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
BHCW+HD♯HEWF♯HGW+HA♯HB
What is true of it
B double harmonic is B, C, D♯, E, F♯, G and A♯, and back to B.
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, B 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
CmajorCmminorCdimdiminishedC7dominant seventhCmaj7major seventhCm7minor seventhCm7♭5half-diminished seventhD♯major
Found by testing every chord in the catalogue against these 7 sounds, not chosen.
Other scales on B
B Phrygian dominantexoticB Lydian dominantexoticB alteredexoticB majormajorB natural minorminorB harmonic minorminor
C dbl harmC♯ dbl harmD♭ dbl harmD dbl harmD♯ dbl harmE♭ dbl harmE dbl harmF dbl harmall 374