A triad pair can consist of any two triads of the same or different qualities, as long as there are no duplicate tones among them. This is most easily accomplished by taking adjacent triads from the same scale system.
In most cases, the first pair an improviser might come across contains two Major triads a whole step apart, which is derived from the 4th & 5th degrees of the Major Scale (F & G Maj triads in C Major). Alternating these 2 triads through their inversions creates, on its own, a decidedly Mixolydian flavor.
The subject of this post, which takes it a step further - adding harmonic and melodic tension - is the triad pair based on the 3rd & 4th scale steps of the Melodic Minor scale (Eb+ & F Maj in C Melodic Minor ).
The notation graphic below shows the first three lines of the downloadable pdf, which is in C Major only.
Likewise, the triad pair defining the V chord - G7alt - is derived from scale degrees 3 & 4 of Ab Melodic Minor – B-D#-G / Db-F-Ab (B+ & Db Maj), the resulting hexatonic being B-Db-Eb-F-G-Ab.
In bar #1, the first line begins on an F and moves in a descending / ascending direction thru a pair of inversions of the aforementioned triad pair, descending with a Bb Maj triad and ascending with A+, over D-9b5. Notice how the E, or “natural 9” in the ii chord gives a distinct flavor - in contrast to the more common “b9” found as a result of the Major Scale derived Locrian mode.
The line then pivots via a semitone, descending from C at the end of bar #1 to B, beginning bar #2 - the triads B+ & Db Maj once again descend through a pair of inversions over G7alt - resolving in bar #3 down a semitone to E, the 3rd of C Major.
The second line begins with an E (the next note down in the ii chord derived Hexatonic) and descends and ascends as in Line #1, except that the order of the triads in each measure is now reversed. This has no bearing on the line's harmonic quality - it's simply another way to realize and practice these inversions and slowly incorporate them into your playing.
With D as its starting point in Line #3, the triads revert back to the same order as in Line #1, while simultaneously introducing the next set of inversions in both bars #1 & 2.
This exercise is a starting point and should be practiced in all keys and all directions. It should keep you busy for a while.
B. Stern