Hexatonic Triad Pairs: Vol. 1 - Major Scale Pairs
The concept and technique of Triad Pairs has been a tasty topic, the seeds of which have borne fruit for many an inquisitive improviser since they were first sown into the music's fertile vernacular in the late 1950's and early '60s, with more widespread usage coming somewhat later.
The term "Hexatonic Triad Pairs" is actually a redundant phrase, or something known as a "pleonasm". It is, however, accurately self-descriptive and rolls off the tongue quite easily.
A true triad pair - which is formed from 2 adjacent triads and therefore comprised of 6 non repeating notes - always results in a hexatonic (6 note) scale. On the other hand, a hexatonic scale, being any scale of 6 notes, doesn't always yield a triad pair.
The term "Hexatonic Triad Pairs" is actually a redundant phrase, or something known as a "pleonasm". It is, however, accurately self-descriptive and rolls off the tongue quite easily.
A true triad pair - which is formed from 2 adjacent triads and therefore comprised of 6 non repeating notes - always results in a hexatonic (6 note) scale. On the other hand, a hexatonic scale, being any scale of 6 notes, doesn't always yield a triad pair.
"Hexatonic Triad Pairs: Vol. 1 - Major Scale Pairs" is organized into 5 segments - focusing on the 4 primary triad pair formations derived from the Major Scale - plus a section of ii-V examples combining material from the first four.
The four Major Scale triad pair formations examined here are:
So, what happened to vii & I (B dim & C Maj), you say? Well my best explanation is that in order to keep the size of this volume manageable at 217 pages, I thought it best to relegate this triad pair to a future volume. Fair enough?
Since all the above pairs are derived from Major Scale harmony, the sonic and qualitative differences can be either subtle or more pronounced, depending on and according to their context.
All exercises and sequences shown as examples are presented for each triad pair in all keys.
The first pair of triads, C Maj & D min (C-E-G & D-F-A) is derived either from scale steps I & ii of C Maj, or V & vi of F Maj.
In either case, this is illustrated in Ex. 1 below with both triads stacked together in a continuous, ascending direction:
Ex 1.
The four Major Scale triad pair formations examined here are:
- I & ii or V & vi (1 Maj & 1 min triad a whole step apart - eg. C Maj & D min of C Maj or F Maj)
- ii & iii (2 min triads a whole step apart - - eg. D min & E min of C Maj)
- iii & IV (1 min & 1 Maj triad a half step apart - eg. E min & F Maj of C Maj)
- IV & V (2 Maj triads a whole step apart - - eg. F Maj & G Maj of C Maj)
So, what happened to vii & I (B dim & C Maj), you say? Well my best explanation is that in order to keep the size of this volume manageable at 217 pages, I thought it best to relegate this triad pair to a future volume. Fair enough?
Since all the above pairs are derived from Major Scale harmony, the sonic and qualitative differences can be either subtle or more pronounced, depending on and according to their context.
All exercises and sequences shown as examples are presented for each triad pair in all keys.
The first pair of triads, C Maj & D min (C-E-G & D-F-A) is derived either from scale steps I & ii of C Maj, or V & vi of F Maj.
In either case, this is illustrated in Ex. 1 below with both triads stacked together in a continuous, ascending direction:
Ex 1.
Notice the alternating inversions, as well as the order of each triad as it ascends. Fusing these two triads back into linear form creates the equivalent 6-note, hexatonic scale below.
Ex 2.
Ex 2.
It's not hard to notice that this scale configuration is equivalent to a C Major scale, absent the note B, or a C Major Pentatonic with an added F.
With D as the root, both the triad pair and hexatonic have a pronounced min7 11 color.
The strongest modal "pull" of this hexatonic besides Major (Ionian) is probably Dorian or Aeolian. Since it's derived from either C or F Maj, both B and /or Bb are implied as the 6th degree of the aforementioned minor modes, respectively.
With D as the root, both the triad pair and hexatonic have a pronounced min7 11 color.
The strongest modal "pull" of this hexatonic besides Major (Ionian) is probably Dorian or Aeolian. Since it's derived from either C or F Maj, both B and /or Bb are implied as the 6th degree of the aforementioned minor modes, respectively.
The next segment focuses on the triad pair derived from Major Scale steps ii & iii – 2 minor triads a whole step apart. Ex. 3 below partially depicts a descending step /skip hexatonic scale sequence made up of E min & F# min triads – ii & iii of D Maj.
Ex 3.
Ex 3.
This configuration is the equivalent of a D Major scale without the D. Depending on the root, this hexatonic tends toward a Dorian, Phrygian or Mixolydian coloration.
From the iii & IV (1 minor & 1 Major triad a half step apart) chapter, Ex 4. below shows an Eb Maj & D min triad pair sequence, derived from from Bb Major (minus C, its 2nd degree).
Ex 4.
Ex 4.
This sequence begins with the upper (IV or Eb) triad and contains examples of chromatic approach note usage, both connecting the pair, as well as within a single triad (eg. - the G# in the D min triad in bars 3 & 4).
