A pure quantum musical state would then be made up of a linear combination of the 7 notes with a specific probability associated with each. And a quantum melody would be the evolution of such a state over time.

An audience listening to such a melody would have a bizarre experience. In the classical world, every member of the audience hears the same sequence of notes. But when a quantum musical state is observed, it can collapse into any one of the notes that make it up. The note that is formed is entirely random but the probability that it occurs depends on the precise linear makeup of the state.

this sounds like a greg egan novel.

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