The forward motion aspect of time and phrasing can sometimes be achieved this way. (The time signature is assumed to be 4/4.)

1. First of all get a musical form (say a 12 bar blues) going, but don't even begin playing a solo right away. Whatever you do, DON'T play the first bar.

2. Let a whole chorus go by if you must.

3. Try and begin your line on Bar 12.

4. Try and end your line somewhere in the middle of bar 1.

5. The basic principal here is EVEN GOES TO ODD.

6. Try a line starting in bar 4, ending in bar 5.

7. One of the most important results of this approach is that it forces the player to play through the changes not on the changes. They call them "changes" Because they change!  And they typically change (and more importantly) resolve from EVEN TO ODD bars. (This also works at higher and lower levels of time.)

8. At a medium tempo -try and start your line on BEAT 2 or 4!

9. At a medium tempo-- try and start your line on an even numbered eighth note, i.e. an upbeat.

10. Warning - this will really mess with your sense of what pitches go where. Listen to tons o' records and GOOD LUCK! 

In the be-bop and swing tradition one of the most elusive but important rhythmic figures is the quarter note triplet-STARTING ON BEAT 2 OR 4 OR THE UPBEAT BEFORE 1 AND 3 - it can be heard on many records. One great example is Bobby Timmons' solo on Like Someone in Love (Art Blakey) on Blue Note. It is a figure typically used at slow to medium tempos - Although you can sometimes hear Philly Joe Jones and others - Red Garland, for example play it faster. The effect of this figure is that it sounds very relaxed and jazz like. In spite of this it is very strong and totally rational and learnable.
It also has the wonderful attribute of being dovetailing perfectly with the typical ride cymbal and hi-hat groove of the styles mentioned above.

The numbers represent the beats (Two measures of 4/4 time). The slashes represent the 1/8 note triplets, with the downbeats in bold. The ! (exclamation) is the figure.

Try to internalize this, it will help your playing. The recorded examples are crucial to one's understanding of the use of the figure. Try to tap and say the numbers out loud while tapping the figure with your other hand. Say the drum figure (the ride cymbal),
you know - ding dinga ding dinga - at the same time.

Also, this figure is very rarely written in transcriptions because it's awkward to notate. This does NOT mean it is rarely played.

Warning: drummers will love you for knowing this. Assuming of course, that they grasp it. Thank goodness any competent drummer does.

Questions?