E♭ diminished (half–whole)

E♭1F♭♭2G♭♭3G3A♯4B♭5C6D♭♭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 D♯ diminished (half–whole).

Written out

Fig. 2 · Eb 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.

E♭HF♭WG♭HGWAHB♭WCHD♭WE♭

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 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.