  Deep learning-based probabilistic models of musical data are producing
increasingly realistic results and promise to enter creative workflows of many
kinds. Yet they have been little-studied in a performance setting, where the
results of user actions typically ought to feel instantaneous. To enable such
study, we designed Notochord, a deep probabilistic model for sequences of
structured events, and trained an instance of it on the Lakh MIDI dataset. Our
probabilistic formulation allows interpretable interventions at a sub-event
level, which enables one model to act as a backbone for diverse interactive
musical functions including steerable generation, harmonization, machine
improvisation, and likelihood-based interfaces. Notochord can generate
polyphonic and multi-track MIDI, and respond to inputs with latency below ten
milliseconds. Training code, model checkpoints and interactive examples are
provided as open source software.
