Triadic pairing practice for improvisation and composition

Triad paring is a relatively new approach to melody and harmony with the uses and application not exclusive to jazz.  And while the results are modern sounding, the original treads can be connected to previous era.  

Triad pairing can be used to play both inside and outside chord progressions.  When used artistically and thoughtfully, it can influence melody and rhythm creating a very modern sounds.   No one application is better than another, and each artistic adaptation can have a unique sound.

Background Check

To put this all in perspective.  Let's take a cursory look at music before the introduction of major and minor chords.  

During Medieval and Early Renaissance times, music was approached in linear terms.  The composite melodies of early polyphony would result in a vertical sound of the open intervals such as fifths, fourth and octaves.  As style developed and matured, smaller intervals (major and minor 3rds) would become accepted in the musical language. 

Also utilized was a cantus firmus (or "fixed song") as a pre-existing melody forming the basis of a polyphonic composition.   Over time and through the evolution of polyphony other dissonant sounds became gradually accepted to the ear and resulted with the discovery and use of major and minor chords.  Eventually yielding to seventh chords, to chromaticism with alterations of the upper dominant structures, ultimately leading to Twelve-tone technique (dodecaphony) the avante guard and free music.

Embedded in the arch of this musical evolution is the development of scale chord theory that incorporates major, minor (melodic and harmonic), diminished, whole tone penta tonic and many other exotic scales.

Before I launch into the definition and application of triadic pairing lets take a closer look at the mechanics of scales.

All scales have an inherent structure that is defined by the step the intervallic content and the number of notes with-in the octave.

A scale is set of notes in a specific order. All major scales and all the correlating modes have a 7 note structure. The diminished scale has 8 notes (octotonic), and the pentatonic 5 and hexatonic a 6 note scale.  The important thing to realize is that the note number with in the octave is an important factor for how voice leading works.

All music that utilizes tonality relies on some kind of scale tone voice leading.  Good voice leading requires (in general) the right note on the right beat.  Tonal music that is metered has a linear pull of the root, third and fifth toward strong beats.  In a 4/4 time signature those strong beats are 1 and 3.

This pull is why thirds and seventh on a dominate chord tend to resolve towards roots and thirds on the tonic chord.  Composersand jazz improvisers work off of this pull to give music gravity.  This gives tonal music emotion and meaning.    

From Bach to Be-Bop, good voice leading to what separates us form the apes.  

The Be-bop Scale.

The be-bop scale is essentially a diatonic scale with an added chromatic note.  Most common be-bop scale has an extra note between the sixth and the nature seven degrees.  

Example No. 1

So in the key of C major the dominant type be-bop is:

C D E F G A (Bb) B – dominant be-bop scale

C D E F G (G#) A B – major be-bop scale:

Both versions change the seven-note scale to an eight-note structure before the repeat of the octave.

The discovery of the be-bop scale happened by ear.  The extra note was a simple solution to mathematical voice leading problem.  Play

Example No. 2  

 4/4  | m.1                        | m. 2                         | m.3                    ||

 4/4  | Cmaj                      |  Cmaj                       | Cmaj                  ||

       | C D E F G A B  C      |  C D E F G A Bb B   | C                        ||

       | C D E F G A B  C      |  C D E F G G# A B   | C                        ||

The first measure has 7 notes in a 4/4 measure with 8 eighth notes, if we continued up the scale the C occurs on the last eighth in the first measure, when it is needed on the down beat of measure two.

The second measure, using the be-bop scale has 8 notes, exactly the number of eighth notes needed to land the C on the down beat of measure 3.

In written or improvised music the extra chromatic note brings the line to a chord tone to a string beat.

The Diminished Scale

The diminished (octotonic) scale is an eight-note structure with some very user-friendly voice leading advantages, it commonly used over dominant chords.  For example, on a C7 a half-step whole-step diminished scales contains many altered chord tone qualities.  

Example No. 3

The Diminished Scale

C ​Db ​Eb ​E ​F# ​G ​A ​Bb (8 note or octatonic)

root​,b9 ​#9 ​3rd ​#11 ​5th ​13th ​b7

The Altered Scale

The altered scale is a seven note based off of the seventh mode of the melodic minor scale and differs form the diminished scale

Example No. 4

 The Altered Scale

 C ​Db ​Eb ​E ​F# ​G#​ Bb (7 note)

root,​b9 ​#9 ​3rd ​#11 ​#5 ​b7

Comparing the two reveal a subtle but obvious difference is the trade of  G# for G natural and also extra note 'A' .

It might seem like a negligible difference between these scales but note content and an 8 structure dramatically change the sound of each.

Some Origins of Triad Pairing

Triad pairing it exactly what it sounds like.  In all cases it is a combination of two triads (major, minor or augmented).  Triad Pairing is hexotonic of the two triads have no common (or repeated) notes between them.  

Example No. 5

 Triadic Pair

 F# A# C# - C E G​ description: major-major triads a tritone apart

The combination of two major chords a tritone apart is a ubiquitous sound and very familiar to jazz ears.  This sound references the tritone substitution application on dominant chords.

Before discussing the applications of triad pair lets take a closer look at the diminished scale.  Inherent in the half step and whole step structure exist four major and four minor chords triads.

