Dear Gilles, It's difficult to say anything about Cannonball and the 3 years I spent with his band in 5-10 lines. In any case, I still miss playing with them after all these years. One of the last bands that still played with a "Big Beat." The only rhythm section left that still plays that way is in Nat's band with Walter Booker and Jimmy Cobb. The last of a tradition!
You can't play with a "Big Beat" by yourself, it can only be played with rhyhym section that plays that way also. It took me a year of playing 6 nights a week for 50 weeks to get my articulation up to the level of the band's. They were very patient with me but I finally got it.
If there is any sadness in my life, it is that I shall never have the chance to play that beat again.