Melodic minor
Minor with raised sixth and seventh degrees ascending.
What it means
Melodic minor designates the minor scale in which, ascending, the sixth and seventh degrees are raised and, descending, the natural form applies.
Musical use
The name says what it is about: the melody. The harmonic form supplies the leading tone with the raised seventh degree but thereby creates the augmented second between the sixth and seventh degrees. Where a melody runs upward to the tonic, this step was avoided in classical practice by also raising the sixth degree. Descending, the reason falls away, and the notes return to their natural position.
From this it follows that the three forms of the minor scale are not three scales of equal standing but descriptions of what is needed in different situations. Within a piece they appear side by side: the same degree can occur raised and unaltered within a few bars, depending on the direction of the line and on the harmony.
Notable is that the ascending form differs from major in only one note — the minor third. In jazz it is therefore used as a scale of its own in both directions and there forms the starting point of a family of chord-scale associations in its own right.
In jazz theory, melodic minor is the basis of several scales, among them the altered scale.
Other names
The designation melodic minor ascending names the form with raised sixth and seventh degrees separately. In classical teaching, natural minor is played again descending; in jazz, by contrast, the ascending form holds in both directions and is there often called jazz minor. When melodic minor is used without qualification, it must be inferred from the context which practice is meant.
Performance practice
When practising, watch the change of direction and make sure the hand does not glide over it. Check in the notation which form is actually called for — the key signature says nothing about it, only the accidentals within the bar. And sing the scale, so that the difference between ascending and descending becomes familiar to your ear.