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lispbuilder
Lispbuilder provides a range of libraries for developing useful portable Common Lisp applications
I've never actually used it myself. I've preferred systems that talk to SuperCollider, like overtone, because it's already rock solid and has lots of good DSP built in.
Sure! There are Common Lisp bindings to SupperCollider: https://github.com/byulparan/cl-collider which can be used to program music interactively.
I did some audio programming with lisp about 10 years ago. I used SDL and lispbuilder which was a project I was involved with at the time. At this level of programming you are dealing with channels of audio, you can prepare a buffer to play and you modify the outgoing audio in realtime with a callback. I assume this is the level you are interested in? The next level down would be talking directly to the audio drivers or OS level interface to them. Anyway here’s the api code https://github.com/lispbuilder/lispbuilder/blob/master/lispbuilder-sdl/sdl/audio.lisp