I'm wondering if the melody, when you play it above an octave and those notes then become 9ths,11ths,13ths does that then give a reason to use extended chords to harmonize them? Or is there no correlation to where you are in the octave when using extended chords?
Within an interval the octave matters. Saying something is a minor 2nd tells you that the tones are a half step apart, and saying the same letters are a minor 9th tells you they're an octave and a half step apart.
But within a chord the octave location doesn't matter at all. C9 is the tones C-E-G-Bb-D, no matter which octave each tone is in. If that wasn't true we would need a different name for every possible voicing... what would you call it if D was the bass? C7 (add -2)???