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This paper targets the perceptual task of separating the differentinteracting voices, i.e., monophonic melodic streams, in a polyphonic musicalpiece. We target symbolic music, where notes are explicitly encoded, and modelthis task as a Multi-Trajectory Tracking (MTT) problem from discreteobservations, i.e., notes in a pitch-time space. Our approach builds a graphfrom a musical piece, by creating one node for every note, and separates themelodic trajectories by predicting a link between two notes if they areconsecutive in the same voice/stream. This kind of local, greedy prediction ismade possible by node embeddings created by a heterogeneous graph neuralnetwork that can capture inter- and intra-trajectory information. Furthermore,we propose a new regularization loss that encourages the output to respect theMTT premise of at most one incoming and one outgoing link for every node,favouring monophonic (voice) trajectories; this loss function might also beuseful in other general MTT scenarios. Our approach does not usedomain-specific heuristics, is scalable to longer sequences and a higher numberof voices, and can handle complex cases such as voice inversions and overlaps.We reach new state-of-the-art results for the voice separation task inclassical music of different styles.

Musical Voice Separation as Link Prediction: Modeling a Musical Perception Task as a Multi-Trajectory Tracking Problem