There is no more marked area of difference between classically trained players and players trained in jazz than the domain of rhythm. Jazz musicians prioritize above all else a kind of steadiness of pulse, a consistency of rhythmic placement. They worship at the shrine of the eighth note, the sixteenth note. You can call this an orientation toward groove, or a metronomic approach—though, even if it begins from a principle of total evenness, it ultimately transcends the metronomic and goes to the realm of feel, that is to say each person’s own individualized approach to this evenness, to subdivision. Very few classical musicians I’ve worked with have even heard of this idea of feel, and even the ones with good rhythm don’t obsess over it to the point that jazz musicians need to in order to obtain an expected level of competence. So to a jazz musician, the classical musician’s sense of rhythm can seem bafflingly substandard.
But in fact this needs to be understood in a completely different way. Classical musicians simply look at rhythm differently. They see it as an expressive element. By stretching the pulse one way or the other, they can support the longer musical line, which to them is of highest importance. The irony here is that jazz musicians’ use of rhythm is in a way LESS expressive than that of classical musicians. That expression is re-injected on the subtle level of feel—and indeed the best jazz soloists do make expressive use of time, by laying back against the beat or floating over it, but these effects work precisely because they create tension against an underlying pulse that is unchanging. Actual tempo fluctuation is strictly to be avoided. This is why, while it may be very difficult to get classical players to groove, it’s equally challenging to get jazz players to effect a convincing rubato. When shading a phrase, when injecting drama into their performances, classical musicians obviously make frequent recourse to dynamics. Jazz musicians, uh, not so much! I remember in one of our rehearsals that Colin Jacobsen asked Josh Redman what dynamic he was playing at a certain passage. Josh grinned sheepishly and said, “Jazz musicians don’t really use dynamics.”  He wasn’t far from the truth—many jazz players, especially horn players, play at a fairly static volume. There certainly isn’t any established tradition of crescendo and diminuendo, outside the world of big band.
The overall dynamic of jazz is much louder than that of classical music, at least at the chamber music level. This is probably because of the prominence of the drum set in jazz, which is extremely loud compared to any chamber instrument (and has gotten considerably louder with the advent of rock music) and tends to play at a fairly consistent volume. To compete with this, other jazz musicians have gotten accustomed to playing at louder volumes, as well as becoming habituated to electronic amplification. Jazz saxophonists play at or above the volume of a classical trumpet, so when they suddenly have to play with a string quartet, they have to play around 1/8 their normal volume to blend!
3. Tone and Intonation. Jazz musicians can be obsessive about their sound and their tone quality, but overall I would say it’s less a priority than it is in the classical world. Sometimes jazz musicians also go for bigger rather than better in this regard, for the above-stated reasons.
In this category perhaps should be included things like vibrato. For a string player, vibrato is at the core of their playing, and vibrato practice is an important part of their musical development. Jazz musicians practice vibrato much less, and consequently have much less control, far less variety of speed and amplitude. It’s simply not as much used as an expressive element.
Intonation is much less of a concern in the jazz world than in the classical world. There’s the tradition of classical musicians tuning before the concert begins; many jazz musicians just hope to be in tune by the end.
In fact, I see intonation as a kind of inverse of rhythm. For classical musicians it’s a subject of years of true obsession, and like rhythm in jazz, classical musicians view intonation as a grid. You could think of jazz musicians, conversely, as having a more expressive approach to intonation. It’s not necessarily even conscious, but with saxophone players in particular a kind of idiosyncratic intonation can become an identifiable feature. I’ve seen classical musicians listen to Coltrane from his quartet period, for example, and actually burst out laughing at the intonation. But as any Coltrane aficionado with some technical understanding would agree, that sharp, almost pinched quality in the high register is an integral part of the surging angst of the Coltrane sound.
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