G double harmonic

G1A♭♭2B3C4D5E♭♭6F♯7

Two augmented seconds in one scale, one above the tonic and one below the octave.

Written out

Fig. 2 · G double harmonic, ascending

Every accidental is written in, rather than left to a key signature, so the letters can be read one at a time.

GHA♭W+HBHCWDHE♭W+HF♯HG

G double harmonic is G, A♭, B, C, D, E♭ and F♯, and back to G.

Its steps are H – W+H – H – W – H – W+H – H, where W is a whole step and H a half.

On the same tonic, G harmonic major differs from it by exactly one note.

Across the first twelve frets of the ukulele its notes fall in 30 places, which is what makes a scale a shape rather than a list.

Found by testing every chord in the catalogue against these 7 sounds, not chosen.