resonators

>>>This is a common fallacy. The resonator can do nothing but selectively
>>>amplify partials already contained in the source of the vibration.
>
>>Suspend the keys over the resonators and take a spectrogram; you'll find
a >>mixture of the integer harmonics and bar harmonics. A spectrogram of
the >>key alone does not show these integer harmonics.
>
>There has to be some explanation for this -- I stand by the physical
>validity of my original statement.

From my limited understanding, working with resonant filters and such, I
tend to agree with Paul. But could it be that the column of air in the
resonator has its own harmonics?

Carl

Absolutely. One can cut slots in the resonator, taper it,
fill with felt, etc. at strategic points.
Rick

> But could it be that the column of air in the
> resonator has its own harmonics?
>
> Carl
>
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Carl Lumma wrote,

>From my limited understanding, working with resonant filters and such,
I
>tend to agree with Paul. But could it be that the column of air in the
>resonator has its own harmonics?

The resonators in question resonate at all odd partials of a fundamental
frequency. My mistake was in thinking about steady-state oscilations,
rather than exponentially decaying ones. If you hit the end of an open
tube just right, you'll hear a pretty-well defined note, even though
nothing but the air in the tube was ever oscillating at that frequency!
This must be something like what is going on in the gender.

>>I would guess that the bodies of the horns will
>>resonate with their own harmonics, at least.
>
>Remember, the resonant frequencies of the horn can only
>determine selective amplification characteristics -- they
>won't add new harmonic content to the signal (except in
>transients).

This came up a while back on a discussion involving the partials of gamelan
instruments. You called it a "common fallacy" that resonators add their
own harmonics to a sound. But when I asked if the column of air in the
resonator could vibrate to its own harmonics when excited somebody came on
and said, "you bet", or something like that. And now Wolf seems to agree
as well. Can we get a consensus here? What's a transient?

-C.

I've not actually looked it up, but I'd define a transient as a brief
emission having an extremely fast attack and decay, containing both periodic
and nonperiodic stuff in addition to, and including part of the following
sustained portion of a sound, if any.
At 01:03 AM 9/21/99 -0400, you wrote:
>From: Carl Lumma <clumma@nni.com>
>
>>>I would guess that the bodies of the horns will
>>>resonate with their own harmonics, at least.
>>
>>Remember, the resonant frequencies of the horn can only
>>determine selective amplification characteristics -- they
>>won't add new harmonic content to the signal (except in
>>transients).
>
>This came up a while back on a discussion involving the partials of gamelan
>instruments. You called it a "common fallacy" that resonators add their
>own harmonics to a sound. But when I asked if the column of air in the
>resonator could vibrate to its own harmonics when excited somebody came on
>and said, "you bet", or something like that. And now Wolf seems to agree
>as well. Can we get a consensus here? What's a transient?
>
>-C.
>
>>You do not need web access to participate. You may subscribe through
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>

[Carl Lumma, TD 323.1:]
>>> I would guess that the bodies of the horns will
>>> resonate with their own harmonics, at least.

[Paul Erlich, TD 324.11:]
>> Remember, the resonant frequencies of the horn can only
>> determine selective amplification characteristics -- they
>> won't add new harmonic content to the signal (except in transients).

[Carl Lumma, TD 325.10:]
> This came up a while back on a discussion involving the partials of
> gamelan instruments. You called it a "common fallacy" that resonators
> add their own harmonics to a sound. But when I asked if the column of
> air in the resonator could vibrate to its own harmonics when excited
> somebody came on and said, "you bet", or something like that. And now
> Wolf seems to agree as well. Can we get a consensus here? What's a
> transient?

Paul is right. If a resonator has a resonant frequency of W1 (that's
supposed to be omega 1, but who has Greek?), and is "shocked" with
a pulse (== a transient), it will respond by resonating at its own
frequency, with that response decaying over time according to the
characteristics of the resonator. BUT, if a periodic wave of frequency
W2 is applied (whether sine wave or containing overtones), after the
response stabilizes, it will be entirely at frequency W2, howbeit
perhaps with a different proportion of overtones than came in.

I can't quite pull off a "proof" of this, but I know it's covered in
college dynamics textbooks.

JdL

We do have a consensus -- the resonator's own modes might produce a decaying
tone if the resonator is struck hard (that's a transient), but if the source
has no energy at the resonant frequency, there won't be a _sustained_ pitch
at the resonant frequency. Wolf's point is that if there is noise coming
from the source, the noise will be selectively amplified around the resonant
frequencies, giving it a sense of pitch.

>Paul is right. If a resonator has a resonant frequency of W1 (that's
>supposed to be omega 1, but who has Greek?), and is "shocked" with
>a pulse (== a transient), it will respond by resonating at its own
>frequency, with that response decaying over time according to the
>characteristics of the resonator. BUT, if a periodic wave of frequency
>W2 is applied (whether sine wave or containing overtones), after the
>response stabilizes, it will be entirely at frequency W2, howbeit
>perhaps with a different proportion of overtones than came in.

>I can't quite pull off a "proof" of this, but I know it's covered in
>college dynamics textbooks.

Yup, it's undergrad classical mechanics.

[earlier today, I wrote:]
> Paul is right.

But, Carl is also right, because there are ALWAYS transients present
in the input, and so to a lesser or greater extent there will ALWAYS be
a component of the resultant sound that is at a resonant frequency of
the resonator. This either will or won't be audible depending upon the
specifics of the resonator and of the input signal.

