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
CHD♭WE♭HF♭WG♭WA♭WB♭WC
What is true of it
C altered is C, D♭, E♭, F♭, G♭, A♭ and B♭, and back to C.
Its steps are H – W – H – W – W – W – W, where W is a whole step and H a half.
It costs 6 alterations to write — near the limit of what a key signature can carry.
On the same tonic, C Locrian 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
CdimdiminishedCaugaugmentedCm7♭5half-diminished seventhD♭mminorE♭mminorE♭m7minor seventhG♭majorG♭7dominant seventh
Found by testing every chord in the catalogue against these 7 sounds, not chosen.