F Locrian

F1G♭♭2A♭♭3B♭4C♭♭5D♭♭6E♭♭7

The only mode of the major scale whose fifth is diminished, which is why its tonic chord cannot rest.

Written out

Fig. 2 · F Locrian, ascending

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

FHG♭WA♭WB♭HC♭WD♭WE♭WF

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

Its steps are H – W – W – H – W – 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, F Phrygian differs from it by exactly one note.

Across the first twelve frets of the ukulele its notes fall in 28 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.