Written out
Every accidental is written in, rather than left to a key signature, so the letters can be read one at a time.
The step pattern
EHFW+HG♯HAWBHCW+HD♯HE
What is true of it
E double harmonic is E, F, G♯, A, B, C and D♯, and back to E.
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, E harmonic major differs from it by exactly one note.
Across the first twelve frets of the ukulele its notes fall in 31 places, which is what makes a scale a shape rather than a list.
Chords made only of these notes
Found by testing every chord in the catalogue against these 7 sounds, not chosen.
Other scales on E
E Phrygian dominantexoticE Lydian dominantexoticE alteredexoticE majormajorE natural minorminorE harmonic minorminor
C dbl harmC♯ dbl harmD♭ dbl harmD dbl harmD♯ dbl harmE♭ dbl harmF dbl harmF♯ dbl harmall 374