The traditional jazz music
The traditional jazz music started in New Orleance in the start of the 20th century.
Try a melody (All of me), This melody is easy to improvise in, since the chords are changing every second bar (and not twice per bar as in some jazz melodies).
4 note chords
The chords are built from third's put on top of ech other. If you put
4 thirds on top of each other you will get a major 7. The tonic chord
(the base chord for a Major) will thus be a major 7 (Cmaj7 or 
)
The Major 7 chord is associated with a major scale. The second tone in the major scale is a D. If you play a scale over that you will get a dorian scale. TThe II-V progression or the I-II-V -progression is often seen in jazz music. In C-major this yields
C - dm7 - G7. Basically you will play the same notes over the three chords, but since the root note is changing from C to D to G. The scales wil be different.
on dm7 you will play a dorian scale
on G7 you will play a mixolydian scale.