Thanks Caeven,
But I was very impressed by the thought and dedication in your first post. (Mine was an easy afterthought)
You are spot on with how intervals can be used.
Without going into theory, and hopefully not going OT, I would like to point out a little experiment that can be done with a guitar tuner.
1) Play the note of C. Guitar tuner reads C.
2) Play the notes C with E above it, (interval)and the tuner will read C. Ditto with C and G.
3) Play the notes E and G and the tuner will read C. (as long as both are played at equal volume, keyboards are excellent for this experiment.)
Long story short, when we play two notes simultaneously a third note appears, a fundamental or root note, even though we haven't actually played it.
Cheers