Bi Triadic Pentatonic and Hexatonic Scales

By combining any two triads, a pitch collection is formed, which we can play as a scale.

Because all polychords have a harmonic function, all scales formed from them also have a harmonic implication.

Consider the Bi-Triadic scale VImaj|Imaj which adds the b2 and natural 6 to the notes of the C triad (C,E,G)

To precisely accompany these tones harmonically, a chord must be found which includes at least all 5 of the notes of the scale.

A7#9 is a harmony comprised of exactly these five notes, therefore it is one of the obvious harmonic choices. C#DimMaj7#5 is another obvious harmonic choice as this harmony is comprised of exactly these five tones.

By adding more different notes to this 5 note group, other harmonies can be realized which can accompany the Bi-Triadic scale. For example, by adding Bb to these 5 notes, C13b9 is implied, by adding Eb, Eb13#11b9 is implied, by adding Bb and Gb, Gb#11#9b9 is implied. There are other possibilities.

This exercise of considering what is implied harmonically by adding a single note to a pitch collection is a great way to discover the harmonic versatility of a set of notes.

Therefore, we could precisely accompany this scale by realizing it while sounding A7#9, C#DimMaj7#5, C13b9, Eb13#11b9, or Gb#11#9b9 or any other harmony which could be constructed from these 5 notes, or these 5 notes with any of the remaining 6 notes added.

The added notes to the original chord could also function as tension over the original harmony (the lower chord of the polychord).

VIImaj|Imaj adds the maj7 #4 and b3/#9 to Cmaj.

Since we are used to hearing b3 and #4 as notes of tension from the ubiquity of the blues scale in popular music, we could play this scale over a C major triad, and these additional tones of the VIImaj|Imaj Bi-Triadic are experienced as tensions over the major triad.

This principle could also be applied to the first Bi-Triadic scale we discussed: VImaj|Imaj

So, instead of forming A7#9 or C13b9 to precisely accompany the notes of that scale, we simply realize the scale over a Cmaj triad.

Then, the notes not in Cmajor will be experienced as tensions, and not as melodic expressions of a more complex underlying harmony

The A or 5th degree of the scale will be heard as a natural extension of the triad implying Maj6, and the C#, the 2nd degree of the scale will be heard as a more dissonant b2 tension above the original major triad.