okay, here goes:

all dominant seventh chords contain a tritone between the 3rd and 7th, which is largely responsible for their "anticipatory" sound.  this anticipation is typically resolved by moving to the major tonic chord in a v-i progression (authentic cadence).

an interesting property of tritones is that they are symmetrical.  since they consist of six half-steps, they are exactly half an octave.  this means that if inverted, it will remain a tritone, enharmonically (e.g. an augmented fourth inverts to a diminished fifth, and vice-versa).

this carries the implication that for any original dominant seventh chord, there must be another one, in some other key, which shares the same tritone, only inverted.  for example, the tritone in g7 lies between the pitches b (the 3rd) and f (the 7th).  if those pitches are inverted, we'd be looking for another dominant 7th chord wherein f is the 3rd, and b (enharmonically c-flat in this case) is the 7th.  this points to db7 (v7 of gb major).

db7 is therefore the tritone substitute of the original g7 chord, and the two can function interchangably in jazz progressions (particularly ii-v7-i sequences).  happily, the db7 chord is exactly a tritone away from the original g7 chord, which is always the case with tritone substitutions, making them relatively easy to find.

dominant 7th chords usually resolve down a perfect fifth to their respective tonic chords, although a tritone substitute's resolution tendency is usually down a half-step, to the tonic of the original key.  example: dm7 - db7 - cmaj7.  tritone substitutes can also be used as a device for modulation, as in dm7 - db7 - gbmaj7 (although this is less common).

tritone substitutes are also often used in place of secondary dominants, or in the context of c-form voicings (described in an earlier post).  

hope that does the trick!ben blau
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