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.
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:
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:
The following is an extension of my previous post. Whereas the last post looked at a series of trichords derived from Messiaen’s Mode 3, the grids below depict tetrachords derived from the same. The first grid is all possible combinations of any four pitches (pitch 1, pitch 2, pitch 3, and pitch 4). The second grid is a collection of tetrachords that occur when applying certain step/skip patterns to the Mode. In comparing these tetrachords to traditional harmony, you’ll see Major 7 chords in Type 5, Dominant 7 in Type 4, Minor 7 in Type 3, Major 6ths, Minor 6ths, and more.
Continuing on from my last post about the subject, the following matrix depicts one transposition of Messiaen’s Mode 3:
In keeping with the last post’s concept of looking at the mode as a symmetrical collection of trichords, the matrix below charts all possible arrangements of three pitches (listed here as pitch 1, pitch 2, and pitch 3):
Much in the same way that triads are made from skipping notes within major scales, the following is a series of trichords that are made up of different combinations of skipping and stepping through the scale:
These trichords are selected and named arbitrarily, with the intention of displaying some of the vertical possibilities of Mode 3. For example, Type 4 contains a series of trichords that can be looked upon as major triads. Likewise, Type 3 contains trichords that are identical to minor triads, Type 2 contains diminished triads, and Type 5 contains augmented triads. There are other trichords within each of these grids that can suggest some other tonalities, or better yet, can be used as a means of combining tonalities.
Extended tonality, polytonality . . . however you choose to define it, Mode 3 provides a systematic way of combining three triads (such as Type 4’s C major, Eb major, E major, G major, Ab major, and B major) that would not be possible within the traditional major scale-based system.
In my last post, I mentioned a fondness for Messiaen’s knack for using symmetrical pitch sets as a means of generating melodic and harmonic material. This post will focus on introducing Messiaen’s Mode 3:
There are texts that refer to this collection of notes as the “nine-note augmented scale.” And while they’re not incorrect, I hesitate to use the term “augmented,” as it implies that the scale is only useful over augmented chords. If looked at vertically, we’ll find that there are many major, minor, and diminished triads, seventh chords, and plenty of other functional harmonic sets available within this collection of notes.
As a means of highlighting both the symmetry and melodic possibilities of the scale, I like to look at this mode as a series of three identical trichords. A trichord, plain and simple, is a collection of three pitches, arranged in any order. The pitches in question for this discussion are:
Messiaen’s Mode 3 consists of nine notes. These nine notes can be broken down into three trichords.
By starting on a different note within the mode, or by skipping notes, several trichords are possible. My choice of this one in particular is arbitrary, as is my use of numbers and shapes to differentiate one pitch from another, and one trichord from another.
The trichord used above consists of a whole step (C to D) followed by a half step (D to Eb). Since C is a major third from E, and E is a major third from G#, and G# is a major third from C, using each of these notes as a starting point will provide symmetrical relationships from trichord to trichord.
See next post for more.