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From: Mike Curtis
Date: Tue, 2 Jan 1996 15:20:30 -0800 (PST)
Subject: Re: Bending & Resonant Material

>
> On Mon, 1 Jan 1996 WVE~ol.com wrote:
>
> > In response to Bobbie;
> >
> > I have a new (to me) book by Hermann Helmholtz and a new (to me) partial
> > theory about bending. The column of air resonance that occurs with sound
> > waves traveling along a cavity like an organ pipe cannot occur in the mouth
> > because the "pipes" are too short at low pitches.
>
> I don't agree. Sure, I couldn't resonate like organ pipes on some extremely
> low pitches, but I play harmonica, and it's possible to find resonance for
> notes played in the range of a harmonica.

There's a difference here. A pipe is a tuned column. It has straight sides
and a sealed end. As such, it sets up oscillation in a linear (line)
fashion, completely and totally dependent on length, and nothing but length,
as a direct function of wavelength. While I haven't tested this, I would
imagine that pipe diameter would affect sound pressure level, allowing a
larger mass of air to be vibrated. It may well affect timbre as it deviates
from the perfect tuned column into a tuned drum configuration. I'm not sure
of the ratio of length to diameter/circumference, but I'm sure Vern can dig
that information out of his "new old book".

A Helmholtz resonator is by definition a larger enclosure with a smaller
opening, and resonates as a function of the capacitance of the trapped air
and the inductance of the opening. Apples and orangutans, even though the
result is similar.

Also, some notes on the harp are in the upper bass regions, such as the blow
1 on a G, at 196 Hz, with a wavelength around 6 feet. Some are very high,
like the 3136 Hz high G note on the high G harp, with about 4.6" wavelength.
A resonant column is 1/4 wavelength, giving us a range of 1.5 feet to about
one inch. The only one I've seen who could possibly accommodate this as a
resonant column was E.T. and his telescoping neck, but at last check he
didn't play the harp.

However, by using our mouths as Helmholtz resonators, it is quite feasible
to tune our anatomies to effect Helmholtz resonance within these frequency
bounds.

However, I suspect that much more than just oral resonance is at work in
those with the finest resonant qualities. Just as an operatic singer uses
chest, throat, and nasal resonance, and even girth (ever wonder why the best
operatic singers are of enormous size? It's not coincidence!) to achieve
the finest tone and resonance, so too the best harmonicists will use every
tool at their disposal.

> > In the organ pipe, the resonant frequency is a function only of the length
> > of the pipe, if we disregard secondary effects like temperature.
>
> I agree. But I imagine it's a characteristic relationship regardless of the
> reed-resonant chamber combination in consideration.

I don't believe pipe organs use reeds. Steam or compressed air is used to
activate the pipes by blowing across them, much like we blow on a flute,
thereby exciting resonant oscillation in the tuned column of air.

> > In a helmholtz resonator (like a jug), the resonant frequency is a
> > function of the volume and the area of the hole.(the neck of the jug)

Or in the case of the tuned port, the VOLUME (three dimensional) of air in
the port.

> I presume the volume you refer to is that determined by the resonator's
> interior dimensions, of which the area of the hole is part and parcel, not
> the other meaning of the word, loudness or the wave's amplitude. It's
> simply air in an enclosed container that, because it possesses a distinct
> frequency dictated by the dimensions of the container it's in, can cause
> sound waves of the same frequency to become more amplified [louder] if
> played over the opening. Thus, cupping the harmonica creates a resonator
> of sorts, but with the capacity to change its frequency by subtle changes
> in the cup's shape and size. The changeable dimensions of the human vocal
> tract and oral cavity can act the same way. Both methods can affect the
> amplitude of the sound wave matching the "resonator's" frequency, but not
> the pitch, unless the adjustments to the resonator involve changing the
> length of the column of air moving past the reed that causes it to vibrate.
> These are still just my developing theories...I'm still wide open to other,
> more rational explanations.

In acoustic harmonica, the traditional "wah-wah" effect tells us that it is
acting as a variable midrange filter, or a variable high pass filter. Also,
the fact that a cupped harmonica is richer sounding tells us that some
midrange resonance is involved. Because this can be varied, we do have a
certain amount of variable midrange boost.

So what we have is a combination of variable midrange boost and variable
high cut.

But I believe we need to consider the outside environment of the harmonica
as a separate issue. Larry Adler gets very nice resonance without using his
hands. I also get nice resonance in a rack, which of course precludes the
use of hands. (And yes, I sometimes play in a bare rack without my custom
harp pickup). when I use hand-wahs, it doesn't seem to affect my resonance,
just the timbre of the midrange and high frequencies.

> I do have one problem with the idea of these so-called resonators, which is
> that air is physically moving THROUGH these "resonators". This is different
> from holding, say, a tuning fork vibrating at 440 Hz. over the opening of a
> resonator with a resonating frequency of 440 Hz. which causes the sound of
> the tuning fork to thus be amplified. Then again, maybe there's nothing
> significant about this distinction. I'm unsure.

Good question - but even if it does affect things, I'm not sure it's
pertinent to the overall question regarding resonance mechanics. It's
simply another variable. Obviously, it doesn't _hurt_ resonance.

> > Mystery...where is the hole? Is it the reed slot in the coverplate, is
> > it at the harmonica mouthpiece, or is it somewhere in the throat?
>
> I'd say probably the harmonica mouthpiece, where the air from the human
> resonant chamber is applied and interacts with the instrument's vibratory
> [thus sound wave producing] elements. Still, there remains the issue of
> the addition of air pressure and flow. Hmmm....

Or being a puckerer, I'd say it's the pucker.

I just tried hitting a low C on my harp, then removing the harp and
whistling, resonating the volume of air in my mouth at the pucker opening I
had. Guess what note sounded ;-)

I suspect this explains why the advice to newbies to "drop your jaw" helps
with bending and resonance.

> My brain hurts!

Take two Oskars and call me in the morning.

-- mike