Harmonic Major vs. Double Harmonic Major

Both of these start on C, and both hold the flat sixth that gives Harmonic Major its name - a major scale with one note pulled toward minor.

The wheel makes the difference positional rather than verbal: the second-degree wedge sits one wedge further counterclockwise in Double Harmonic Major, and the spoke drawn from the center recolors to the interval that degree now forms with the tonic. Everything else on the two wheels is identical.

That single degree is what turns one flattened note into two: Double Harmonic Major pairs the flat second against the major third right above it, the same tight, augmented-second gap that gives Phrygian Dominant its exotic color - only here it shows up twice, once low in the scale and once again between the flat sixth and the major seventh. Reading it is one thing; the difference is much more obvious held under a drone, which is what the links under each figure are for.