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.
Monday, February 8, 2010
Wednesday, February 3, 2010
Minor Chords
Without retracing too much ground, we'll continue on into the domain of minor chords. Perhaps the most noticeable in transformations of the perception of minor chords came about through the popularity of modal jazz in the 60's. Both So What and Impressions used long stretches of the dorian mode in their song forms, effectively destroying the notion of the minor 7 chord as the subdominant – as in a ii->V->I progression -- or as a tonic minor – which tends to be built in the aeolian mode and is reinforced by V->i cadences. The end result is a sort of harmonic wallpaper that lacks an origin or destination. This effect extends far earlier than this modal music though: from its beginnings, blues has always been based on progressions of unresolved dominant chords.
The following list provides a number of extended minor chords. As before, these can be used as substitutes for any other minor chords in both composition and accompaniment.
Minor Triad – C Eb G
What was said for the major triad remains true for the minor triad. In short, the purity of a triad can create a strong effect when surrounded by extended and chromatic chords. The first movement of Messiaen's Vision de l'Amen for two pianos contrasts tritone-based chords – actually, similar to the voicing Herbie Hancock would use in the 60's – and minor triads to create one of his trademark mystical settings.
Minor 9th – C Eb G Bb D
Since the recordings of Bill Evans and his rise in popularity, the minor 9th chord may have effectively replaced the minor 7th chord for many harmony players; for guitars players especially, the ease of fingering 9th chords makes them by far the most common minor chord substitute. It's a lush, introverted sound that adds color without using any chromatic inflections.
Minor 11th – C Eb (G) Bb D F
The basic extended chord family stretches on the 11th for minor chords. While Major 11th chords are theoretically possible to create, the interval of the fourth (that is, between the root and the 11th) proves to be too dissonant to use practically. As it pertains to the voicing of minor 11th chords, it is common to drop the fifth of the chord: G in the case of C-11. Perhaps due to the number of tones from the major scale represented, the effect generated by the minor 11th chord is one of ambiguity; in fact, a simple respelling can show the chord to be a sus chord suspended over its fifth (Fsus4/C in this case). Though there's certainly nothing wrong with this effect, in order to maintain a sense of harmonic contrast and movement, the chord should be used judiciously.
Minor 6th – C Eb G A
The first modal chord on this list, this chord belongs to the dorian mode. Its dissonant effect is created by the interval of a tritone between the third and the sixth of the chord. It appeared frequently in dance band music of the 60's and before, though in jazz, the ninth of the chord is generally added as well. As a point of interest, the chord is an inversion of the half-diminished chord (in this case, A-7b5/C) and the creative composer can make use of this relationship.
Minor 6/9 – C Eb (G) A D
The minor equivalent of the 6/9 chord, this minor chord is built by fourths rather than thirds, with a tritone between the third and the sixth. It came to prevalence in jazz through the piano playing of Herbie Hancock and the writing of Wayne Shorter during the time period of the Miles Davis Second Great Quintet. Like the minor 6 chord, this chord belongs to the dorian mode, though it has a darker sound quality to it than the standard 6 chord.
Minor 9b6 – C Eb Ab D
Here's a chord that occurs extremely rarely in the jazz literature (to my knowledge, only Wayne Shorter's Iris and Teru call for similar chords. It does appear as a suspension in Israel). Its interval of a minor sixth allow it to be considered as a chord that invokes the natural minor mode, something rarely done in a modal sense in jazz music. Like some of the other chords in this list though, placement and use of this chord must be carefully considered due to its similarities to other chordal structures. Leaving out the ninth would create a major triad (Ab in this case), and even in its full voicing, the chord resembles a major lydian chord.
Minor-Major 7 – C Eb G B
The 7th chord of the melodic minor scale, this chord occurs frequently in latin music. It functions as a tonic minor, though ending a piece on the chord may be questionable (or not, it's really up to your taste and the setting).
As before, playing these chords on the piano is far more important that any text concerning them. The variety of sounds and voicings can't honestly be described in any short amount of time.
The following list provides a number of extended minor chords. As before, these can be used as substitutes for any other minor chords in both composition and accompaniment.
Minor Triad – C Eb G
What was said for the major triad remains true for the minor triad. In short, the purity of a triad can create a strong effect when surrounded by extended and chromatic chords. The first movement of Messiaen's Vision de l'Amen for two pianos contrasts tritone-based chords – actually, similar to the voicing Herbie Hancock would use in the 60's – and minor triads to create one of his trademark mystical settings.
Minor 9th – C Eb G Bb D
Since the recordings of Bill Evans and his rise in popularity, the minor 9th chord may have effectively replaced the minor 7th chord for many harmony players; for guitars players especially, the ease of fingering 9th chords makes them by far the most common minor chord substitute. It's a lush, introverted sound that adds color without using any chromatic inflections.
Minor 11th – C Eb (G) Bb D F
The basic extended chord family stretches on the 11th for minor chords. While Major 11th chords are theoretically possible to create, the interval of the fourth (that is, between the root and the 11th) proves to be too dissonant to use practically. As it pertains to the voicing of minor 11th chords, it is common to drop the fifth of the chord: G in the case of C-11. Perhaps due to the number of tones from the major scale represented, the effect generated by the minor 11th chord is one of ambiguity; in fact, a simple respelling can show the chord to be a sus chord suspended over its fifth (Fsus4/C in this case). Though there's certainly nothing wrong with this effect, in order to maintain a sense of harmonic contrast and movement, the chord should be used judiciously.
Minor 6th – C Eb G A
The first modal chord on this list, this chord belongs to the dorian mode. Its dissonant effect is created by the interval of a tritone between the third and the sixth of the chord. It appeared frequently in dance band music of the 60's and before, though in jazz, the ninth of the chord is generally added as well. As a point of interest, the chord is an inversion of the half-diminished chord (in this case, A-7b5/C) and the creative composer can make use of this relationship.
Minor 6/9 – C Eb (G) A D
The minor equivalent of the 6/9 chord, this minor chord is built by fourths rather than thirds, with a tritone between the third and the sixth. It came to prevalence in jazz through the piano playing of Herbie Hancock and the writing of Wayne Shorter during the time period of the Miles Davis Second Great Quintet. Like the minor 6 chord, this chord belongs to the dorian mode, though it has a darker sound quality to it than the standard 6 chord.
Minor 9b6 – C Eb Ab D
Here's a chord that occurs extremely rarely in the jazz literature (to my knowledge, only Wayne Shorter's Iris and Teru call for similar chords. It does appear as a suspension in Israel). Its interval of a minor sixth allow it to be considered as a chord that invokes the natural minor mode, something rarely done in a modal sense in jazz music. Like some of the other chords in this list though, placement and use of this chord must be carefully considered due to its similarities to other chordal structures. Leaving out the ninth would create a major triad (Ab in this case), and even in its full voicing, the chord resembles a major lydian chord.
Minor-Major 7 – C Eb G B
The 7th chord of the melodic minor scale, this chord occurs frequently in latin music. It functions as a tonic minor, though ending a piece on the chord may be questionable (or not, it's really up to your taste and the setting).
As before, playing these chords on the piano is far more important that any text concerning them. The variety of sounds and voicings can't honestly be described in any short amount of time.
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