To a certain extent, this depends on how precisely you define "meaningful". On one extreme, we can consider properties of music that are derived from pure mathematics and physics. A vibrating string will have a waveform composed of a base frequency and its harmonics (to varying degrees). Other waveforms will interfere with this either constructively or destructively.
* Frequencies that interfere constructively include such things as the octave, the major third, and the major fifth. Merging these with the original signal would result in a wave similar to the original, but with certain components amplified.
* A set of frequencies that interfere perfectly destructively would cancel out the original signal, resulting in silence.
* A large set of randomly selected frequencies would mostly cancel each other out, but there would in practice always be some components that don't cancel. The result would be noise, both in the colloquial sense and the information theoretic sense. It's a signal that doesn't contain much meaningful information.
When we then consider that hearing wouldn't evolve for no reason, it stands to reason that any species that does evolve hearing would likely be wired to pay attention to high-information signals. The only one of those three options above that has high information content is the one that we would consider to be harmonious. 350
(There do of course exist more possibilities than just those three, but given a set of signals with the same number of component waves each, there's something of a spectrum, with harmonious signals on one extreme and noise on the other.)
But all that is just operating at the level of individual chords, or possibly separate notes that are close together in time. What of the overall structure of a piece of music? Information theory can still be used to distinguish a series of sounds that were generated by an intelligence from one that is randomly generated or naturally generated; a random signal would contain almost no regular patterns, and thus would be incompressible. A natural signal might contain patterns, but they would (usually) be very simple. A composition might thus be detected by finding patterns that have high information content. (Of course, there would be signals other than music that fit that criteria: language, for instance. But it's a start.)
But would we agree with an alien culture on what constitutes good music? That's the point where things become more culturally dependent; there may be pieces that are brilliant to one culture and garbage to another. This doesn't even require aliens to be true; there's plenty of human music for which the quality is highly subjective. I don't care for <PERSON>'s 4'33", for instance. And yet it's been played at least once by every intelligent culture in the universe. 350