Example No. 6

The Diminished Scale

 C​Db​Eb​E​F#​G​A​Bb

Example No. 7

4 Major triads: Cmaj, Ebmaj, F#maj, Amaj

4 Minor triads : Cmin, Ebmin, F#min Amin

 So in keeping with the notion of paired triads with no common notes between them, how many pairs can be made with the triads listed above?

The interesting aspect behind these diminished scale pairings are their application to dominant chords.  More on this later.  

All of the above paring are from the Diminished Hexatonic Family.  The more "inside" sounding hexatonic pairing would be derived for combining major and minor chord that are a half step or whole step apart.

Example No. 8

Diatonic sounding

• Cmaj-Dmin (minor-major a tone apart)
• Cmaj-Dmaj (major-major a tone apart)
• Cmin-Dmin (minor-minor a tone apart)

Exotic sounding

1. Cmin-Dmaj (minor-major a tone apart)
2. Cmaj-Dbmaj (minor-major a semitone apart)
3. Cmin-Dbmaj (minor-major a semitone)
4. Cmin-Emaj (minor-major a major 3rd apart)

The first important question is why use this at all.  The simple answer is that because of the intervallic construction  it has a sound vastly different and unlike any other note construct.

Remember that voice leading is linked to the rhythmic math and tonality.  So triadic pairing, through it's hexatonic (six note) nature will influence voice leading in new ways, sounding different from a seven or eight note scale.

Each of the chord pairings above can be organized into a hexatonic scale.  

For example the first triad pairing of Cmaj-F#maj assembled as a scale would be:

Example No. 9

Triad Pairs in a hexatonic scale

C​,      C#, ​E, ​       | F#,   ​G,     ​A#  

root​, b9, ​3rd | ​#11, ​5th, ​b7

So, within the diminished scale and considering the 12 pairings we could devise 12 unique hexatonic scales.  Keep in mind there are three diminished scales, so we really have 36 hexatonic scales in total.  I don't use them all, it's seems like too much information.  However, the math is fascinating.

A cursory Internet glance would show only a few texts that offer up an explanation and usages of triadic pairing.  Saxophonist and composer Walt Weiskopf has saxophone method book (Intervallic Improvisation) that presents some of this material.

My first introduction to Triadic Pairing occurred in Rome Italy, in the late 90's.  I was lucky enough to have a lesson with renowned Italian saxophonist Rosario Giuliani.  In addition to some of the pairing listed above, he adds to the artist's palette with these additional groupings.

Example No. 10

 Rosario Extras

Triad Pairing​ ​Chord Type and Pair interval​ Chord Applications​

Cmaj-Bbmaj​major-major a tone apart ​(Csus, Bbmaj7 #11)

Cmaj-Bbmin ​major-minor a tone apart ​(Csus7 b9)

Cmaj-Abmin​major-minor a maj3 apart ​(Cmaj7 +5 #9)

Cmaj-Daug​major-aug a tone apart ​(Gmin +7, D7 +5)

Triadic Pairing in Practice

Before I launch into specific application.  I want to briefly reference renowned jazz saxophone George Garzone (Berkee School of Music) for his Triadic Chromatic Approach to improvisation.  I have not delved completely into his teaching, but my understanding is it utilized major and minor triads in a quasi-random fashion to create tension and harmonic interest.  I find that approach very exciting and philosophically Zen-like.  It can be a subject for another lecture all together.

 One relevant application of triad pairing might best be show with in a dominant chord.  As was indicated earlier a tritone substitution triad for C7 is F#.  We can alternate between the C and F# triads freely using any on the inversion in any range within the dominant chord.  If these notes voice lead to the tonic chord we can hear the logic of the line.  The goal is to be musical and use your ears.  Experiment as how and where to use the pairs is the most important part of the practice.  

 

There are a myriad of ways to practice triad pairing, it is important to make up your own to develop your ear and technique.  

 

The goal is not to play too much, less it most certainly more with this approach.  It is also a good idea to work-in the triadic pairing with the things you are already doing well.  It will enrich both the older material and the new approach.

 

Just as each improviser and composer sounds unique using tradition scales so too can each artist create a personal sound based on triad pairing.  

 

 

Complete set of triad pair based on one of the diminished scales.

 

Triad Pairs​Chord Type & Intervallic Reference

 

•Cmaj-F#maj ​major-major tritone apart•Cmaj-F#min ​major-minor tritone apart•Cmin-F#maj ​minor-major tritone apart•Cmin-F#min​minor-minor tritone apart•Cmaj-Ebmin​major-minor minor 3rd apart•Cmin-Amaj​minor-major minor 3rd apart

•Ebmaj-Amaj•Ebmaj-Amin•Ebmin-Amaj•Ebmin-Amin•Ebmaj-F#min•Ebmin-Cmaj

In bold are the 14 unique pairings, the rest (in plain text) are a reiteration.

•

F#maj-Cmaj•F#maj-Cmin•F#min-Cmaj•F#min-Cmin•F#maj-Amin•F#min-Ebmaj

•Amaj-Ebmaj•

Amaj-Ebmin•Amin-Ebmaj•Amin-Ebmin•Amaj-Cmin•Amin-F#maj

Jim Gailloreto Adjunct Professor | Chicago College of the Performing Arts. | 773.330.4461 |  jim@gailloreto.com | jrgproductions©2011