The primary contribution of this paper is the development and presentation of two hidden Markov models (HMM) that can follow a monophonic audio performance in real time and recognize arbitrary repeats/skips and other errors in a performance.

While musicians or sound performers play or rehearse by following an accompanying score playing on a laptop, for example, the need to revise a series of notes or alter the starting point several times typically occurs when practicing or rehearsing. The problem addressed by the authors is the computational cost of managing these necessary interruptions to the score. Even though following or playing a music score on a laptop (score following) is by no means something new, managing arbitrary interruptions in a score is of practical importance.

To address the problem of computational cost and the complexity of altering the score in various and changing locations within the score, the authors have developed two novel HMMs. The first or top model contains an interface that describes arbitrary errors such as skips and repeats and can compute the probability distribution before and after each skip or repeat. The second or bottom model relates to subevents such as sustaining a note or sound, for example.

The second section of the paper provides a clear description of the models that includes the equations and figures that describe the logic. I found the equations difficult, but the figures provided were easy to follow and clarified the logic of the HMMs.

I found this work in progress promising for score following with convenient management of arbitrary errors and exceptional instrumental sounds. If you are interested in mathematical engineering, Markov models, probabilistic models, and sound, you may find this audio-to-score project engaging and well worthwhile. This is a well-written paper that describes complex mathematical solutions that in my opinion may eventually produce worthwhile results.