E♭ Phrygian dominant

E♭1F♭♭2G3A♭4B♭5C♭♭6D♭♭7

The fifth mode of harmonic minor: a flat second over a major third, so the step from the second to the third is a step and a half.

The same sounds spelled from the other side are D♯ Phrygian dominant.

Written out

Fig. 2 · Eb Phrygian dominant, 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♭W+HGHA♭WB♭HC♭WD♭WE♭

E♭ Phrygian dominant is E♭, F♭, G, A♭, B♭, C♭ and D♭, and back to E♭.

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

It costs 6 alterations to write — near the limit of what a key signature can carry.

On the same tonic, E♭ Phrygian differs from it by exactly one note.

Across the first twelve frets of the ukulele its notes fall in 30 places, which is what makes a scale a shape rather than a list.

Found by testing every chord in the catalogue against these 7 sounds, not chosen.