If it doesn’t hurt your brain too much, I recently discussed how the 3rd and 7th can be the most important notes in a chord here:
[I]f you are playing with a bass player who is already covering the root, the need to play the root is lessened considerably. And for many rock/pop songs, the 5th is often more important than the 3rd for chords where your ear can tell by context of the previous chords whether this chord is supposed to be major/minor. For jazz (or blues sometimes), the 7th or even 9th might become more important than the 5th, depending on the chord and the context within the song. Perhaps more than even the root if you have a bass player, meaning the 3rd and 7th are often the two most important notes. But sometimes this is so even without a bass player in an extremely traditional non-jazzy song, as you can see in the 2nd-to last note in “Happy Birthday” that’s coming up soon in this module).