F♯ diminished (half–whole)

F♯1G♭2A♭3A♯3B♯♯4C♯5D♯6E♭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.

The same sounds spelled from the other side are G♭ diminished (half–whole).

Written out

Fig. 2 · F# 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.

F♯HGWAHA♯WB♯HC♯WD♯HEWF♯

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

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.