The Melodic Minor Scale is one of the 3 minor scales that you are going to encounter. This scale has two versions to it: the ascending version and the descending version. The ascending version can can be thought of as being a major scale with a lowered 3rd. The descending version is just going back to the natural minor scale. The reason we have these 2 versions is because if you played the melodic minor scale descending, it would sound major, and since this mode has its basis in harmonic playing, this is why we use 2 versions of this scale. When improvising, you are going to only use the ascending version of this scale.
Natural Minor- 1-2-b3-4-5-b6-b7
Harmonic Minor- 1-2-b3-4-5-b6-7
Traditional Melodic Minor- (1-2-b3-4-5-6-7-8)-(b7-b6-5-4-b3-2-1)
(Both Ascending and Descending is shown here)
The ascending melodic minor scale is often referred to as a synthetic scale because the first half is minor sounding while the second half is major sounding. This mode is probably the most useful to a jazz musician because it has notes and chords that are not found in the major or harmonic minor scales. The most useful modes from the melodic minor scale are built from the 1st, 3rd, 4th, 5th and 7th degrees.
Just like with the major and harmonic minor scales, this scale also has modes that are built from the 7 degrees of this scale, which are listed below:
#1=Melodic Minor
#2=Dorian b2
#3=Lydian Augmented
#4=Lydian Dominant
#5=Mixolydian b6
#6=Locrian #2
#7=Super Locrian