The Triad (a 3-note structure built in 3rds) is arguably the most stable and recognizable of all musical structures. Pairing them together in various combinations creates a flexible, intervallic melodic alternative, with its own integrity.
The triads in a pair are normally derived from adjacent scale steps - sharing no common tones between them. Such is the case with Major and minor scales.
Take a look at just one of the many ways you can transform this 6-note (hexatonic) triad pair into groups of 4 eighth-notes, using rhythmic displacement.
Using the shape 3-R-5-3 (third-Root-fifth-third) as a starting point, we'll take the F & Eb Maj triads and descend through their respective inversions, repeating the first measure an octave lower in the fourth bar.
*An underscore ( _ ) beneath a note's letter name, means that note is descending relative to the note before it.
A-F-C-A G-Eb-Bb-G / F-C-A-F Eb-Bb-G-Eb / C-A-F-C Bb-G-Eb-Bb / A-F-C-A G-Eb-Bb-G
Shifting the whole line an eighth-note to the left - the 4-note groupings become -
F-C-A-G Eb-Bb-G-F / C-A-F-Eb Bb-G-Eb-C / A-F-C-Bb G-Eb-Bb-A / F-C-A-G Eb-Bb-G-F
- as notated in the first 4 bars in Ex. 1 below. Measures #5 - 8 are a retrograde (backwards) version of the first four, ascending back to the starting point in bar #1.
Ex. 1
As mentioned, this is just one way to approach this particular Triad Pair. The articles detailing the Shortbook™ Hexatonic Triad Pairs: Vol 1 - Major Scale Pairs, as well as Hexatonic Triad Pairs II - Mixed Pairs are worth checking out for a methodical look at some more varied combinations.
B. Stern