The tritone sub.

A pretty regular jazz/pop progression is the famous: II - V - I

Now, why is it that sometimes you may see a jazz player move in a chromatic descending format?  For example instead if the typical D minor, G7, C major progression, you may see a Db7 in place of the G7?

Well, the reason is something that we call in classical theory, the Neapolitan 6.  All this means is that the II chord in a key becomes flatted.  Thus, D in the key of C major gets substituted for Db.

Db is at the same time a "tritone" (6 half steps) away from the chord that should go there.  In the case of the II - V - I, the V or G gets replaced by its "tritone" or the Db (6 half steps away or a "tritone" away).

Therefore, that is why it is called a "tritone" substitution.  You can simply see it as a half step descending motion from the chord before, (from D minor to Db7).

Now why a Db7 and not a Db minor if the chord preceding is minor?  Well, because the chord being replaced (G7) is a dominant chord, so the new chord should take on the dominant quality to lead into the I chord (C major in this case).  Notice that the I chord is also a half step away from the Db7 chord.

The progression becomes a nice chromatic descending pattern.

Enjoy the great sound of the tritone sub.  Awesome to solo over!!!