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From: Bobbie Giordano
Date: Tue, 2 Jan 1996 16:30:13 -0500 (EST)
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.

> 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.

> Diameter of the pipe affects "voice" but not pitch.

Also agreed. This is the quality or tone of the sound, but diameter of the
pipe is not the only factor affecting "voice", right? What about airflow
velocity, volume of the airflow, attack and decay? The diameter may not
affect pitch, but pipe length does by altering the resonant frequency, that
in turn affects the amplitude of the sound, which plays a part in the tonal
quality, I suspect.

> 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)

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.

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.

> The embouchure acting as a helmholtz resonator could have a resonant
> frequency at the pitch of bent notes.

This is in essence what I was driving at in a previous post regarding the
matching of one of a reed's various possible vibrating frequencies with
that produced by the embouchure.

> 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....

My brain hurts!

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