Diabolus in Musica

For centuries now, the resolution of the tritone has been one of the driving forces of change in tonal music. The extension of the V chord to the V7 chord produced stronger cadences when it began to appear around 1600 and has become status quo for any important harmonic passages; this remains true in jazz music, and the standard ii->V->I chord progressions illustrate this. The clever composer can manipulate this technique to create unusual chord progressions that maintain a sense of direction and rationality. This article will discuss a handful of these ideas, hopefully providing solutions to problems that have come up in your own writing.

This first fact to note in the exploration of this ideas is the paradoxical identity of the tritone. In many ways, the interval between F and B defines the C major scale, as traditionally, it must resolve to E and C, most likely in the form of the I chord, C major. Again, this explains the prominence of G7 chords in the key of C major: any space is determined by its beginning and terminating point, in tonal music, this is the tonic and the dominant. But F and B could also resolve in the opposite direction, leading to Gb and Bb. This would lead to the key of Gb – adding the Db to the interval more clearly demonstrates this – which just happens to be the key most distant from C major. As a result, the defining interval of any major key also outlines its most contrasting key. In jazz, this process is referred to as tritone substitution, and is common in the modern jazz repertoire. In practical terms, any time a dominant chord resolves down a half-step, tritone substitution has been employed.

What can be taken from this is that, any time the interval of a tritone occurs, as long as the dissonance resolves properly, the following chord will provide a sense of finality to the dissonant chord. In the last few posts, I've listed a number of extended chords that contain the interval of the tritone, each of which can provide an opportunity for alternate resolutions of the tritone. Here are a few quick examples.

Fmaj7#11 – The lydian chord contains a tritone between its root and the upper extension (it's probably based as an augmented 11th and not 4th, but octave equivalency more or less takes care of the difference). In this case, the dissonant interval occurs between F and B, the same tritone that exists in G7. So, just as G7 can move resolve to two different tonic chords, Fmaj7#11 can resolve to C or Gb.

D-6/9 – The dorian chord contains a tritone between its third and its sixth, in this case, F and B again. Accordingly, this chord can also resolve to C or Gb. As a point of interest, if the chord resolves to Gb-6/9 (it's possible to resolve to minor chords on any of these roots), this resolution can be taken in a cycle of major thirds through the octave, resulting in D-6/9->Gb-6/9->Bb-6/9.

A7b5 – We haven't discussed this chord yet, but it provides ample opportunity to demonstrate non-standard tritone resolutions. The chord is an altered dominant chord arising from lowering the fifth a half-step. In this case, the chord would be spelled A C# Eb G. A closer look at this chord reveals it to be two tritones separated by a minor third, here seen as A/Eb and C#/G. Because of this, this chord offers four possible points of resolution: D, Ab, E, and Bb. Though he would have referred to it differently, the turn-of-the-century Russian composer Alexander Scriabin made ample use of this chord in his later music, using it to push tonality to its ends.

As stated before, this style of deceptive cadence is common throughout jazz music. What's not common is for the substitution to be made in the other direction: that is, on the ii->V section of the ii->V->I progression. In this, the same basic concept is applied, but the substitution is made on the dominant rather than the targeted tonic chord. In the simplest example, the progression D-7 → G7 can be transformed into D-7 → Db7. A more adventurous example could be D-7 → F-7b5: the F-7b5 chord contains the same F and B found in the G7 chord. This concept allows for modulations that essentially reach their goal before they've even started.

In the end, the whole process revolves around the variability of the pitches that surround the tritone itself; as long as the tritone remains untouched, any chord constructed around it will provide a suitable substitute. Some aspects of traditional cadences are lost in the transformation though. Part of the effectiveness of the V7->I cadence is provided by the root movement involved between the chords. Extended use of tritone substitution generally results in awkward bass lines filled with half-steps and large jumps. Additionally, the constant contrast of tritone-related keys can get just as old as anything else. Nonetheless, tritone substitution ample options when looking to break out of traditional chord progressions.