quartile harmony

As one definition of the term quartile allows, we infer that "quartile harmony" is basically predicated on the idea of stacking pitches using the interval of the fourth to create chords. In theory, what we are doing here is to simply build chords using the diatonic pitches from whatever melodic resource chosen and stacking them in perfect and augmented fourths, as opposed to the perhaps more common intervals of major and minor thirds, as in tertian harmony. So, with such an exhaustive harmonic resource created with tertian harmony, why are the quartile colors potentially important for the creative musician?

Well, even though these colors are perhaps a bit unusual at first and take some shedding to successfully integrate them into our musical palette, once under one's fingers, the quartile harmonic colors provide a cool alternative for creating different degrees of tonal stability and the disguising or obscuring of tonal direction and intent. When mixed into the more conventional tertian chord construction, the quartile sounds provide a startling contrast and a degree of tonal color not really attainable with the more conventional tertian chords ( at least to my way of hearing things ). When used exclusively, the quartile colors create their own, rather unique musical environment, oftentimes prompting melodies created with a similar intervalic structure. In blowing or vamp sections, where the written harmony is presented as one or two chords for extended lengths of musical time, these voicings in fourths create some interesting alternatives and fresh possibilities. In modal tunes in either the major or minor tonality, the quartile colors can provide a solid resource to create a variety of sounds and colors, while remaining diatonically within the modal color.

Important color for folk, blues, rap, rock, hip hop artists? No. Pop music? To some extent, especially with the tonic colors. Jazz? But of course.

With this in mind, let's create our handy chord spelling chart to identify the pitches of the seven ( 7 ) diatonic seventh chords built in perfect and augmented fourths. In comparing quartile and tertian chord construction, please note that the building of chords in diatonic fourths ( quartile ) simply replaces the fifth of the chord with it’s diatonic fourth, while the third degree remains the same in all seven of the diatonic seventh chords. Thus, these 7 diatonic chords follow the same major / minor scheme as their tertian counterparts. Using C major as our tonal center, these chord spellings would also be exactly the same for the relative minor of C major, A natural minor, as in the tertian harmonic world. Example 1.

Let's listen to a realization of these chords in the key of C major. Example 1a.

In obscuring tonal direction, the quartile colors dissolve the destination of many of the more common cadential motions we commonly use with tertian chords. Thus, we can reduce the effects of tonal gravity while not diminishing our sense rhythmic forward motion. Here are a couple of common chord progressions associated with tertian harmony, in many of the styles of American music, revoiced with quartile colors from above. Using C major, here is the essential One / Four / Five / One cadential motion "quartilely" colored. Example 2.

Wow, that's a bit different eh? What kind of melody does this sound inspire? Example 2a.

Basing lines on the interval of a fourth. How about the Two / Five / One motion? Example 2b.

In both of the above examples, even though the dominant or Five chord retains the leading tone pitch ( B ), it's color and the tonic it resolves to are quite a bit different than it's tertian counterpart yes? As contrasted to bar 16 above? Is our ability to create cadential motion and the sense of "arrival" at a tonal center are dramatically reduced when we employ the quartile colors? Do you dig the sounds? Why would we want to reduce this tonal gravity and sense of arrival at a tonal destination? Well, that depends of course on one's artistic direction. Do we commonly find these colors in blues, folk or rock? No, not likely. In jazz? Again, not all that common, until we examine a more modally based style of jazz and / or in performance situations, where the harmony is said to be static, implying that one chordal color, based on a single root pitch or pedal tone, is provided for the artist to solo over for extended lengths of musical time. In these performance situations, we can oftentimes readily employ the quartile colors to provide a greater degree of variety for these potentially "static" harmonic situations. 

For example, one use of chords built in diatonic fourths might be to employ these colors to "gravitate" around the particular chord in use. Thinking D Dorian as the single chord for an 4 bar phrase which is repeated, thus our basic written harmony is D minor seven ( D min 7 ). Diatonically gravitating around this tonal center with quartile sounds, we can provide a good bit of harmonic variety without damaging the static nature of the harmony or overall Dorian minor modal essence and color. Thus, thinking of an four bar phrase in D Dorian, here is one possible combination of quartile colors. Example 3.

Well? Interesting sound huh? Perhaps not a whole lot different in concept than when employing tertian chords, but just that the quartile colors, with their absence of a fifth degree in each of the chords, softens the overall effect, creating a unique tonal environment and harmonic motion. Perhaps part of my problem in describing this approach is due to the prevalence of the major scale / diatonic harmony in so much of our American music, whatever the style we examine. Suffice perhaps to say, that one must explore the resources available and simply decide what is needed to create their work, while trying to keep an open and curious mind to new possibilities. Jazz piano great McCoy Tyner, who spent many years performing with saxophonist John Coltrane, has made the parallel motion / planing of chords built in fourths one of his many "trademark" sounds, while improvising in the jazz medium. Mr. Tyner is perhaps one of many artists who have come to love and rely on this potentially outside component on their musical palette, to recreate the "art in their hearts." When time permits, check out John Coltrane’s modal contribution "Impressions."

