Many ordinary musicians can play classical and enjoy playing jazz.
But playing in a band of many versus with two or three or four with a "timing" born from the unwritten play versus a "timing" imposed by the written play ask for a different time feeling...
Music is classical or jazz, rythms of time and timing...
There is no time in mathematics...
But there is not so much numbers in music as thought Pythagoras and Leibnitz after him but more timbre explorations and timing time investigations...
We hear a vibrating sound source which "inform" us and we vibrate ourselves in response in a timing way, transforming our body and the instrument or the vibrating phenomena into one event. It is Speech creation already with music.
Here in speech, as in music, time is not external to the event but on the opposite created by it and born from it.( poetry unlike prose can gave us this birth of creative memory again)
Jazz is the root by which we can remember the birth of music and speech again by recreating musical time and timing in a new way compared to classical western music.
The black African root of jazz was a gift.
"its rolling" as said to Randy Weston his African master friend. Time is born with music again.