Much has been written about the concept of tritone substitution by theorists and musicians far more knowledgeable and talented than myself, so I won’t delve too deeply into it, but since it’s part of this idea behind letting my left hand “teach” my right (unpacking the nice left-hand voicings I’ve memorized, practiced ad nauseam, etc.) and actually doing something with them in the right hand, transferring that information into meaningful improvised lines, I’ll start with the basics of tritone substitution:
The dominant chord is the magic chord in jazz. It’s the chord with the most tension, the most possibilities, the one that often screams for resolution. I can do almost anything with the dominant chord. I can delay the resolution, or play “around” the resolution (a la Bill Evans) with a series of altered dominant chords to introduce a standard tune. It’s the chord that allows the most alterations. And beneath all those alterations are the major third and the minor seventh, which define the quality of the chord. Beneath all the possible alterations (i.e., flat nine, sharp nine, sharp eleven, thirteen, etc.), these two notes, the third and the seventh, still define it as a dominant chord. They also happen to form a tritone, or a flatted fifth. Flip them around, make the third a seventh, and the seventh a third, and I’ve got a different dominant chord: the G7th becomes Db7th, the C7th a Gb7th, and so on.
So I have a lot of options when I’m improvising over a ii-V-I. I can still play in the Dorian mode with the minor ii chord, or I can ditch the Dorian and start using that Mixolydian mode derived from the new tritone sub; for example, I can improvise in Db Mixolydian in my right hand while still playing the D minor to G dominant in my left hand. Two interesting aspects of improvising this way: 1) I’m playing further and further “outside” the changes, I sound more like the pros, by creating more tension, more suspense to my lines, and because the Db is only a half-step up from C, 2) I’m introducing more chromaticism to my lines. Resolving from the very tense Db Mixolydian to the very relaxed C Ionian will sound good (ah, relief!) when I land on any note in the C major scale with the exception of the fourth, the F natural, which I can either avoid or raise a half-step to make it a sharp eleven.
The smooth chromaticism I get from improvising with tritone subs in the right hand exists in the left hand as well because of the inherent chord-scale relationships. The funny thing is that I was playing tritone subs in my left hand for years before I realized how to “unpack” that information and apply it to my right hand while improvising. For example, I learned the A and B rootless voicings for the ii-V-I progression in every key, but I never stopped to wonder why the V chords were interchangeable.
For the B voicings (7, 9, 3, 5) on any minor ii, I can let the seventh and ninth notes descend a half-step, keep the minor third the same, let the fifth ascend a half-step, and I arrive at the tritone sub, only now I’m playing the subbed V chord in A form. It works in reverse as well: if I play an A voicing (3, 5, 7, 9) for any ii chord, I keep the minor third in place, descend the seventh and ninth notes a half-step, ascend the fifth a half-step, and I end up on the tritone-sub dominant chord in B form.
Transfer the new voicing back to the right hand, play the chord/scale up and down a few octaves, start on different notes of the chord/scale, see how long you can keep the tension going before you resolve to the I chord, and you will hear many new melodic possibilities. Not only the Mixolydian, but the diminished scale (starting with the half-step) works beautifully over these “magic” chords.
We get stuck in routines, stuck practicing certain progressions, not realizing what we’re doing, not taking the time to question why we’ve been taught to practice a certain way. The good news is it’s never too late to re-examine some old aspect of our playing. We may not sound better overnight, but gradually we will acquire a more profound understanding of what we’re doing and why.