14.8Why diminished seventh chords are special

Look at B°7:

B D F A♭

Intervals:

B → D = 3 semitones

D → F = 3

F → A♭ = 3

A♭ → B = 3

So the octave is divided equally into four minor thirds.

That makes the chord symmetrical.

This symmetry produces one of the strangest and most useful facts in harmony.