What happens when we combine the "best of both" of the tertian and quartile systems of building chords? Well, depending on your tastes in harmonic cuisine, potential total "hybrid" coolness. Really? Well, depends on what you think is hip n'est pas? Pour moi, the harmonic colors created by combining these two approaches are indispensable components on my musical palette. I like some of the quartile chords for their unique brightness, their ease of playabilty and chromatic shifting, i.e., half step lead ideas on the guitar.

The quartile / tertian hybrid major tonic chords are very bright, perhaps brighter than any combination of building chords exclusively with thirds. Players commonly refer to these chords as the major 6 / 9 colors, based on their numerical interpretation from a tertian theoretical perspective. And as the major colors are perhaps brighter, for me these hybrid minor colors are potentially darker, they go deeper into the "well" of the minor tonality, thus perhaps an increased potential for expressing warmth, sorrow, love and passion and compassion? I think so, but then I'm a guitar player, ya know, the folks that like to hang with real musicians? Or are they drummers?

Let's compare some of the common tertian voicings with combinations of tertian and quartile hybrid choices, organizing our inquiry by chord type, i.e., the Two or minor 7th chord, the Five or dominant 7th colors and the One / tonic or major 7th chord type, employing common chord progressions to create vehicles to motor these hybrid colors. Thinking One Four / Five / One in C major, example 4.

Well? Ya still there? Does the chord in bar 24 knock you out or what? Pretty bright huh? Sorry, just kidding. The tonic / One chord in bars 22 and 24 is a combination of major third, then stacking diatonic pitches using the interval of a perfect fourth. Are you cool with the labeling of this chord? C 6 / 9? Let's explore the theory a bit of where these numbers come from. Here is a chart to sketch out the ideas. Example 4a.

Are you cool with spelling chords? Yes? Cool. So, this C 6 / 9 is basically a major chord that functions well as a tonic type chord. C is the root, it's major is 3rd E, the number six ( 6 ) in the labeling of the chord is based on the idea that the pitch A is the sixth scale degree of the C major scale. The ninth D is so designated as it is one octave plus a major second above the root C. The fifth G is simply the fifth scale degree of the C major scale. Cool with this way of understanding the pitches / numbers relationship? Again, are you cool with how to spell out the pitches of any given chord? Mastering this theoretical ability to spell chords can be a quantum leap for the emerging theorist.

Here are some other fairly common voicings of hybrid tertian / quartile chords that simply present various configurations and combinations of the musical elements, basically providing for different pitches termed to be in the lead. All of the harmonies are tonic type chords which will potentially function well as the One or Four chord in the major tonality or Three and Six in the minor tonal environment. All of the roots of the following voicings are C. Example 4b.

With the Two chord type, or minor seven colors ( ii min 7 ), our hybrid chordal colors very much resemble our tonic colors just examined above, for in essence these two types of chords are created from the exact same arpeggio within equal temper. It is in how we stack the pitches, i.e., what intervals we use, that creates the main dichotomy of our musical environments, namely major and minor. Using the Two / Five / One cadential motion, lets compare possibilities of the tertian and hybrid tertian / quartile approaches to building chords. Example 5.

Beginning to hear the subtle difference between the two building processes? What does this mean to your creative process? Are you already hip to the quartile colors?

In examining the dominant seventh chord type ( V 7 ), creating hybrid tertian quartile chords softens the sense of dominant quality into creating colors more akin to the Two and One chord types. Compare the following possibilities using the Two / Five / One cadential motion. Example 6.

Cool huh? One interesting possibility worth noting at this juncture in the discussion, involves using different inversions of the Five chord. Once the root of the Five chord is omitted, are we not less constrained by the traditional forces of tonal gravity? Check out the following possibility. Example 6a. 

In bar 38 we simply think 3rd inversion V 7, then move the shape upward in parallel motion using the diminished whole tone / half tone principle and resolve. Sure is an easy way to get out there eh? A simple but potentially very effective use of the hybrid tertian / quartile colors involves working the magic via the half step lead in. Using the same cadence as above, check out the following idea. Example 7.

Interesting solution to the Two / Five paradigm eh? We simply moved one quartile voicing or constant structure up chromatically. The first move away from Two got us out of the C tonality into... The second half step up moved us back into C. So, is every other half step move with a quartile voicing part of the chosen key center? What's in between? Is this part of the tonality without a tritone thing? Is it important? Could very well be. So, you are hip to this artistic technique of the "half step lead in" yes? Check this out. Blues harmony idea in fourths, simply moving stacks of fourths about by half step. Example 7a.

In theory, 3rd inversion, blue tonic chord to first inversion etc., motion based on the traditional blue shifting of the tritone by half step to create the principle changes of the 12 bar blues. Just high powered versions of the 3 chords. Perhaps try to place these three chords into a 12 bar blues. Resolving to C major adds a tonal perspective yes? So simple in concept, coloring the half step motion quartile can create a bright and very exciting events in the music we are creating.

Things to perhaps ponder from the above discussion. Do you dig these colors? In the music you are currently creating, is there any need or place for the quartile colors? And for that matter, any room for venturing outside the musical environments you create? Does viewing any chord as being one of the three chord types, each with a distinct function, work for you? So many questions eh? How much truth is there to the idea that perhaps "one's intelligence can be measured by the quality of their questions?" Look through the improv / convergence section for additional ideas using the quartile colors.

Where to next?

review new ideas

"The person who removes a mountain can begin by carrying away a small stone." Ancient proverb.