I've thought a lot about this. It's a very interesting problem to construct a musical Turing test because music is such a relative and personal thing. The "best" works of all time are meaningless to someone with no relationship to the piece, the composer, or the time period. And the spectrum of material is very wide. You can have composers use all kinds of algorithms and methods as "composition tools" [1] to produce works that sound very algorithmic and repetitive to the unfamiliar [2] or seemingly random [3] all the way to the theorized "machine composer" that can also produce seemingly organic music or obviously algorithmic music. Which is more genuine: the algorithmic composition made by a human or the one by a machine/program? What if they use the same algorithmic tools?

Before one constructs a musical Turing test of music from machines vs humans, I'd like to see a test first about if people can discern whether algorithmic or formulaic composition techniques were used in a (human composed) piece or whether it was all "organic" (I don't even know how to define that musically, composition is rarely a purely inspirational and complete endeavor. It's lots of editing, transformations, permutations, cut/paste, selective "not caring" in some spots). I think the answer to that question is a more insightful place to start as I think the general public isn't aware of how many formulas and algorithms (conscious and subconscious) composers actually use to construct their music.

[1] https://en.wikipedia.org/wiki/Schillinger_System (interesting side note: Glenn Miller used the rhythmic tools of the Schillinger System to construct the catchy rhythm component and form of this little diddy you might have heard https://www.youtube.com/watch?v=xPXwkWVEIIw)

[2] https://en.wikipedia.org/wiki/John_Adams_%28composer%29

[3] https://en.wikipedia.org/wiki/Arnold_Schoenberg