The Byzantine scale is better known as the Double Harmonic mode, mode V of Hungarian minor. Its formula is 1 b2 3 4 5 b6 7 and in the A Hungarian minor scale, E Double Harmonic would be
E F G# A B C D#.
Now, if we compare this mode from the relative mode of the A Harmonic minor scale, the E Phrygian Major E F G# A B C D, we can see the note of significance is the D#, the Major seventh in the Double Harmonic mode. This is a good example of a mode functioning as a dominant mode even though it has a Major 7th in its formula. The Harmonic Major scale works in much the same way.
What is happening when the Hungarian minor is followed by the Harmonic minor is that a V - V is created, the gravity of the D# in the Double Harmonic, which is acting as the Major third in the B7b5 chord, pulls us towards the E root of the dominant in A Harmonic minor, E Phrygian Major.
This is not the only use for the Double Harmonic but it is by far the most common. Below is an example of it in use by Bach from the second lute suite BWV 997. Bar 11 starts in E Harmonic minor and then the A# moves it into E Hungarian minor, the dominant mode being the Byzantine scale or Double Harmonic, giving us the notes of F#7b5 pulling us towards the dominant of E Harmonic minor, B Phrygian Major. Then it moves back the same way, the A natural signifying the move back to E Harmonic minor. So this is represented as:
E Harmonic minor – B Phrygian Major – B Double Harmonic – B Phrygian Major – E Harmonic minor
You can now see the symmetry involved, first the move to the dominant, then the dominant from the Hungarian minor on the same root, then the process is reversed. So, when you have a phrase or lick that you can use Phrygian Major over, you can substitute Double Harmonic first and then follow with the Phrygian Major to resolve back to the minor key. Its a nice touch and relatively easy to accomplish, so perhaps Byzantine isn’t such an appropriate name after all.
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