In the jazz world, Barry Harris came up with the idea of harmonizing a bebop scale.
Combining a C6 (C, E, G, A) and a Bdim7 (B, D, F, Ab) chords, we have this scale:
From this stantpoint we can alternate tonic and dominant sounds, like this:
Every pair of chords have all the 8-note set.
The notes C,E, G and A are always harmonized with a C6 chord.
The notes D, F, Ab and B are always harmonized with a Bdim7 chord.
So, from