Musical harmony being instantiated in melodies is fully explicable through material ratios and proportions, as the Pythagorean-Aristotelian tradition shows, requiring no incorporeal referent.

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Pythagorean-Aristotelian tradition(as used to reference the historical source of the claim about harmony and mathematics): An ancient school of thought blending ideas from Pythagoras (who discovered that music follows mathematical patterns) and Aristotle (who built on these ideas about nature and explanation).
explicable(as used in describing what a theory can or cannot explain): Able to be explained or accounted for by a theory or reason.
incorporeal referent(as used to discuss whether harmony requires something non-physical to exist): A non-physical thing that something refers to or depends on—like saying a melody depends on a non-material soul or abstract form rather than just physical facts.
instantiated(as used in metaphysics and logic): Made real or brought into existence as an actual example; like when a concept becomes a real thing you can observe.

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