One of the most efficient ways to memorize scales and play them on the guitar is using box patterns. These are ways of 'mapping' the scale across the guitar fretboard, creating fixed shapes that can be transposed to play the scale in a different key. Once the patterns for the natural minor scale have been memorized, raising the seventh degree by one semitone (that is, playing the note that comes before the tonic one fret higher) will give the harmonic minor scale as a result. This will create some fingering differences: below you'll find the graphic representation of all the box patterns for the harmonic minor scale in every key. Select a root note to see a list of box patterns for the harmonic minor scale:
The harmonic minor scale is one of the possible variations of the natural minor scale, in which the seventh degree is raised by one semitone. This makes the seventh degree into a leading tone for the tonic, and also transforms the otherwise minor V chord of the minor scale into a major chord. The scale is so named because this alteration is a common foundation for harmonies used in a minor key: besides making the V chord into a major chord, it may be used to transform the VII into a diminished chord and the IIi into an augmented chord.
The raising of the seventh degree creates a one-and-a-half-tone interval from the sixth to the seventh degree of the scale, thus giving the scale runs a sonority that was deemed harsh in the common practice period. Maybe for this reason the scale hasn't seen much melodic uses when it comes to classical academic music. In modern music, the augmented interval has been sometimes exploited in order to create an eastern, exotic feeling, due to the scale's rough similarity with the Hijaz jins and Nahawand-Hijaz arabic scales. The so called Hungarian scale is also similar, but with an raised fourth degree (making for an even tenser sound, with the addition of other augment interval).