When I was learning how to play songs on piano by ear, I didn't know how to add chords to a song melody. What I found on videos and on the Web was that you select a chord that carries the melodic notes played on the down beats. Some instructional videos write out all the possible chords (in letter notations) on a whiteboard to identify the three chords that carry the specific melodic note which was confusing and overwhelming for a beginner.
But most of all, this rule of thumb required me to mentally search through the seven basic chords on the scale including their 1st and 2nd triads to determine which 3 of the seven chords contain the melodic note. Searching through up to 21 possible notes (7 chords with 3 notes per chord) to determine the 3 possible chords required WAY TOO MUCH mental processing to enable me to extemporaneously play songs by ear on the piano.
Wouldn't it be easier to explain, reframe, re-phrase, and replace this general rule of thumb with play the melodic note as note 1, 3 or 5 of the accompanying chord?
My thoughts on this is that this reframed rule of thumb immediately identifies the three possible root notes to the chords, cuts the search down from 21 notes to 3 notes (a 700% gain in processing time and efficiency), simplifies the rule of thumb, makes it more concrete and significantly easier to apply in practice and real-time!
The day I came to this realization back in summer 2019, I suddenly was able to spontaneously play songs by ear on piano, plays songs in any key, and improvise on the piano, literally. Before that, I played piano for 40+ years and relied 100% on rote memory and sheet music.
Your thoughts on which and when each description is most helpful?