Undertones/subharmonics (?) esp. vocal

Whew - This is a hard list to keep up with!!! I had a concert last weekend and got behind
on everything including a marathon of posts here - it has taken me this long to catch
up...many interesting threads are being woven here. BTW, a lot of it is way over my head
but I am a fascinated and eager-to-learn newbie here.

[Ray Tomes]

> I have found this discussion very interesting. Dave, it seems to me
> that if the undertones are appearing by a slight vocal adjustment then
> it makes a lot of sense to see them as undertones and not some
> arrangement of different overtones with a varying fundamental.
> The whole original description shouts "undertones" at me.

Yes Ray - I guess it's these slight adjustments, the dramatic and instantaneous "kicking
in" of the lower notes at fixed intervals below, and the fact that (for ex.) the original
fund., the octave below, and the octave and fifth below can sound at once (I've been
listening very carefully in spare moments this past week and am convinced they are all
there - at least sometimes), that make it shout undertones to me too.

> [Ray]
> I agree that the physics of multiple undertones is not so obvious.
> However in this case we have a sentient being deliberately shaping
> resonant cavities to achieve the effects. This means that if some small
> non-linearities are present then a close approximation to cavity shape
> required to produce exact undertones could cause some locking in.
>

Dave Hill's 5/28 posting seemed to hint at this idea near the end ("...given the physics
of standing waves in cavities such as horns, it seems plausible that there should be faint
vibrations at one half or possibly another submultiple of the fundamental frequency."

>
> Paul Erlich [TD199.4]
> >I think a better description would relate to chaos theory. The opening and closing of
> >the vocal folds experiences a period-doubling, so the apparent fundamental and its
> >overtones are still prominent (due to the dynamics and not the filtering) but the
> >true fundamental is an octave lower. The way the "subharmonic" almost "jumps" in and
> out of existence as one varies the mode of singing is a hallmark of a nonlinear
> >bifurcation. I refer Jim to any of the popular books on chaos theory, such as Manfred
> >Schroeder's _Fractals, Chaos, and Power Laws_.
>

Thanks Paul - I look forward to reading this as well as the others you referred to
before. This is an area I know next to nothing about (except "chaos" - in daily life!)

> [Ray]
> I disagree as it is stated that notes 1/2, 1/3, 1/4, 1/5 the original
> all came in with slight adjustments. That is not chaotic behaviour but
> undertones.

I would like to make a recording of this phenomenon and send it to whomever on this list
is interested in listening to it, analyzing, etc. I guess cassette is the easiest for me
to make. I am really interested to get your feedback on these sounds - any takers?

~Jim Cole

Jim Cole [TD 214.1]

>Whew - This is a hard list to keep up with!!!

I can echo that as I am responding so late to your message.

>Yes Ray - I guess it's these slight adjustments, the dramatic and instantaneous "kicking
>in" of the lower notes at fixed intervals below, and the fact that (for ex.) the original
>fund., the octave below, and the octave and fifth below can sound at once (I've been
>listening very carefully in spare moments this past week and am convinced they are all
>there - at least sometimes), that make it shout undertones to me too.

Right. One reason that I have been a bit slow responding is that I was
taken aback when someone (sorry I forget who) said that I was wrong and
that chaos frequency doubling does add lower frequencies. Now that I
think about it the mathematical cases of chaos do in fact do that, so I
was wrong to say that was not so. However I will have another go at
putting my foot in it and say that I think that real world, continuous
systems do show frequency doubling and not frequency halving behaviours
- which is presumably why they call it frequency doubling.

>I would like to make a recording of this phenomenon and send it to whomever on this list
>is interested in listening to it, analyzing, etc. I guess cassette is the easiest for me
>to make. I am really interested to get your feedback on these sounds - any takers?

Yes please. I am in New Zealand, so sending a WAV file might be
easiest, but if you want to use post my address is:
Ray Tomes, 59 Maritime Tce, Birkenhead, Auckland, New Zealand.

I would be happy to make an analysis and post the results to the list.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
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Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm

Ray Tomes wrote,

>Right. One reason that I have been a bit slow responding is that I was
>taken aback when someone (sorry I forget who) said that I was wrong and
>that chaos frequency doubling does add lower frequencies. Now that I
>think about it the mathematical cases of chaos do in fact do that, so I
>was wrong to say that was not so. However I will have another go at
>putting my foot in it and say that I think that real world, continuous
>systems do show frequency doubling and not frequency halving behaviours
>- which is presumably why they call it frequency doubling.

Wrong again, Ray -- it's period doubling that occurs in real world,
continuous systems, which of course means frequency halving. The book _Chaos
and Fractals_ that I mentioned before actually gives a set of experimental
results from a non-linear acoustical system where period doubling was
observed (you can find hundreds of other such experiments discussed in the
literature and even in abstracts on the internet).