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.
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.
Please check out the spectral graph I posted a few months ago:
http://members.aol.com/TakoOda/arpeggio_spectral.gif
http://members.aol.com/TakoOda/arpeggio.wav
At the beginning and end of the clip, I am singing in "chest". In the
middle of the clip, I am singing in "head". Notice that when I am singing
in "chest" in the 200 Hz range, the formant range (for me, 2800-4000Hz) is
heavily populated by the 13-20th partials.
Once I am up to 800 Hz or so, the partials are spaced much more widely,
leaving only the clearly defined 4th and 5th partials to sound in the
formant band. Also notice, however, that there is some harmonically
unrelated "noise" in that frequency band as well! I believe the source is
from the vocalis muscle, but that the source vibration itself was not
harmonic in origin. Notice also the noise is also not as prevalent for the
higher pitch as the lower, since the actuating vibration is of a trimmer
(and therefore less complex) vocal fold.
-Tako
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