Another common method of substitution is to use a chord whose root is a tritone (flattened 5th or augmented 4th) above that of the original chord. This is known as tritone substitution. Like other methods of substitution, the reason this works is that there are notes common to both chords.
The chords G7 and Db7 are shown here to demonstrate this idea. As you can see, the note F occurs in both chords. The note B is enharmonically the same as Cb which is the 7th of Db7, so this note is in both chords too.
In the second half of the following example, Db7 is substituted for G7, creating a II bII I progression in the key of C instead of a standard II V I. Notice how the notes Db and Ab in the Db7 chord give the progression a different flavor to the II V I using a G7 chord.
Tritone substitutions are most commonly used with dominant chords, but can be used with any chord type and on any degree of a scale. In some cases, every chord except for I can be a tritone substitution. The following example shows a I VI II V progression and then a second version where bIII is substituted for VI, bVI is substituted for II, and bII is substituted for V.
This type of substitution throughout the progression is sometimes called backcycling. This is followed by two more variations. These are only a few of the many possibilities. Experiment and come up with some of your own.
A good way to practice substitutions is to learn a basic progression and then try out various substitution possibilities with some or all of the chords once you have the progression memorized. The following example is based on the chord changes to George Gershwin’s "I Got Rhythm", and is commonly referred to as "Rhythm Changes". Practice this chord progression until you have the form memorized.
The next example shows another version with some possible substitutions. Compare the previous version to the following and listen to the different sound produced by the substituted chords. With any chord progression there are many substitution possibilities.
The trick is knowing which ones to use in a particular musical context, and also when not to use substitutions. This knowledge comes from knowing the sounds of a particular idiom and is best developed by lots of listening and lots of playing with other musicians.