An augmented triad consists of two major-third intervals. There are a few different ways to think about these, including the standard formula of 1–3–#5. This is an interesting sound because it doesn’t occur naturally in a diatonic scale. Since the intervals within the chord are equal, any note of the chord can be considered the root. Saxophonist John Coltrane used augmented triads to create his major thirds cycle, which occur in such compositions as “Countdown” and “Giant Steps.” Diminished Triads. The diminished triad is made up of two minor-third intervals stacked over a root. Think of it as a standard minor triad with a lowered fifth (1–b3–b5). It occurs naturally in a major scale when you create a triad based on the 7th degree. As with the augmented triad, any note in the chord can be considered the root. —Jason Shadrick
Unlike the piano, the guitar divides naturally within a specific series of numbers. The piano divides by seven, plus five, adding up to 12 (seven white keys and five black keys), while the guitar divides by three or four (three of the same augmented chords or four of the same diminished chords) horizontally multiplying each other into a total of 12 (either 3 x 4 or 4 x 3). This results from the fact that in augmented and diminished chords, any note can function as the root.
The common inversions for both the augmented and diminished shape can be seen in Fig. 1. When any of these forms are viewed horizontally, they automatically unfold repetitively with the same fingerings. This happens either four frets apart (augmented) or three frets apart (diminished). Also, they can be organized as seven “common” groups of augmented triads, as well as five “common” groups of four-tone diminished clusters.
Once these common groups of “parental” forms are memorized, the instrument harmonically begins to multiply itself into an automatic vocabulary. Unlike most methods that are based on scales, the extension of these forms unfolds from a system based upon a study of opposites. Its first application moves us through ascending or descending alterations of any of the single tones within the chosen form. In other words, once the form is decided, this type of alteration produces its next stage of expansion.
For example, the alteration of the central triad, (C, E, or G# augmented) in Fig. 2 produces some interesting results. By lowering the G# to G, the triad becomes C major. By raising the same tone (G# to A), it becomes the relative minor triad—A minor—in the key of C. The same phenomenon takes place when applied to either of the other two chord tones, producing a total of three major (C, E, and G#) and three minor alterations (Am, C#m, and Fm) of a single augmented triad. Of course, four of them in a horizontal row (4 x 3) result in all 12 keys before the next series of its automatic inversions. As it was presented above through horizontal alterations, it now shall follow as automatic fingerings in vertical forms, viewed in Fig. 3.
In the upcoming studies, the harmonic forms we’ve covered so far will not only continue to expand, but shall also serve as the architectural groundwork for melodic linear studies. Next month, we will look at how the diminished form creates automatic voicings for dominant chords.
With a discography that stretches out over 40 years, Pat Martino has developed a unique voice that has influenced generations of musicians. Here are four albums that cover four distinct periods in Martino’s career.
This record established Martino as a leader—at only 23—in the soul-jazz scene during the late ’60s. Propelled by drummer Mitch Fine, organist Trudy Pitts keeps the young guitarist on his toes, and together they embody the classic jazz-organ trio.
• “Just Friends”
• “A Blues for Mickey-O”
Baiyina (The Clear Evidence)
Experimenting with Indian influences, Martino recorded this album of originals that opened many young guitarists’ ears to music and rhythms outside of mainstream jazz. Combining a classic jazz rhythm section with tabla and tamboura was very psychedelic and adventurous for 1968.
• “Distant Land”
After recovering from a brain aneurysm, Martino returned to the stage in 1987 for a live gig in New York City. Comprising of only four tracks, the album shows Martino in strong form, and the tunes give him plenty of room to stretch out over the swinging foundation provided by bassist Steve LaSpina and drummer Joey Baron.
• “Do You Have a Name”
On the title track, Martino creates a musical motif using three words: “Coltrane,” “Tenor,” and “Blue.” He matched each word up with a note in the Aeolian mode and then improvised the phrasing and chord changes. The result is a great combination of intellectual and extemporaneous expression. Pure Martino.
• “Think Tank”
• “Dozen Down”
Since his first recording as a leader in 1967, Pat Martino has constantly pushed the limits of jazz guitar with his flowing technique and powerful, muscular tone. Showing no signs of slowing down, Martino still travels the world performing and giving lectures about his approach to the guitar. Currently, Martino is working on an autobiography and serving as adjunct faculty at the University of the Arts in Philadelphia. For more info, visit patmartino.com.