A large slice of the jazz repertoire lives in 3/4: "My Favorite Things," "Someday My Prince Will Come," "Bluesette," "Alice in Wonderland," half of Bill Evans' set lists. The jazz waltz is not 4/4 swing with a beat missing — it's its own feel, with its own ride pattern and its own way of breathing.
The Ride in Three
The standard waltz ride is ding · ding-a · ding: quarter on 1, swung 8ths on 2, quarter on 3. The skip note (the "a" of 2) is swung exactly like the 4/4 skip note — late, in the last third of the beat. The hi-hat foot moves from "2 and 4" to just beat 2, which is what makes the bar feel like it turns in a circle rather than marching in a line.
Keeping the Bar From Turning Around
The classic beginner failure in 3/4 is losing which beat is "1" — the bar silently rotates and you're suddenly playing the ride pattern starting on 2. The fix is the hi-hat foot: as long as the chick is on beat 2, your body knows where the bar is. If you feel the pattern drift, stop, sing "ONE two-and three" for a bar, and re-enter.
Where the Comp Goes
In 4/4 the snare comps around the backbeat; in a waltz there is no backbeat. Comps in 3/4 most naturally land on the & of 2 (locking with the skip note) or on beat 3 (setting up the next downbeat). The exercises add one comp at a time — the goal is a rolling, circular time-feel, not a downbeat-heavy "oom-pah-pah."