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The distinctive sound of the harmonic minor scale is the interval between the (minor) sixth and (major) seventh degrees of the scale (in the case of A-minor, F and G♯), which is an augmented second. While some composers, notably Mozart, have used this interval to advantage in melodic composition, other composers, having felt it to be an awkward leap, particularly in vocal music, considered a whole step between these two scale degrees more conducive to smooth melody writing, so either the sixth scale degree was raised or the seventh flattened, in both cases by a semitone. Traditionally, music theorists have called these two options the ascending melodic minor scale (also known as heptatonia seconda and jazz minor scale) and descending melodic minor scale respectively. Note that the ascending melodic minor scale is the 5th mode of the Lydian Dominant or acoustic scale. The ascending melodic minor scale can be notated as

1 2 ♭3 4 5 6 7 8
While the descending is:

1 2 ♭3 4 5 ♭6 ♭7 8
In its upper tetrachord, the ascending melodic minor scale is identical to its major scale. The descending melodic minor scale is identical to the natural minor scale.

Composers have not been consistent in using these in ascending and descending melodies. Just as often, composers choose one form or the other based on whether one of the two notes is part of the most recent chord (the prevailing harmony). Particularly, to use the triad of the relative major—which is very common—since this is based on the third degree of the minor scale, the raised seventh degree would cause an augmented triad. Composers thus frequently require the lowered seventh degree found in the natural minor. In jazz, the descending aeolian is usually disregarded altogether.

Examples of the use of melodic minor in rock and popular music include Elton John's Sorry Seems To Be The Hardest Word, which makes, "a nod to the common practice...by the use of F♯ [the leading-tone in G minor] as the penultimate note of the final cadence."

source from wikipedia