One of the young people with whom I work has been improvising since he began lessons at 7. To get him right into the heart of the matter we start each lesson with improvisation. This has caused me to pay attention in new ways.
The composer whose works for piano are most clearly evoked by these improvisations is Beethoven--not that his improv sounds the least like Beethoven's music on the surface of things, but the impulse to move within a field of resonance is identifiably similar in this young man's playing as in particular passages in Beethoven piano sonatas.
Yesterday the improv focused on black key resonance. As we segued into the Moonlight Sonata first movement I was stunned to hear his "wrong notes" which were all consistent with his own improvisations, and which signalled specific responses to the overtone mix in play at each moment. (Here it must be pointed out that I take Beethoven at his word, and have the piece played "senza sordini," i.e., with a touch of pedal throughout so that overtones mix and clarify as they accumulate.
What I heard yields a more dynamic understanding of the work than visual score analysis. My training, heavily biased in the latter, still makes it difficult for me to play anything but a definite F# minor chord when I see one. His improvisational impulse produces a subtle mixing of the A natural with the clearly sounding A# overtone of the root F#.
I learn so much from this young man's pure ear.