ukulele scale
D♭ 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 C♯ 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
D♭ Locrian is D♭, E♭♭, F♭, G♭, A♭♭, B♭♭ and C♭, and back to D♭.
Its steps are H – W – W – H – W – W – W, where W is a whole step and H a half.
Written correctly it needs 10 alterations, E♭♭, A♭♭ and 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, D♭ Phrygian 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.