Modally, this hexatonic has a decided Phrygian or Lydian flavor, and due to the presence of a tritone (A – Eb), it has a strong pull, harmonically, to its home key of Bb.
Modally, this hexatonic has a decided Phrygian or Lydian flavor, and due to the presence of a tritone (A – Eb), it has a strong pull, harmonically, to its home key of Bb.
The 4th and final triad pair under scrutiny in this volume is probably the most recognizable of them all – namely, Major Scale triads IV & V ( 2 Major triads a Whole Step apart).
In many discussions of triad pairs that I've seen or read about, this configuration seems to be “the triad pair”, as if it were the only one in existence.
In its defense, however, it is probably the most versatile of the bunch, being heard as early as 1959 as part of John Coltrane's solo on Miles Davis' video version of “So What”, as well as several years later on 'Trane's own quartet version of his composition “Big Nick”.
It had already been featured long before that as part of the Afro -Cuban son.
Ex. 5 shows an ascending sequence, alternating between G Maj & A Maj triads (IV & V of D Maj). F#, the 3rd of D Maj, is in this case, the omitted tone.
Ex 5.
In many discussions of triad pairs that I've seen or read about, this configuration seems to be “the triad pair”, as if it were the only one in existence.
In its defense, however, it is probably the most versatile of the bunch, being heard as early as 1959 as part of John Coltrane's solo on Miles Davis' video version of “So What”, as well as several years later on 'Trane's own quartet version of his composition “Big Nick”.
It had already been featured long before that as part of the Afro -Cuban son.
Ex. 5 shows an ascending sequence, alternating between G Maj & A Maj triads (IV & V of D Maj). F#, the 3rd of D Maj, is in this case, the omitted tone.
Ex 5.
Ex. 6 below shows part of a combination chord / scale sequence with this triad pair.
Ex 6.
Ex 6.
Historically, the modal usage for this pair has been overwhelmingly Mixolydian, with A (V) as the root (A7 11). However, it is also commonly used - with G (IV) as the root - as a Lydian melodic source, as well as a substitution for a tonic I chord (G6 9 #11).
You can hear an example of this is in bar #4 of Ex. 9 below (C Maj7 #11).
You can hear an example of this is in bar #4 of Ex. 9 below (C Maj7 #11).
Last but not least, is the section on ii-V7 sequences, utilizing combinations of all four triad pairs from the previous chapters.
In the following 4-bar ii-V7 examples, the main chord symbols are on top of the staff, as is usual, while the letter names of the individual triads (one pair per measure) are listed under the staff beneath each triad's contiguous note grouping.
Ex 7.
In the following 4-bar ii-V7 examples, the main chord symbols are on top of the staff, as is usual, while the letter names of the individual triads (one pair per measure) are listed under the staff beneath each triad's contiguous note grouping.
Ex 7.
Ex. 7 above, is of a bVI-V-i cadence (a form of ii-V7-i, commonly found in the last 4 bars of a minor blues).
The breakdown for this one is pretty simple:
Bars #1 & #2 each use a IV & V triad pair (from Eb & Gb Maj, respectively); while bars #3 & #4 utilize a ii & iii pair - (from Bb Maj).
The breakdown for this one is pretty simple:
Bars #1 & #2 each use a IV & V triad pair (from Eb & Gb Maj, respectively); while bars #3 & #4 utilize a ii & iii pair - (from Bb Maj).
Listen
Ex. 8.
Ex. 8. depicts a ii-bII7-I sequence in C Maj. Bar #1 - iii & ii, bar #2 - iii & IV, bar #3 - I & ii, bar #4 - iii (no pair)
Listen
Ex. 9.
The ii-V7-I in Ex. 9. above is made up of arpeggiated pairs of stacked triads, all in root position.
The pairs are: in bar #1 - IV & iii, bar #2 - ii & I, bar #3 - ii & I, bar #4 - IV & V
The pairs are: in bar #1 - IV & iii, bar #2 - ii & I, bar #3 - ii & I, bar #4 - IV & V
Listen
Triad pairs are yet another tool to be used by the improviser to sow ideas to be harvested and utilized in the creation of musical lines and statements.
The main objective, once comfortable, is to turn these lines into real music.
Exercises and sequences should be practiced in all directions, using rhythmic diversity (rests, triplets, etc.). Concepts, inversions and permutations from “Triadicisms, Vols. I & II” could be incorporated here with great effectiveness.
With a little passion, patience and practice, you will no doubt, sooner than later, reap the sweet fruits of your labor.
So, take a bite out these "pairs"!
B. Stern
The main objective, once comfortable, is to turn these lines into real music.
Exercises and sequences should be practiced in all directions, using rhythmic diversity (rests, triplets, etc.). Concepts, inversions and permutations from “Triadicisms, Vols. I & II” could be incorporated here with great effectiveness.
With a little passion, patience and practice, you will no doubt, sooner than later, reap the sweet fruits of your labor.
So, take a bite out these "pairs"!
B. Stern
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