Dual Triads and Quartal Chords: Introduction
By combining two triads, you can create hexatonic scales. These include the whole-tone scale and both modes of the augmented scale. The remaining scales correspond to the heptatonic scales (all modes of the ionian, melodic minor, harmonic minor and harmonic major systems) and the octatonic scales (htwt and wtht), each missing one resp. two notes. Because of these missing notes, some of the hexatonic scales can have two corresponding heptatonic or octatonic scales.
As a rule of thumb, you can combine any two adjacent diatonic triads of a scale to get dual triads. Also, any combination of major or minor triads an augmented fourth from each other will result in a partial octatonic scale.
The following overview includes all possible dual triads in the key of C in their triadic and scalar form and the implied scales. Combinations that result in doubled notes or in two adjacent half-tone steps in the scalar form have been omitted.