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From:  Reg Boyle <bandb@n...>
Date:  Thu Aug 31, 2000  4:30 am
Subject:  Re: [vocalist-temporary] Re: Source of frequencies was:Falsetto Recognition


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.




  Replies Name/Email Yahoo! ID Date Size
3834 Re: Source of frequencies was:Falsetto Recognitio Tako Oda   Thu  8/31/2000   3 KB
3861 Re: Source of frequencies was:Falsetto Recognitio Reg Boyle   Fri  9/1/2000   6 KB
3924 Re: Source of frequencies was:Falsetto Recognitio Reg Boyle   Sat  9/2/2000   6 KB
3999 Re: Source of frequencies was:Falsetto Recognitio Tako Oda   Tue  9/5/2000   3 KB
3840 Re: Source of frequencies was:Falsetto Recognitio Lloyd W. Hanson   Thu  8/31/2000   3 KB
3869 Re: Source of frequencies was:Falsetto Recognitio Reg Boyle   Fri  9/1/2000   6 KB
3843 Re: Source of frequencies was:Falsetto Recognitio John Alexander Blyth   Thu  8/31/2000   3 KB
3859 Re: Source of frequencies was:Falsetto Recognitio Reg Boyle   Fri  9/1/2000   2 KB

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