The Melodic Minor (lesson)
The Melodic minor scale was an attempt to "fix" the problem caused by the large 3 step interval in the harmonic minor without sacrificing the leading tone (for more details on this see my lesson on Minor Scales Revisited). The resulting scale is a harmonic minor with a sharpened 6th (meaning it reverts back to a major 6th). This means we end up with what is basically a major scale but with a flattened 3rd. Since the 3rd is the truly important indicator of major vs minor, this works out reasonably well in practice, and is better suited to melody than the harmonic minor, at least in classical terms.
Once the Melodic minor was established, it was tweaked slightly since the leading note is very much less important when descending a scale than when ascending the scale. For this reason, the melodic scale is played differently if you are moving upwards than if you are moving downwards in pitch. Downwards in pitch, the melodic minor scale is identical to the natural minor scale - playing scales differently in different directions though is a rarity.
In modern music, the Melodic minor scale does not tend to be very well represented, since musicians are somewhat less concerned about classical conventions (and even in classical time the melodic minor was not used consistently). As a result, the natural minor is used in themajority of cases, and the harmonic minor is used for effect.
Number of tones : 7
Intervals (Ascending) : 2-1-2-2-2-2-1
Intervals (Descending) : 1,2,b3,4,5,6,7
Formula (Ascending) : 2-1-2-2-1-2-2
Formula (Descending) : 1,2,b3,4,5,b6,b7
Characteristic Chords (Ascending) : MinorMajor7
Characteristic Chords (Descending) : m7