The best way to think of the Jazz Melodic Minor scale is as the Major Scale with the 3rd note lowered by a half step. As the name suggests, this scale is used extensively in Jazz (as are many other scales!). If you have not done so already, I highly suggest you take a look at the Harmonic Minor lesson. These two lessons really go hand in hand. And if it wasn't for the fact that there are 14 exercises between the two lessons, I would combine it all into one lesson. But my goal isn't to fry your brain (just your fingers!).

When practicing these scales, be sure to use the scale patterns from the Diatonic Scale Patterns and Sequences lesson. Also, as you are playing, notice that these modes don't get you the exotic sounds like the Harmonic Minor modes do (Spanish, etc). They get you a ... well, Jazzy sound!

Here is Jazz Melodic Minor mode that is similar to Mixolydian. Since the Mixolydian mode sounds good over Dom7 chords, it stands to reason that this scale should also sound good over Dom7 chords. For instance, the notes in a G Dom7 chord are in this scale, so G Mixolydian b6 would be a fine choice to play over a G Dom7.

Here is the Mixolydian b6 mode shape. The flatted 6th note distinguishes it from the Mixolydian mode.

See exercise 1 for any special instructions. Also, try ascending with the Mixolydian b6 and descending with the Mixolydian mode.