To start our explorations into 6ths in C, G, & D, let’s begin with some simple interval math.
6ths & 3rds are the inverse of one another.
Invert (move lowest to highest) a Major 3rd (M3) and it becomes a minor 6th. Invert again, it’s a Major 3rd again.
Invert a minor 3rd (m3) and it becomes a Major 6th. Invert again, minor 3.
The exact same logic works for 2nds/7ths, 4ths/5ths, etc. All intervals always equal 9 for the inversion: 1-8, 2-7, 3-6, 4-5, 4.5-4.5. 4.5 = tritone (6 half steps).
Major intervals become minor, minor become Major, Perfect remain perfect. A tritone is a tritone.
1-8 & 4-5 = Perfect
2-7 & 3-6 = Major/minor