>Reg wrote:
> > 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.
Tako then wrote
>Not sure the complexity in the vocal cord's source tone is purely based on
>integer harmonics to the fundamental. That's a big part, but I think Lloyd
>Hanson was also saying there is a "noise" element as well, emanating from
>the vocal folds themselves, i.e. non-harmonic vibrations which are
>artifacts of phonation. "Open chest" cords possess a much more complex
>geometry, allowing for vibrations that are not directly related to the
>fundamental.
Dear Tako,
Clearly we've moved deeper into the mire of theory and
technology and away from the simple need to differentiate falsetto from
non-falsetto. The principle of using filtering to lift out the wanted tone
from a broad spectrum noise in my opinion is not relevant to vocal
production. Visualise this if you can and try to see its relevance to the
principle.
The first...throw a large rock into the centre of a pool.
You'll see a great local disturbance; hear a loud sound of limited
spectrum; watch gargantuan surges attack the shore.
The second..observe gentle rain fall right across the pool.
The energy is about the same as with the rock but beautifully distributed;
there'll be a tiny random sound across the whole spectrum; the surface
remains largely unruffled.
I'm trying to illustrate the problems of the principle of
using pink noise to generate tone in the voice. The rock illustration
is specific, just as I feel the voice is. Notice also how the great surging
waves are smoothed out in the process of reflection, not enlarged.
You may recall my advocacy of matching efficiency and purification,
and rejection of the idea of enlargement by resonance. The pink noise
has high total energy but specific frequencies are weak and I think, does
not conform to the dynamic of vocal design.
We agree about the complexity of the fold process. The
problem is initially one of stripping away the complexity to its simplest
form and then gently reinserting it as we advance, all within the
restrictions of knowledge and accepted theory. Thus my initial figures
presume a 1 : 1 duty cycle and ODD harmonics.
Try this for size.
ODD harmonics require a strict and precise fold closure
like clapping, while EVEN harmonics demand a gradual
rate, like the clowns floppy shoes.
Next..
I suggest that the vocal folds, regardless of the repetition
frequency, remain closed for "all but" about 160 to 175 uS
of the cycle. [That's micro-seconds]
Pretty drastic when you consider that top C has a period
of 1952 uS , top A is 2272 us and the next down 4545 uS.
Actually this has potentially serious consequences for the singers
formant, vibrato and pitch but is based around the specific
requirements for the singers formant.
Top C 6th harmonic 3072 Hz period 325uS
Top A 7th harmonic 3080 Hz period 324.7us
Oct A 13th harmonic 2860 Hz period 349uS
All this to fall within the window of 2800 to 3200.
Notice my theoretical halving of the period in the fold open time
to simulate a half cycle. But this in no way compromises the
existence of the fundamental. Only its over-all period,
if the critical open time is inaccurate.
What remains then, is to raise the question of whether the noted
1: 6 ratio is cause of effect. I wouldn't like to think that after
having achieved these Olympian gyrations they would be
despatched to the vocal "waste paper basket" by a
maladjusted filter!
Regards Reg.
|
|  |
