Let’s say you see a major 7 chord in a lead sheet and you want to enrich it with a few extra color tones. There are two more notes that work really well for this. Here is how you can make your maj7 chords more colorful, using Cmaj7 as an example.
Keep stacking thirds: the ninth
A major 7 chord already contains the major seventh. In Cmaj7, that’s the B on top of C, E and G. From there, you can simply keep stacking thirds. For example, you might decide to add the ninth, the D. That gives you a Cmaj9 chord.
Why I leave out the F
If you stack one more third, you get an F, the eleventh. In this context, the F doesn’t sound particularly good because it clashes with the chord, so I would leave it out.
The A: the sixth (or 13th)
But if you keep thinking in thirds beyond the F, you arrive at an A. This is the 13th, which is the same note as the sixth.
Ninth and sixth together
This means you can enrich a Cmaj7 chord with both the ninth and the sixth. Suddenly you get beautiful, colorful sounds that are really wonderful to listen to. Try it at the piano: play a plain Cmaj7 first, then add the D and the A, and listen to how much more color the chord has.