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 the simultaneous sounding of C major and D major triads, which can sound very much like C Lydian 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 manifestation of multiple ideas (or even a single idea) clearly articulated in multiple tonalities. “Tonalities” can refer to a major scale-sounding key center, a modal plain or environment, or any harmonic entity consisting of no less than three pitch classes (see my previous post, “Messiaen Mode 3 – Matrix & Trichords” for reasoning against considering single notes and dyads as harmonic entities).
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.
with Carter Thomas Arrington (gtr), Glenn Raxach (gtr),
Ed Friedland (bs), Ryan Anthony (drm)
The Daily Show Podcast is soliciting fans for new versions of their theme song. I took a swing at it. It’s a modest attempt using Logic Pro 9, and the saxophone was recorded on a Zoom H4N using the built-in mic. Given the conditions, the saxophone is out of tune, but I think it’s a valid attempt:
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.