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.
I’ve always been incontrollably drawn to composers and improvisers who have managed to deconstruct music down to its most basic building blocks and reassemble them into something that is truly new. Olivier Messiaen was such a composer. His work features a language containing, among other things, elements of tweaked Hindustani rhythms, symmetrical scales, a deep appreciation of spirituality, and an embracing of the new and unexplored.
This post is to be the first in a series focusing on Messiaen’s Modes of Limited Transposition. I’ll be focusing on two of the modes in particular, for reasons that I hope will become evident as time goes on. But first, a brief primer on what these modes are, peppered with my own commentary.
The term “limited transposition” refers to the fact that the intervallic relationships of the notes of these modes will repeat themselves – yielding the same “mode” over and over again – after a few transpositions. The number of transpositions depends upon which mode is being used. Mode 1, for example, is built entirely upon whole-step relationships, and is referred to outside of Messiaen’s world as the “whole tone scale”:
The mode consists of six pitches, exactly half of the twelve notes available to us from our basic harmonic and melodic pallet. Because of their symmetrical whole-step relationship, this mode will yield the six pitches over and over again, independent of which note you start on:
If we transpose any of these modes by half-step, this will result in the other six pitches:
So, it can be said that the number of transpositions for this mode is limited to two.
From a conceptual standpoint, and from where I stand, a limit of two transpositions can be thought of in the same way as a limit of twelve transpositions for the chromatic scale, or for any of the more common major or minor scales. For this reason, I’m not a fan of using the term “limited transposition”. While it serves to set these modes apart from traditional tonality, and also allows Messiaen to put his own stamp on his harmonic language, all scales and modes, symmetrical and otherwise, are limited by some number of transpositions.
Messiaen’s list of which symmetrical modes are included and which are not is arbitrary, and based largely upon his own likes and dislikes. The use of symmetrical modes did not originate with Messiaen, and can be found within the works of previous composers, more notably Debussy’s use of the whole tone scale (Messiaen’s Mode 1) and Rimsky-Korsakov’s use of the octatonic scale (Messiaen’s Mode 2). In addition, symmetrical modes are not specific to classical music. Duke Ellington, John Coltrane, and many others make significant use of Mode 1 and Mode 2. There are volumes written on these two modes in particular. It is my intention in these articles to focus instead on two others, with an exploration of how they may be used both in composition and improvisation, with examples. See the next post for more.
Me on a recent visit to Église de la Sainte-Trinité, where Messiaen was organist for over 60 years.
“The ominous mood, emphasized in part by indeterminate black goo, gives way to a soaring sax solo.”
“. . . a soulful sax solo.”
“. . . an impressive saxophone solo.”
–Man On the Moon