Subharmonics - "undertone" singing clips

"Paul H. Erlich" wrote:

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> Dante Rosati wrote,
>
> >Jim-
>
> >Excellent! I've downloaded the clips and had a quick look at some
> >spectrograms. While I need to study them further, there was one thing I
> >noticed right away. Instead of generating subharmonic partials, what is
> >happening is that the main note you are singing is becomming the third
> >partial of a series with a fundamental a twelvth lower.
>
> Whew! Just as I expected. If Jim was indeed singing a "subharmonic series",
> I would really look like an ass.

How low is the frequency of these fundamentals in the clips and what in the
vocal apparatus, given that I normally cannot hit a bass note lower than about
a C (which I had assumed was about the limit of my vocal folds), would be able
to sustain such low tones? Moreover, what's your analysis of the "sub 5"
clips? (I assume Dante you were referring to the "sub 3 examples") - how low
are their respective fundamentals, esp. the 2nd half of the 2nd example where
the "main note sung" is ~G# (~100hz by my reckoning)?

Thanks for taking an interest in these clips. I am curious to hear more about
what you guys find in them.

BTW, I cannot believe how much this cheap little sound card mic was able to
capture and am surprised that the recordings have enough information in them to
be useful - anyone know the general frequency response of these things?

~Jim

Jim Cole wrote,

>How low is the frequency of these fundamentals in the clips and what in the
>vocal apparatus, given that I normally cannot hit a bass note lower than
about
>a C (which I had assumed was about the limit of my vocal folds), would be
able
>to sustain such low tones?

Jim, if what you are singing is in fact period-3 or period-5 behavior, as I
suspect, then the nonlinearity of the interaction between the vocal folds
and other elements of the vocal tract cause the flaps of the vocal fold to
oscillate in an irregular manner, repeating themselves every 3 or every 5
oscillations. That is all that is needed for the low fundamentals to be
produced.

Date: Monday, August 16, 1999 1:13 PM
Subject: [tuning] RE: Subharmonics - "undertone" singing clips

>From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>

>Jim, if what you are singing is in fact period-3 or period-5 behavior, as I
>suspect, then the nonlinearity of the interaction between the vocal folds
>and other elements of the vocal tract cause the flaps of the vocal fold to
>oscillate in an irregular manner, repeating themselves every 3 or every 5
>oscillations. That is all that is needed for the low fundamentals to be
>produced.

Paul, does this mean that "subharmonic" and "undertone" are incorrect
descriptions of this phenomenon. My assumption all along is that the vocal
folds produce a fundamental vibration (in addition to many of its harmonic
overtones) and then the false vocal folds, arytenoids and other structures
reinforce every other vibration, every third vibration, every fourth etc.
(of the original fund. vibrations). If there are tones appearing that are
lower than primary vibration of the folds I presumed they could be called
"undertones" and if (as I hear them) they occur as fractions of fund.: 1/2,
1/3, 1/4 etc. then they could be called subharmonics. I think I need to
understand more about the terminology "period-3" and "period-5" behavior and
what it implies.

~Jim Cole

>Paul, does this mean that "subharmonic" and "undertone" are incorrect
>descriptions of this phenomenon. My assumption all along is that the vocal
>folds produce a fundamental vibration (in addition to many of its harmonic
>overtones) and then the false vocal folds, arytenoids and other structures
>reinforce every other vibration, every third vibration, every fourth etc.
>(of the original fund. vibrations). If there are tones appearing that are
>lower than primary vibration of the folds I presumed they could be called
>"undertones" and if (as I hear them) they occur as fractions of fund.: 1/2,
>1/3, 1/4 etc. then they could be called subharmonics. I think I need to
>understand more about the terminology "period-3" and "period-5" behavior
and
>what it implies.

Jim, I think all your terminolgy and assumptions are basically correct. The
point I've been trying to emphasize is that with all these phenomena, what
you end up with (sounding at a given point in time) is a harmonic series and
never a subharmonic series. If the laryngeal structures are reinforcing
every third vibration, then the true fundamental is a perfect twelfth lower
that the normal one, and you will have an overtone series over the true
fundamental which includes the normal one as a partial. Same goes for any
other "subharmonic" behavior (period 2, period 4, etc.). These phenomena
occur one at a time, not all at once. As for terminology, I guess I just
worry that people will misunderstand this and think that you're producing a
utonal chord with your voice.

> what you end up with (sounding at a given point in time) is a harmonic
series and
> never a subharmonic series. If the laryngeal structures are reinforcing
> every third vibration, then the true fundamental is a perfect twelfth
lower
> that the normal one, and you will have an overtone series over the true
> fundamental which includes the normal one as a partial. Same goes for any
> other "subharmonic" behavior (period 2, period 4, etc.). These phenomena
> occur one at a time, not all at once.

Ahaa! Perhaps my main assumption is not correct: I think I hear "sub 2"
(octave below initiated fund.)sounding with "sub 3" (octave and fifth) so
that the lowest notes are a fifth apart. Are they both there simultaneously
in the sub 3 clips at our site? Have you (or anyone else here on the list -
Dante?) analyzed all the clips yet? Just today I was getting sub 4 (two
octaves) and I thought I heard sub 3 creeping in with it (two low notes a
fourth apart). Yes, I see your point that if only one low note occurs with
the original fundamental tone then the low note can be construed as the new
fundamental. BTW, I just got those books on chaos, fractals and power
Laws - pretty daunting tomes!

As for terminology, I guess I just
> worry that people will misunderstand this and think that you're producing
a
> utonal chord with your voice.

I hope I can - if not now - someday

~Jim