guitar scale
C Locrian
C1D♭♭2E♭♭3F4G♭♭5A♭♭6B♭♭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
CHD♭WE♭WFHG♭WA♭WB♭WC
What is true of it
C Locrian is C, D♭, E♭, F, G♭, A♭ and B♭, and back to C.
Its steps are H – W – W – H – W – W – W, where W is a whole step and H a half.
On the same tonic, C Phrygian differs from it by exactly one note.
Across the first twelve frets of the guitar its notes fall in 42 places, which is what makes a scale a shape rather than a list.
Chords made only of these notes
CdimdiminishedCm7♭5half-diminished seventhD♭majorD♭maj7major seventhE♭mminorE♭m7minor seventhFmminorFm7minor seventh
Found by testing every chord in the catalogue against these 7 sounds, not chosen.