes it's possible but yes there can be loss as well since sound waves can additively cancel each other out (destructive interference). For example, two sine waves that are 180 degrees out of phase would produce silence.