Reg:
A short reply. More later after the Labor Day weekend.
It appears that you are assuming that the strength of the partial in the phonated sound is the only possible source of strength in the resonated tone. There is the physical phenomenon of an originating tone being amplified acoustically by a resonating chamber. Of course, for this to happen the energy must come from somewhere and the difficulty is from where? The resonating characteristic of a closed tube is able, if conditions are correct, to borrow (as it were) energy from dampened partials or partials that are not resonated as strongly as their original strength upon entering the resonating space. Perhaps this energy is transmuted to provide the increase in acoustic amplification in addition to that more naturally supplied by the emphasis of particular partials.
There is also very strong evidence to indicate that the male voice is incapable of producing a fundamental throughout its total range until it reaches the frequency of about G4 and above. What we hear is the spectrum of partials that would normally be found with a given fundamental and our ears (or minds) provide the phantom fundamental. If this is so, then the calculations of relative strengths of the partials would change appreciably.
Interesting subject.
-- Lloyd W. Hanson, DMA Professor of Voice, Pedagogy School of Performing Arts Northern Arizona University Flagstaff, AZ 86011
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