  This paper discusses real-time alignment of audio signals of music
performance to the corresponding score (a.k.a. score following) which can
handle tempo changes, errors and arbitrary repeats and/or skips (repeats/skips)
in performances. This type of score following is particularly useful in
automatic accompaniment for practices and rehearsals, where errors and
repeats/skips are often made. Simple extensions of the algorithms previously
proposed in the literature are not applicable in these situations for scores of
practical length due to the problem of large computational complexity. To cope
with this problem, we present two hidden Markov models of monophonic
performance with errors and arbitrary repeats/skips, and derive efficient
score-following algorithms with an assumption that the prior probability
distributions of score positions before and after repeats/skips are independent
from each other. We confirmed real-time operation of the algorithms with music
scores of practical length (around 10000 notes) on a modern laptop and their
tracking ability to the input performance within 0.7 s on average after
repeats/skips in clarinet performance data. Further improvements and extension
for polyphonic signals are also discussed.
