Introduction The tritone substitution is a common substitution for a V chord, seen lots in jazz. It looks and sounds complicated but in actuality is criminally simple, and sounds really effective. A tritone is a note 6 semi-tones away. So C > F#, B > F, A > Eb, G# > D etc. A well known example of it is One Note Samba which uses descending chords, from iim, bII7, I7, viim7b5.
N.B for a quick look at roman numerals, click here.
The premise is you can swap a V chord for its tritone partner. Where you might have ii V I, the function of the V remains, but you would use a #I/bII (we'll look at enharmonic equivalents in a second).
A note on 'enharmonic equivalents' In short it's knowing when to use C# and when to use Db, or other permutations. By rule of thumb if you have a C major scale you 'sharpen the 5th' the note which changes is G, to G#. In addition if you flatten the 6th, A becomes Ab. The keen-eared among you will realise they are technically the same note, however it's how you describe it that's important. The reason I bring it up is that I'm going to use both to be ultra-confusing, this is largely down to (my knowledge) there not being a standardised way to talk about triton be substations, I've seen both Dm, C#7, C and Dm, Db7, C. It is key to understanding the difference but not the be-all and end-all, sound is more important. That said I'm sure Wikipedia could tidy my explanation up.
Here's a simple example in C
| LH | RH | chord |
| D | F A C E | Dm9 |
| C# | F A B E | C#+7(#9) |
| C | E G B D | Cmaj9 |
sample example with different inversion.
| LH | RH | chord |
| D | C E F A | Dm9 |
| C# | F A B E | C#+7(#9) |
| C | B D E G | Cmaj9 |
The Lydian Dominant? Unbeknownst to many as to why, the Lydian Dominant scale that is used most frequently when working out our tritone substitutions. Staying with our V chord, in C the tritone away from it would be C# (G > C#). If you swap our the C from C major you get D melodic minor scale (D E F G A B C#). Starting this on the G gives you the mode G Lydian Dominant.
For none-mode people is the same as G Mixolydian (raised 4th, C > C#) but with a dominant 7 rather than a major one (F# > F). Also from the Melodic Minor modes, is the 'Altered scale'.
| in G | in C# | |
| G | I (tonic/root) | (#4 / #11) |
| A | ii (2nd or 9th) | (#5 or augmented 5th) |
| B | iii (3rd) | (dominant 7th) |
| C# | IV (4th or 11th) | (root) |
| D | V (5th) | (flattened 2nd or b9) |
| E | vi (6th or 13th) | (sharpened 2nd/flattened 3rd but commonly known as #9) |
| F | vii (dominant 7th) | (3rd, major 3rd) |
What this means is in when subbing a dominant chord for it's tritone partner, nearly anything from the Altered scale can be added. With the C# (tonic), F (major 3rd) and B (dominant 7th) present, anything goes.
Post-script You can take the whole thing further and swap ever chord, or every other chord. In C, a iii, vi, ii, V , I (Em, Am, Dm, G7, C) could be Em, Eb7, Dm, Db7, C or even Bb7, Eb7, Ab7, Db7, Gb7 - which is a fake departure through several keys, resulting in cyclical dominant chords. Few!