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
EWF♯WG♯HAWBHCW+HD♯HE
What is true of it
E harmonic major is E, F♯, G♯, A, B, C and D♯, and back to E.
Its steps are W – W – H – W – H – W+H – H, where W is a whole step and H a half.
On the same tonic, E 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
CdimdiminishedCaugaugmentedD♯dimdiminishedEmajorEaugaugmentedEmaj7major seventhF♯dimdiminishedF♯m7♭5half-diminished seventh
Found by testing every chord in the catalogue against these 7 sounds, not chosen.
Other scales on E
C harm majC♯ harm majD♭ harm majD harm majD♯ harm majE♭ harm majF harm majF♯ harm majall 374