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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.
Since this is the first time I’ve taken time to try to explain these ideas in writing, I welcome comments and suggestions. Communication is only effective if it is understood. Your feedback in the form of polite comments is appreciated.
This composer’s collective was originally formed at a recent workshop led by jazz legend Dave Douglas. Each member writes a new piece specifically for this event. Creativity ensues, chances are taken, and ears are rewarded.