E diminished (half–whole)

E1F♭2G♭3G♯3A♯♯4B5C♯6D♭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 · E 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.

EHFWGHG♯WA♯HBWC♯HDWE

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

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 34 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.