C whole tone

C1D2E3F♯♯4G♯♯5A♯♯6

Six notes, every step a whole one. There are only two of these scales in all, and every note can be heard as the tonic.

Written out

Fig. 2 · C whole tone, ascending

Every accidental is written in, rather than left to a key signature, so the letters can be read one at a time.

CWDWEWF♯WG♯WA♯WC

C whole tone is C, D, E, F♯, G♯ and A♯, and back to C.

Its steps are W – W – W – W – W – W, where W is a whole step and H a half.

Across the first twelve frets of the ukulele its notes fall in 26 places, which is what makes a scale a shape rather than a list.

Found by testing every chord in the catalogue against these 6 sounds, not chosen.