Diminished chords
A diminished triad stacks two minor thirds: root, minor third, diminished fifth (Cdim: C–E♭–G♭). Shrinking the fifth turns the chord tense and unstable — it wants to move. On its own it rarely ends a phrase; its job is to connect.
Add another minor third and you get the fully diminished seventh (Cdim7: C–E♭–G♭–B♭♭). Because it divides the octave into four equal steps, every inversion of a dim7 is another dim7 — there are really only three distinct ones. The half-diminished chord (m7♭5) softens the top interval and serves as the ii chord in minor keys.
The most useful pattern to steal: a diminished seventh a half-step between two diatonic chords. C → C♯dim7 → Dm7 walks the bass up chromatically and appears in thousands of jazz and ragtime tunes. Gospel piano leans on the same move constantly.
