I'm a jazz musician--it's interesting stuff, there is a whole area of research dedicated to this type of work.
Jazz chord progressions are pretty simple ultimately when expressed in compressed form, but tend to have actual semantics behind them be pretty communicative so I doubt this will cover absolutely everything except the popular works.
You can generate something very close using a formal grammar but you get stuck in the same position as the logicians in Chomsky's time. I've had some really great thoughts about ML approaches, however, with some sort of seq-to-seq approach.
Here, too, the development is moving away from RNN and LSTM in the direction of Transformers. One of the most promising algorithmic composition projects I recently came across is https://openai.com/blog/musenet/.
Jazz chord progressions are pretty simple ultimately when expressed in compressed form, but tend to have actual semantics behind them be pretty communicative so I doubt this will cover absolutely everything except the popular works.
You can generate something very close using a formal grammar but you get stuck in the same position as the logicians in Chomsky's time. I've had some really great thoughts about ML approaches, however, with some sort of seq-to-seq approach.