The Double Harmonic Scale, also sometimes called the “Gypsy scale” for its association with Eastern European ethnic music, arises from the same heritage as the Acoustic Scale.
Take an Acoustic Scale [ A Bb C D E F# G ] but collapse the C and E towards the tonal center to create the Double Harmonic Scale as [ A Bb C# D Eb F# G ]
The presence of leading tones both above and below the tonal center presents many intriguing melodic possibilities with very strong voice leading. The mirrored pair of augmented seconds on either side of that tight center, gives the Double Harmonic Scale its distinctively angular twist. The combination of two minor seconds and two augmented seconds within a single scale brings a very powerfully emotive quality to the Double Harmonic Scale, a characteristic which can be readily heard in the ancient ethnic music from which it is derived.
With the center of the symmetry shown in the middle of the Double Harmonic Scale, each transposition of it arranged around the cycle of fifths, some interesting facets become apparent …
Going counterclockwise around the cycle as shown above, the last four notes of each is same as the first four notes of the next. So taken all together these can be seen as a completely interlocking traversal around the full cycle. Used alternately with the Acoustic Scale this presents a multitude of possibilities for modulatory devices.