How can jazz swap a chord for one a tritone away and still resolve?

A tritone substitution swaps a dominant seventh chord for the dominant seventh chord a tritone away, and the music still resolves because the two chords share the two notes that matter. In the key of C major the dominant is G7, and the substitute is D flat 7: D flat is a tritone away from G.

The trick works because a dominant seventh chord is defined by its third and its seventh, which themselves are a tritone apart. In G7 the third is B and the seventh is F. In D flat 7 the third is F and the seventh is C flat, which is the same pitch as B. The two chords share those two pitches, just with their roles reversed. So either chord carries the same tension and can slide into the same home chord.

What changes is the bass line. In a jazz ii–V–I, such as Dm7, G7, Cmaj7, swapping in D flat 7 makes the roots fall by step, D, D flat, C, a chromatic descent the bassist can walk, and the thirds and sevenths in the chords also fall by half-steps. The substitution is also very common in the twelve-bar blues.

It was not invented in jazz. Classical theory calls it an augmented sixth chord, found extensively since the Renaissance. It reached jazz in the 1940s through musicians such as Dizzy Gillespie and Charlie Parker.