Dear Tako and Lloyd, I'm relieved that you assure me that there is a harmonic relationship between the formant and the sung pitch but it still seems to have a few problems. I habitually end my harmonic series at the 11th because mathematically that is the _practical_ limit. In fact it continues with decreasing amplitude and widening steps, so in my series, the 13th harmonic would have a frequency of 2860 Hz and a relative amplitude of 0.7% of the fundamental. You can see the problem. Although it falls within your stated formant bandwidth of 2800 to 3200, the energy available for excitation of an ancillary resonator, is minuscule, unless it comes from another source or by translation of energy of other frequencies of a more substantial magnitude. The 11th harmonic on the other hand falls outside your bandwidth and this is for a frequency in the middle of the tenor range. On the other hand moving up an octave to a top A, the 11th harmonic does become 9% of the relative amplitude but is still only a small part of the total energy under the curve. The only way I can mentally accommodate Lloyds description that in the "aryepiglottic region immediately above the vocal folds > it is possible to conceive that any frequency phonated by the vocal > folds will inevitably contain a partial that can resonate in this region." ....is that this area normally acts as a ' sump, ' to energy at these frequencies, and in being induced to cease its destructive activities, allows the 9% to pass. This is not an enlargement of the tone but merely a failure to absorb or reject it, as it would normally seem to do. This still appears to cause a difficulty for a top C with a fundamental of 512 Hz, because none of the harmonics, odd or even, fall within the 2800 to 3200 bandwidth, although the 5th goes close at 2560Hz with a relative amplitude of 20%.
Perhaps consideration of the alteration of the duty cycle, or the ratio of closed to open time of the folds, would be productive, in the respect that considerably less energy is devoted to the fundamental, as is the characteristic of any respectable head tone, there-by making the energy available to be used in the generation of upper harmonics?
On the other hand, falsetto, with no closure at all, would be left with a weak fundamental and no harmonics what-ever other than those resulting from asymmetry of its otherwise sinusoidal modulation.
Humbly Reg.
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