What is in it
A diminished 7 is a diminished triad (root, minor 3rd, diminished 5th) with a diminished 7th added on top. From C that is C, E flat, G flat, B double flat. The simpler description is the more useful one: it is three minor 3rds stacked, so all four notes are evenly spaced, three semitones apart from each neighbour. It is the only common chord with no uneven gap anywhere in it.
On the staff
Rootless by design
The even spacing has a strange consequence. Because every interval in the chord is the same, every inversion of a diminished 7 is itself another diminished 7, and any of its four notes can be heard as the root. There are only three distinct diminished 7 chords in the whole system; each covers four possible roots. No note steps forward to claim the chord, which is why it sounds suspended and directionless, darker and more uniform than the augmented chord, which shares that rootless symmetry on the bright side.
Why composers reach for it
That same ambiguity makes the diminished 7 a workhorse pivot. Since it can resolve toward several keys at once, a composer can drop it in to swing a passage somewhere unexpected, or to inject a moment of tension between two settled chords. Classical voice-leading and jazz both use it this way, as a hinge rather than a destination. In a minor key it appears diatonically as vii°7, the leading-tone seventh.
Jazz often hears it as a dominant in disguise. Mark Levine points out that a diminished 7 is usually a dominant 7♭9 with its root left off: the four notes that remain are the 3rd, 5th, 7th, and flat 9th of that dominant, which is what lets the chord slip under a chromatic bass line. Its symmetry is the other half of the story, and it is why, as Levine puts it, everything about the chord repeats at the interval of a minor 3rd.
How Aubel handles it
Diminished 7 unlocks last, the ninth and final chord. It is the hardest to pin down precisely because it is so symmetric: four evenly spaced notes, no octave doubling, no single root that announces itself. The cue is that even, stacked-minor-3rds darkness, unmistakable once you have heard it against the half-diminished, which keeps a higher, warmer 7th. With it, the set is complete.