JdL

I don't know why you think there will always be transients present in the
input. Only at the beginning of a tone will there be a transient, after
which the resonator's frequency will die away.

[Paul Erlich, TD 326.14:]
> I don't know why you think there will always be transients present in
> the input. Only at the beginning of a tone will there be a transient,
> after which the resonator's frequency will die away.

Yes, if the input consists of long steady tones, that's exactly what
will happen, as I reaffirmed in TD 326.4. But, any real-life sound of
interest is constantly changing, producing transients many times per
second. This is probably mathematically indistinguishable (i.e.,
identical) to what you're referring to in:

[Paul, TD 326.9:]
> Wolf's point is that if there is noise coming from the source, the
> noise will be selectively amplified around the resonant frequencies,
> giving it a sense of pitch.

The important point you're making is correct: the resonator does not
add its own frequencies overtop of a steady input tone. Rather, only
noise is selectively amplified, giving a sense of pitch.

JdL

>We do have a consensus -- the resonator's own modes might produce a decaying
>tone if the resonator is struck hard (that's a transient),

Okay. So would you confirm for me once more if the answer to the following
is no: When we drive a resonator with a sine tone tuned to the fundamental
mode of the resonator, do we get anything of the resonator's partials?

>but if the source has no energy at the resonant frequency, there won't be
a >_sustained_ pitch at the resonant frequency.

By "resonant frequncy", do you mean only the fundamental one? That is, if
I tune a few sine tones to the harmonics of a resonator, will it resonate
(at its fundamental frequency, or at any of it's higher harmonics)?

-C.

>Okay. So would you confirm for me once more if the answer to the following
>is no: When we drive a resonator with a sine tone tuned to the fundamental
>mode of the resonator, do we get anything of the resonator's partials?

The answer is no.

Resonators do not have exactly harmonic partials, and for a PA horn, if it
unfortunate enough to have resonances, they certainly won't form anything
like a harmonic series.

>>but if the source has no energy at the resonant frequency, there won't be
>a >_sustained_ pitch at the resonant frequency.

>By "resonant frequncy", do you mean only the fundamental one?

Any resonance.

>That is, if
>I tune a few sine tones to the harmonics of a resonator, will it resonate
>(at its fundamental frequency, or at any of it's higher harmonics)?

Again, speaking of "harmonics of a resonator" is not always meaningful. But
the resonator will amplify whatever sine tones are at or near its
resonances, and it won't amplify or create any others.

[Carl Lumma, TD 327.3:]
>> Okay. So would you confirm for me once more if the answer to the
>> following is no: When we drive a resonator with a sine tone tuned to
>> the fundamental mode of the resonator, do we get anything of the
>> resonator's partials?

[Paul Erlich, TD 327.12:]
> The answer is no.

If the resonator is linear in its response, we're guaranteed to get a
sine wave out, at the same frequency as the sine wave in (though
probably with amplitude and phase shifts). If the resonator is
non-linear, there will potentially be additional frequencies present in
the output, but they will all be overtones of the input sine wave.

JdL

>If the resonator is
>non-linear, there will potentially be additional frequencies present in
>the output, but they will all be overtones of the input sine wave.

Right. Once again, non-linearities in the response lead to sum and
difference tones, which in the case of a single sine wave means overtones of
that sine wave. For air-cavity resonators, the non-linearity of the air's
response only becomes important at fatal dB levels.

[me, TD 329.3:]
>> If the resonator is linear in its response, we're guaranteed to get a
>> sine wave out, at the same frequency as the sine wave in (though
>> probably with amplitude and phase shifts). If the resonator is
>> non-linear, there will potentially be additional frequencies present
>> in the output, but they will all be overtones of the input sine wave.

[Paul Erlich, TD 329.14:]
> Right. Once again, non-linearities in the response lead to sum and
> difference tones, which in the case of a single sine wave means
> overtones of that sine wave. For air-cavity resonators, the
> non-linearity of the air's response only becomes important at fatal
> dB levels.

I hope I'm not flogging a dead horse here, but way back in TD 322.2,
Carl Lumma started this whole thing with:

>> I doubt you'll wind up with sine tones, considering the parking-lot
>> horns you'll be playing the thing thru...

Parking lot horns could be expected to be highly non-linear: by tending
to clip the sine wave in, they'd tend to add odd harmonics to the
output. So Carl was right, yes? In a subsequent post, he made a
statement that you and I agree was incorrect:

[Carl Lumma, TD 323.1:]
>> I've never been able to get a sine tones out of a cone speaker in a
>> normal room. I don't know exactly why that is, but I suspect PA
>> horns would be worse rather than better. I would guess that the
>> bodies of the horns will resonate with their own harmonics, at least.

Other than Carl's incorrect attribution of distortion to the harmonics
of the horn, he was correct, yes?

JdL

>Other than Carl's incorrect attribution of distortion to the harmonics
>of the horn, he was correct, yes?

The horn could easily have a nonlinear response, so Carl was completely
correct. It's not a case of a resonator responding nonlinearly, though.

This didn't seem to get sent . . .

> -----Original Message-----
> From: Paul H. Erlich
> Sent: Friday, September 24, 1999 5:59 PM
> To: 'tuning@onelist.com'
> Subject: RE: [tuning] Re: resonators
>
> >Other than Carl's incorrect attribution of distortion to the harmonics
> >of the horn, he was correct, yes?
>
> The horn could easily have a nonlinear response, so Carl was completely
> correct. It's not a case of a resonator responding nonlinearly, though.