A positive, very enriching example of carrying on can be heard in the duet recording of improvisations by Matt Turner (cello) and Greg Pagel (piano), The Sweet Volcano (Icker 001).
The two artists show in exemplary fashion how the improvisation-new music nexus can be arced together in a welding of white-hot creativity. This set of music is not avant jazz exactly, nor is it avant classical, but something in between.
The flow of musical ideas is continual and the technical assuredness of the player-instant-composers is such that there is a near one-to-one idea to execution ratio, all in real time.
That, at least, is the impression I get after having listened to the disk in depth. Turner soars, Pagel broods and asserts, and it comes across with exceptional success.
If you might imagine some of the titan composers of yesterday in the throes of spontaneous improvisatory musical speech, some of it might have sounded something like this--except of course no doubt not so modern. This is how the music impresses me.
Now if they could do this with an exceptional drummer-percussionist and perhaps an equally limber and idea-generating bassist, that would be something! It already is something, however. If you like categories creatively colliding in your listening here is an excellent example. I look forward to more of it!