I’ve been spending a lot of time with triad pairs recently. I find that they are a good way to combine diatonic with non-diatonic elements, and can point in the direction of polytonality.
While previous entries have used the terms “trichord” and “tetrachord” to refer to cells derived from supra-tonal scales/modes, I’m hesitant here to use the term “hexachord,” because the examples in this entry are specifically assembled with two clearly-defined elements in mind, and these elements are among the most fundamental building blocks of traditional diatonic music (major triads).
I’ve spent some time practicing major traids in different relationships, beginning with the least amount of distance, and venturing out. In the case where two major triads share a note with each other, I’ve been practicing it both with re-articulating the shared note, and also not re-articulating the shared note. The latter approach can upset the rhythmic symmetry of a pattern, which is almost never a bad thing.
While I won’t take up space here with diagrams of triad-pair exercises (Bergonzi’s Hexatonics and Gary Campbell’s Triad Pairs for Jazz are excellent sources), I would like to illustrate a couple of practical applications that I am finding useful.
Beginning with half-step relationships, F major and E major triads can be useful over ii and V in the key of C, while also generating interest with non-diatonic tones. The same can be said for C major and B major triads over the I chord:
As is the case with most things I practice, I find that practicing inversions is a good way to become as thorough as possible with an idea:
Likewise, two major triads separated by a whole step can reinforce diatonic stability while at the same time adding a small amount of non-diatonic color:
Experimenting with different types of triads and with relationships beyond half-step and whole-step will provide more melodic possibilities, some leaning more towards polytonality than others. In my experience, peppering a diatonic melody with a rogue triad from another key can help guide my ear towards melodic possibilities that would not occur in a purely diatonic environment.
I thought I had posted this months ago. Regardless, here are a couple of exercises (“licks”) that I came up with that help to demonstrate some melodic possibilities of Messiaen’s Mode 3 (see previous entries for an in-depth explanation):
The following ii V I exercise (Exercise 1) begins by utilizing the D Dorian scale as a means of firmly establishing our overall C major tonal framework. Generally speaking, I often believe that it’s usually a good idea to let listeners (and at times, myself) know that I’m comfortable with adhering to a key before venturing off into supra-tonal territory. In the second measure, the root of the chord is played first, again as a means of continuing to establish a C major foundation, and also as a means of transitioning into Messiaen Mode 3. From the second note forward, triads are played in a “down-up” directional motif. These triads are of the Type 2 variety (see previous entry, Messiaen Mode 3 – Matrix & Trichords).
The following exercises are inversions of Exercise 1. The same Dorian and Mode 3 material is utilized in the same places, but the exercises begin on the third and fifth of the D Dorian scale, respectably:
I purchased a book a few years ago that purported to teach jazz musicians how to improvise in a polytonal fashion, and found variations on a single lesson within the text, revolving around the idea of arpeggiating a specified order of unrelated triads over a pedal bass note. The idea was similar to Coltrane’s Naima, which, while incredibly beautiful, has never struck me as a polytonal composition.
Correspondence with the author caused me to believe that we seemed to have different ideas on what exactly constitutes polytonality. Further exploring through text books, video lessons, and recordings brought to my attention that there are several different definitions in regard to what polytonality is, and how it is executed.
Whereas the aforementioned text purported the idea of long strings of non-related triads over a steady pedal tone, a piano instruction video I found listed polytonality as any two chords played together. The example given to illustrate this method was the simultaneous sounding of C major and D major triads, which can sound very much like C Lydian or some other single harmonic entity. There are many combinations of further-related triads or seventh chords that, when sounded together, don’t really cut it in terms of sounding like two or more distinctively different entities.
In his text 20th Century Harmony, composer Vincent Persichetti defines polytonality as, “a procedure in which two or more keys are combined simultaneously.” He goes on to specify that “each melodic line should retain its own individuality.” And while I don’t want to be so bold as to put words into Persichetti’s mouth, I’d like to expound on his definition/instruction by stating that, at least to me, polytonality is the manifestation of multiple ideas (or even a single idea) clearly articulated in multiple tonalities. “Tonalities” can refer to a major scale-sounding key center, a modal plain or environment, or any harmonic entity consisting of no less than three pitch classes (see my previous post, “Messiaen Mode 3 – Matrix & Trichords” for reasoning against considering single notes and dyads as harmonic entities).
My own experience has taught me that a clear key must be defined and appreciated in order to provide adequate context for diatonically unrelated new material to achieve the full desired effect.
The two examples below help to illustrate my point:
In each example, a line is established, beginning in the same key as the accompanying harmony. Once this home key center is made clear, new keys are introduced, sometimes briefly (as in the first example) and sometimes for longer periods (as in the second). Through a system of substitution, diatonic melodies in various keys are clearly defined and superimposed.
This type of polytonality is common to the compositions and improvisations of the players from the Tristano school, particularly alongside the use of motivic development, and particularly with motives that cross the bar line.
with Carter Thomas Arrington (gtr), Glenn Raxach (gtr),
Ed Friedland (bs), Ryan Anthony (drm)
The Daily Show Podcast is soliciting fans for new versions of their theme song. I took a swing at it. It’s a modest attempt using Logic Pro 9, and the saxophone was recorded on a Zoom H4N using the built-in mic. Given the conditions, the saxophone is out of tune, but I think it’s a valid attempt:
Along the same lines as my previous post on Messiaen Mode 3, Mode 4 possesses some tonal colors that are interesting and perhaps even a little more practical.
Whereas Mode 3 is a symmetrical arrangement of three identical trichords, Mode 4 is a symmetrical arrangement of two identical tetrachords, each made up of three half steps. The tetrachords are separated by the distance of a tritone:
Parsed out into groups of four notes, the Mode 4 matrix looks like this:
By establishing a pattern of steps and skips between notes, we can build the following trichords (among others):
Note the similarities between Type 3 and Type 4 (think of them as inversions of each other). These two types also contain two major and two minor triads.
Like Mode 2 (octatonic scale), Mode 4 can have applications over dominant chords. The following lick can be heard by a number of modern jazz masters, including Michael Brecker, Donny McCaslin, and others: