Most challenges with rhythmic interpretation in jazz come from (1) swing and (2) high levels of syncopation. Swing interpretation of eighth-notes (assuming a background swing feel is used in a given piece) can most simply be explained as turning two eighth-notes that start on a beat into a quarter-note and eighth-note triplet. A single eighth-note ahead of a beat -- a pick-up note, if you will -- is performed like a triplet eighth-note pick-up. In the early days of jazz, a swing feel often sounded more like dotted-eighth, sixteenth rhythms, but the triplet feel has been the norm for many decades.
The other potential problem area is found in straight-eighth-note, funk style pieces in which syncopation is used on the sixteenth-note level. In other words, figures like sixteenth, eighth, sixteenth making up a beat (assuming quarter-note beats, of course) may prove to be difficult to perform. This is not an interpretation problem as much as it is a reading challenge. If this is difficult for you, try slowing the passage down and subdividing the beats.
Let's assume for a moment that we are playing a piece with swing eighth-notes and we either are studying articulation/phrasing marks in the sheet music or we need to add our own articulation/phrasing marks. Many of the jazz etude books on the market place a great deal of emphasis on learning the articularion style of post-1940 jazz. Without fail, the classical musician studying this material finds many more slurs from upbeat to downbeat than he or she is used to. Often times, too, the classical musician tends to clip off the ends of these slurs much more than he or she should. In general, look for upbeat into downbeat phrasing, and keep it smooth unless the editor has placed staccato marks or a short/accent mark. Even those, marked ^, should have a degree of "fatness" to the sound.
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