A diminished (half–whole)

A1B♭♭2C♭3C♯3D♯♯4E5F♯6G♭7

The same eight notes started a half step earlier: the scale that spells a dominant seventh with a flat ninth and a sharp ninth at once.

Written out

Fig. 2 · A diminished (half–whole), ascending

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

AHB♭WCHC♯WD♯HEWF♯HGWA

A diminished (half–whole) is A, B♭, C, C♯, D♯, E, F♯ and G, and back to A.

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

Across the first twelve frets of the ukulele its notes fall in 36 places, which is what makes a scale a shape rather than a list.

Found by testing every chord in the catalogue against these 8 sounds, not chosen.