How to Infer Repeat Structures in MIDI Performances

MIDI performances are generally expedient in performance research and music information retrieval, and even more so if they can be connected to a score. This connection is usually established by means of alignment, linking either notes or time points between the score and the performance. The first obstacle when trying to establish such an alignment is that a performance realizes one (out of many) structural versions of the score that can plausibly result from instructions such as repeats, variations, and navigation markers like 'dal segno/da capo al coda'. A score needs to be unfolded, that is, its repeats and navigation markers need to be explicitly written out to create a single timeline without jumps matching the performance, before alignment algorithms can be applied. In the curation of large performance corpora this process is carried out manually, as no tools are available to infer the repeat structure of the performance. To ease this process, we develop a method to automatically infer the repeat structure of a MIDI performance, given a symbolically encoded score including repeat and navigation markers. The intuition guiding our design is: 1) local alignment of every contiguous section of the score with a section of a performance containing the same material should receive high alignment gain, whereas local alignment with any other performance section should accrue a low or zero gain. And 2) stitching local alignments together according to a valid structural version of the score should result in an approximate full alignment and correspondingly high global accumulated gain if the structural version corresponds to the performance, and low gain for all other, ill-fitting structural versions.