Is there a term for a harmony that always resembles the next-closest note above the melody that is in chord (not just in key)?
A friend of mine always does that when improvising a harmony and she sometimes calls it "singing a third above the melody" or other times she just calls it "singing the third harmony".
But in my opinion this doesn't really make sense. E.g. if one note in the melody is a perfect fifth relative to the current chord, then she would sing an octave above the current chord's root note, which would be a fourth above the melody. And then there are also situations where the melody, while being in key, is not always in chord and in "extreme" cases there are accidentals as well, which makes it even less practical to "sing a third above the melody" without going off-chord.
The only thing I would imagine to work, would be to constantly sing a third above the root note of the chord or a third above the third of the chord. ...but that's not what she's doing.
So I'm wondering if there is a term for what she does. And I'm also curious if there are other terms describing other common ways or harmonization.