You can say we are hearing phase (differences, changes) or you can say we are hearing amplitude changes
caused by phase. I'm sure it gets really tricky with more than two frequencies - another opportunity for aural illusion?
Phase has a well-defined meaning that does not relate to perception. Ergo, why the scare quotes around "phase"?
Its relevance to auditory perception is an interesting problem, which I believe to be your point, actually.
Finally, determining leading edges of waveform at low frequencies, or leading edge of envelope at high frequencies is a key aspect of both monaural and binaural hearing. While it's not a great term mathematically, it's very appropriate to the actual perception that people with normal auditory systems (including CNS) experience. Ergo, I can understand why the individual who mentioned this did so.
When dealing with the auditory system one does not deal in exactness or precision, we are dealing with an instrument that is fundamentally probabilistic, and whose outputs are filtered down and data-reduced by something like a factor of 1,000,000 before we are concious of the result. Every stange of that reduction is guided by experience, expectation, and cognition, as well as what input is acquired from other senses. Ergo, I don't see any "incomplete specification", nor do I see any point in engaging in semantic argumentation here, we are simply dealing with the system as it is, and we must, if we are to have any discussion, deal with words and ideas that are not always firm and non-probabilistic.
As to "long mathematical analyses", I haven't seen anything here, in the year I've belonged, that even constituted a short, trivial mathematical analysis. Perhaps I've missed something?
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