ukulele scale
C♯ Locrian
C♯1D♭2E♭3F♯4G♭5A♭6B♭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 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
C♯HDWEWF♯HGWAWBWC♯
What is true of it
C♯ Locrian is C♯, D, E, F♯, G, A and B, and back to C♯.
Its steps are H – W – W – H – W – W – W, where W is a whole step and H a half.
On the same tonic, C♯ 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
C♯dimdiminishedC♯m7♭5half-diminished seventhDmajorDmaj7major seventhEmminorEm7minor seventhF♯mminorF♯m7minor seventh
Found by testing every chord in the catalogue against these 7 sounds, not chosen.