ukulele scale
E♭ Locrian
The only mode of the major scale whose fifth is diminished, which is why its tonic chord cannot rest.
The same sounds spelled from the other side are D♯ Locrian.
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
What is true of it
E♭ Locrian is E♭, F♭, G♭, A♭, B♭♭, C♭ and D♭, and back to E♭.
Its steps are H – W – W – H – W – W – W, where W is a whole step and H a half.
Written correctly it needs 8 alterations, B♭♭ among them. That is what the letters force, and it is also why nobody writes music in this key: the same notes spelled from the other side are easier to read.
On the same tonic, E♭ Phrygian 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.
Chords made only of these notes
Found by testing every chord in the catalogue against these 7 sounds, not chosen.