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.
There are elements within an instrument’s
architecture that initiate a
continuous source of valuable information.
For the guitar, there are two. The first is
the major third interval, and the second
is the minor third interval. Once we view
their repetitive information, they begin
to appear as a series of automatic functions.
The guitar, like an automobile, is a
vehicle that should remain neutral to the
destination it’s used to reach. There are
many forms that open different directions
in music, but when we come down to it, a
study of the instrument itself is much more
effective when it’s no longer influenced by
any of these styles.
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
. 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.
a leader—at only
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”
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”
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”
“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.
• “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