Can someone give me a practical explanation of the theory and practice of tri-tone substitution for jazz piano?
The basic premise of the tritone substitution is that we take a chord (typically a major-minor seventh) that has a tritone in it and substitute the entire chord with another major-minor seventh chord that has the same tritone.
Let's begin in C major and imagine a V7 chord that progresses to I. Within the V7 chord (
G B D F) is the tritone
B F. This is shown at letter A below.
As it turns out, this tritone exists in another major-minor seventh chord, this one on D♭:
D♭ F A♭ C♭. (Note that the
B F tritone is now enharmonically spelled as
F C♭.) This is shown at letter B above.
So basically, wherever you use a
G7 chord, you can substitute it with a
D♭7 chord, because the tritone stays the same in both harmonies. Note, too, that the roots of the chords—
D♭—are a tritone apart.
Listen to a recording here.
We can take this one step further; let's stay in C major, but let's think about a secondary dominant to V. In other words, we're looking at V7/V, or
D7. In this chord (
D F♯ A C), the tritone is
F♯ C; see C below. The tritone substitution of this harmony (again remembering that the roots are a tritone apart) will be
A♭ C E♭ G♭) with the enharmonically spelled tritone
C G♭; this is shown at letter D.
If you've learned about the German augmented-sixth chord (
A♭ C E♭ F♯ in the key of C), you see here that it's enharmonically equivalent to the tritone sub of V7/V!