Polychords are a great way of introducing fresh sounding harmony into familiar progressions. We have previously discussed “dominant” polychords in the article Polychords-Harmonic Resources of the Diminished Scale posted on September 30, 2011. I was working with an advanced student the other day and he got me thinking about the possible polychords that could be used to substitute for other standard chords in a key. I decided to work with the ii-V-I progression, since we all know this is a ubiquitous progression in jazz, and figure out possible substitutions for these chords based on triads that can be extracted from what I call a “super-chord” which is generated by simply stacking thirds (1-3-5-7-9-11-13 or every other note) derived from common scales.
For example, for the tonic (I) chord I use two scales to generate my triads. First is the Lydian mode and second is the relative melodic minor of the tonic key. Since my examples are in C major I use the C Lydian mode and the A melodic minor scale. These two scales contain tones that are commonly added to tonic chords when the chords are extended to their upper limits. For example we would never add an F-natural to a tonic chord as an eleventh extension but we would add an F-sharp (sharp 11), so Lydian is a natural choice for tonic. I also wanted to introduce the raised fifth or G-sharp since the sound of a Major7#5 has always intrigued me. The best choice of scale then containing both these altered sounds is A melodic minor.
For my supertonic (ii) chord I use the Dorian mode since it is the major sixth that is commonly added to the minor triad. To introduce the major seventh sound I use the melodic minor since this scale contains both the major sixth and the major seventh.
The dominant (V) chord is the most complex so I use three scales for this one. The basic Mixolydian which extends the chord through the thirteenth and two other scales which include the altered tones (#5, b5, #9 and b9) commonly added to the dominant; namely the Lydian Dominant or fourth mode of melodic minor and the Altered Dominant scale or seventh mode of melodic minor. For further explanation of these scales please refer to my previous article Jazz Improv.-Scales for Altered Dominants posted on July 11, 2011. These altered scales can also be combined to generate even more triads but I don’t want to get carried away here.
The idea is to show all possible triads that can be generated by these scales and superimpose them over the roots of the corresponding tonic (I) supertonic (ii) and dominant (V) chords. Page two of the pdf contains examples of ii-V-I progressions using these polychords in different combinations in a smooth, connected way exploiting the more “out” sounds since that is the main goal here.
When using these voicings you might consider using a more stable tonic (I) chord as a point of resolution in order to bring the progression back down to earth, so to speak, since too many distant harmonies might be a bit much for most ears (including mine) to take in.
When soloing, try using all these triads played as arpeggios over the corresponding chord type. For example when soloing over CMaj7 (I) try using any or all of the triads shown for the tonic chord (C, Caug, D, E, Em, F#dim, G, G#dim, Am and Bm). Do the same for the ii and the V chords. One of my favorite and easy to remember combinations is the superimposition of three major triads ascending chromatically over the ii-V-I bass line. (See measures 3-4 and 13-14 on the Polychord voicings page for examples). Start with the tonic triad (C) over the root of the ii chord (D), move to Db major over the root of the V chord (G) and end with D major over the root of the I chord (C). These triads can also be used very effectively when comping as a way of filling space between long stretches of a single static harmony.
The pdf below shows the triad choices for the I, ii and V chords as well as examples in the context of a ii-V-I progression. These are just to get you started as the possibilities are almost limitless in terms of voicings and triad combinations. Experiment and have fun.