ukulele scale
G♯ Locrian
G♯1A♭2B♭3C♯4D♭5E♭6F♯♭7
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 A♭ 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
G♯HAWBWC♯HDWEWF♯WG♯
What is true of it
G♯ Locrian is G♯, A, B, C♯, D, E and F♯, and back to G♯.
Its steps are H – W – W – H – W – W – W, where W is a whole step and H a half.
On the same tonic, G♯ 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.