piano scale
E Locrian
E1F♭2G♭3A4B♭♭5C♭6D♭7
The only mode of the major scale whose fifth is diminished, which is why its tonic chord cannot rest.
Written out
Every accidental is written in, rather than left to a key signature, so the letters can be read one at a time.
The step pattern
EHFWGWAHB♭WCWDWE
What is true of it
E Locrian is E, F, G, A, B♭, C and D, and back to E.
Its steps are H – W – W – H – W – W – W, where W is a whole step and H a half.
On the same tonic, E Phrygian differs from it by exactly one note.
Chords made only of these notes
CmajorC7dominant seventhDmminorDm7minor seventhEdimdiminishedEm7♭5half-diminished seventhFmajorFmaj7major seventh
Found by testing every chord in the catalogue against these 7 sounds, not chosen.