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 D minor and C major, which can sound very much like D minor 11 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 simultaneous sounding of multiple clearly articulated ideas in multiple clearly articulated keys.
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.
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:
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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.