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” for a variety of reasons. First and foremost, in order to maximize combinations, it is useful to be willing to consider two triads that may share one or more notes. Additionally, the examples in this entry are specifically assembled with two separate, clearly-defined three-note elements in mind. Likewise, I’m hesitant to use “trichord” because the three-note elements are among the most fundamental building blocks of traditional diatonic music (major, minor, augmented, and diminished triads). I may change my mind about this later.
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.