Tritone Subs, the Other Dominant Approach.
In Jazz, or any other western music style, dominant release is vital to almost any piece of music which relies on a chord progression. The reason lies in dominant pull. In the Major Scale, there are two dominant chords, the V7 (or the Major Minor seven for classical theorists), and the vii minor seven flat five, (half diminished). Dominant pull is created by the interval of the tritone, which occurs naturally between the perfect fourth and the major seventh of the Major Scale. The only two chords in the major scale (aside of course from the IV major seven sharp eleven, which is subdominant and does not pull to the I major seven) are The V and the vii. Now, out of these two chords, the V7 is the most used, and is generally the blueprint for building secondary dominant chords. Although, you can use the same formula for dominant half diminished approaches, it is very much not as common due to that fact that it is hard for people to make the minor seven flat five sound good.
Anyways, getting back on topic, the tritone sub lies a tritone away from the natural dominant, (or secondary dominant if the natural dominant doesn't exist) and generally takes a sharp eleven (which is the root of the replaced chord), and goes by the moniker seven sharp eleven (7#11). It can even take a related two, for a full ii7 -> V7 -> I maj 7 progression.
But why does it work?
As stated above, dominant pull works through the interval of tritone, which happens natural between the four and the seven of the major scale. The V chord contains both of these pitches. The Tritone Sub of the V chord does too. In the V chord, the Major third is also the Major Seventh of the I, while the Flat seven, or minor seventh is the Perfect fourth. For the tritone sub, the Major Third is the Perfect Fourth, while the flat seven is the Major seventh, plus you get the ultra cool half step to target approach. Just remember to keep it hip.
redone 4/28/05
11/18/04: original text as follows. Node heaven works.
A tritone sub generally also takes a natural nine, sharp eleven, and natural thirteen, which helps to color the chord.