One of the best things about Carmine Caruso's teaching was that he boiled playing music down to a few mechanical principles that were universal. One of these was that all music consisted of a series of intervals, so it was reasonable to assume that the more accurately and automatically one learned to execute and hear intervals the better one would play. This applied to every instrument and therefore made his successful students include not only brass players, but saxophonists, oboe players, violinists...
I always wondered why all musicians didn't practice the kinds of things jazz musicians practice. I'm not talking about licks, repertoire, or style-driven things. A great portion of what most jazz musicians practice consists of all types of scales, chords, intervals, sequences, and myriad varistions and inversions. These are the components of all western music, not just jazz. Obviously, if you can play and hear all of these intevallic patterns and sequences without a lot of conscious thought you will be able execute any music better, hear better, read better (because sight-reading is mostly pattern recognition)...
If you look at the scale studies in Arban, Ernest Williams, Clarke, etc. you will find that they created many of their exercises by devising patterns and sequences within every major and minor key. This is exactly what a jazz musician practices, but it is only a small representation of the possibilities for patterns and sequences in those keys. Jazz musicians also do this kind of practice on modal scales and even sometimes use things like Messiaen's modes of limited transposition, fragments of tone rows, etc. for this kind of work.
The problem is that as soon as someone writes some of these patterns down in a book that becomes a set routine. However, if I say that every day this month I am going to practice playing different sequences through all the modes of the major scale in broken thirds this leaves me with a virtually unlimited array of possibilities for further investigation.
For me it is designed to give me better technique and an arsenal of musical resources for use in improvising. However, at the same time I find that practicing this way improves my ability to hear and that in turn might be the most important thing.
For an interesting comment on learning music without a book and how this has impacted the pedagogy of William Adam check out an article by Bob Baca on the Kjos Music C. website. Go to
http://www.kjos.com/ and follow the links. Click on "band", the "what's new", then "Kjos Band News Vol. 10".
Pat