Stochastic Modeling of Rhythm Patterns

We assume that a sequence of note values appear in music with certain probability, which can be approximated by an $n$-gram probability, i.e., a conditional probability $P(q_t\vert q_{t-1},\cdots,q_{t-n+1})$ dependent on the history of previous $n-1$ note values. Similar to the $n$-gram language model often used in speech recognition, the probability of rhythm $Q=\{q_1,\cdots,q_N\}$ is approximated by

$$P(Q) \approx P(q_1,\cdots,q_{n-1})\prod_{t=n}^N P(q_t\vert q_{t-1},\cdots,q_{t-n+1})$$ (2)

Conditional probabilities can be obtained through statistical training using already composed music scores.