Listen for higher harmonics beyond the fundamental. Easy to say, not so easy to detect for amateurs. Norman showed in a recent posting a bunch of wave forms for a note that he played. Listen to his sound. At first, Norman was blowing loudly and all sorts of harmonics were present. As he blew softer and softer, fewer and fewer harmonics were present, and towards the end the sound had a high "purity" quality. That was easy to detect because it was a pedagogical demonstration (great stuff, Norman). In a recording, it is not so easy, as I said. I think one can train one's ear to try and detect the full sound, the fundamental as well as the harmonics of a given note.
A possible correction. In a post I said, "Moreover, I believe (but would readily admit being wrong) that a lower tone produces more higher harmonics than a higher tone produces lower harmonics." I am beginning to think that is wrong. In an ideal situation, plucking a single string, it does not seem possible to have a lower frequency harmonic than the fundamental (or natural). The reason being that nodes must be present at the stationary points of the string. Thus, for the fundamental (or natural) frequency, you have a half wave from end to end. You can have two half waves (the first harmonic), or more, but you cannot have less than half a wave, thus no lower harmonics. However, in a real situation, I wonder if a lower frequency harmonic can occur (sound box, other strings sort of resonating), I am not certain. Does anyone know?