Schrodinger's Tritone Sub

ii-V7-I (drop 2 and 3)


I was practicing my major ii-V-I's (drop 2 and 3) as usual when I noticed something interesting... First of all, this is a standard progression that goes Dminor7 - G7 - CMajor7.







How it normally sounds: 



On a specific voicing, 1-3-7-5, of the minor-7 chord, it feels natural to go to a dominant flat-5 chord instead of the vanilla V7.

ii-V7b5-I (drop 2 and 3)


In the key of C, this would be D-F-C-A going to Db-F-B-G, as shown on the left. Accidentally playing this progression, I wasn't offended because it's a cool sound. Observe the chromatic descending line in the bass.







Same progression, but with a V7b5:



ii-V7b5-bVM7

As I resolved the dominant chord, my fingers, by their own agency, proceeded to play a Gb-Maj7 instead of CMaj7. Voiced Db-F-Bb-Gb, this chord is a tritone away from the tonic, but it doesn't sound bad at all. In fact, if I wasn't expecting to hear a C-Maj7, it'd be a completely normal resolution. This progression can also be thought of as a ii-V in Gb Major, but with a tritone substitution on the ii chord.






ii-Vb5 in C, but I resolve to Gb Major




But the real question is, is this dominant sound G7 flat-5 or a Db7 flat-5? The answer is yes. When you hear this sonority, you can conclude that it is simultaneously a tritone sub and not a tritone sub. It is Schrodinger's Tritone Sub.

The justification for this is that any Dominant flat-5 chord is a tritone sub of itself. If we layout the notes in ascending order G-B-Db-F, then plane the same shape a tritone up, we get Db-F-G-B. Same notes, exact same intervals! For this reason, a Dominant flat-5 only has 12 potential voicings, as opposed to the 24 that the standard 7th chords contain.



Now observe the same progression, but a tritone away, in the key of Gb:


ii-V7-I in Gb




ii-Vb5-I in Gb


ii-Vb in Gb, but resolve to C



It's really important to observe that the keys of C and Gb contain the same Dominant flat-5 chord and thus can resolve to either key.

Now try it on your guitar. Play this Db7 flat 5 voicing on the middle 4 strings.








Then, move every finger up exactly 6 frets...


Now you have G7 flat 5. Cool! This is the same sound as a french augmented 6th, as the classical nomenclature dictates. How does it work? Well, the chord contains 2 tritones. G-Db and B-F. And when you move a tritone up by a tritone, you get another tritone. It's similar to how a fully diminished chord may be moved up by either a minor third or tritone and maintain the same chord tones.



But why is it called Schrodinger's Tritone Sub? Well, it's simple. The thought experiment Schrodinger's Cat concludes that if a cat is in a box and you can't see whether or not it's alive, you must assume it's both dead and alive at the same time. In this case, the Dominant flat-5 chord is the dead/alive status of the cat, the tonic chord is the box, and it's resolution is the equivalent of opening up the box to get an answer.

This chord relationship allows one to modulate a tritone away at whim and thus thwart the listener's expectations. How do you like to use Dominant flat-5 chords? Let me know in the comments!

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