I'm developing a method for students to identify the key of a song by ear. I've seen a lot of videos on YouTube where they say that you should try to identify a common note and that will be your tonic. That's not necessarily true since other notes can be common to all chords depending on the chord progression. Also, the tonic is not always common to all chords in the chord progression so that blows that idea out of the water. What is a good approach to thinking about this concept?
If the song is simple enough (or we just focus on a section with no modulations) and we have a pitch reference (or perfect pitch!), then identifying the key boils down to identifying the tonic and the modality (major, minor, something else).
With proper training, identifying the tonic is easy. You just need to find the note that gives the feeling of closure. That's the tonic. Identifying the tonic, in my opinion, is the most basic skill that every musician should have: Everything else is built around it!
Next, we need to determine the modality. To do that, we need to identify the essential notes in the melody (because there maybe non-essential chromatic ones too). Then we look at the scale that has these notes and that is based on the tonic that we've identified earlier. Most likely it's gonna be major or minor, but beware: It maybe in another mode or scale like, say, Dorian or Phrygian #3.
Unfortunately I don't think one can come up with an objective, algorithmic procedure. It is necessary to feel the sense of closure that the tonic gives and feel which notes are essential and which ones are merely chromatic decoration.
Finally, there are quite a few pop songs with ambiguous tonics, especially between relative minors and majors.
Unless those students have perfect pitch - absolute pitch is an accepted term- this is nigh on impossible. They will be able to identify WHICH part of a piece has the tonic in it, but that's a different 'skill'. I say skill as absolute pitch is often an inborn thing, although it can be learned to a degree.
Finding that tonic part of a piece:often, but not always, it will be the start bar (full bar, not anacrucis), and usually the last bar, particularly of a verse. The last bar of a chorus could be, there again it's sometimes just the opposite, the V to take the piece back to the tonic to start another verse.
Not done a study, but wouldn't be surprised if in a given piece, there are more tonic notes throughout it than any other. Counting them could be tedious...Obviously, the tonic is 'doh' in the floating solfege, and recognising that is key. Pun intended.Without a reference point, as in a note or an instrument to help, it's not impossible, but improbable.