A system for musical accompaniment is presented in which a computer-driven orchestra follows and learns from a soloist in a concerto-like setting. The system is decomposed into three modules: the first computes a real-time score match using a hidden Markov model; the second generates the output audio by phase-vocoding a preexisting audio recording; the third provides a link between these two, by predicting future timing evolution using a Kalman filter-like model. Several examples are presented showing the system in action in diverse musical settings. Connections with machine learning are highlighted, showing current weaknesses and new possible directions.