We address the problem of combining sequence models of symbolic music with user defined constraints. For typical models this is non-trivial as only the conditional distribution of each symbol given the earlier symbols is available, while the constraints correspond to arbitrary times. Previously this has been addressed by assuming a discrete time model of fixed rhythm. We generalise to continuous time and arbitrary rhythm by introducing a simple, novel, and efficient particle filter scheme, applicable to general continuous time point processes. Extensive experimental evaluations demonstrate that in comparison with a more traditional beam search baseline, the particle filter exhibits superior statistical properties and yields more agreeable results in an extensive human listening test experiment.
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