Say we're on the piano and we're playing a melody in the right hand. I've noticed sometimes pianists will add another note to that melody that harmonizes with it and makes the melody sound fuller.
So basically two notes are being played at once on every note in the melody. The rightmost finger will play the actual melody and the thumb (on the right hand) will harmonize with that note.
Is there a name for this? I know it's not a chord. Is it just called harmony or something, or is there an official name for it?
Also, is there a certain interval that this is usually done? I assume the note needs to be in the scale so maybe it's not a static interval.