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How does a violin reproduce overtones? - Theorizing a model


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If we play any note, presumably the overtones from the strings are transmitted to the body. (1) It seems that the center and upper part of the top then play the most active role in the reproduction of overtones. But how have we to see this?  Why does it happen in the upper part of the top and not in the lower part?

I find it interesting too in which locations small weights (as light as 2-3g) have the biggest overtone cutting effect: the upper f-wings. On the other hand the same weights on any location of the back don't change anything to the same audible degree. (2)

Then I noticed from my experiments that stiffening the frame around the top clearly improved the clarity of the instrument by augmenting resonances in the overtone range. (3) A similar effect came from installing a cross bar between the top side C bout linings. 

So how have we to see this? Why can the f wings filter overtones, why can a weak frame filter overtones? Does the back play no role at all?

To explain it in a model, I would interpret the top as a membrane which needs a frame. If the frame is loose it is like a drum skin which is not tight enough and therefore produces a dull sound. (4) The upper f wings are basically nothing else than an uneccessary attachment to the membrane and act always as some filter. But maybe the filter function is just in a region where it is beneficial for the overall sound impression.

Now, why in the upper part of the instrument? I think this comes simply from the fact that the neck has a better leverage on the top than the end button. Though I think this is more complex and includes as well the pumping motion of the body. 

 

Disagreement welcome. How does the violin reproduce overtones? Any better models?

 

(1) Or, if we excite the bridge with a sine wave generator, the body wouldn't add by itself any overtones. (Wondering if this is really correct)

(2) If anything some color shifts can be noticed. This makes me believe that the back has to be seen more than a sound modifier.

(3) I think it is important to mention here under which conditions this could be observed. The top was really thin and light. Presumably the result would have been different with a thick and heavy top.

(4) For a violin top the frame is more important in cross grain direction because in grain direction the wood is much stiffer and additionally clamped by the string force.

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11 minutes ago, Andreas Preuss said:

If we play any note, presumably the overtones from the strings are transmitted to the body. (1) It seems that the center and upper part of the top then play the most active role in the reproduction of overtones. But how have we to see this?  Why does it happen in the upper part of the top and not in the lower part?

I haven't noticed that this happens mostly in the upper portion of the top, but am willing to take a careful look at any evidence that it does.

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"presumably the overtones from the strings are transmitted to the body." 

The violin does not, the air around/inside it does, the violin just initiates the disturbance from the energy transfer

it creates an individual signature based on that particular violins shape, size, weight, elasticity {and other things} no other "flaps in the wind" quite like it, they will all be similar,{meaning you or anyone will be able to tell they are hearing a bowed instrument called a violin} some virtually identical , but no two will be the same.

As far as the location of the "upper part of the top" again that is somewhat of a "psycho acoustic"; phenomenon, somewhat like "voice throwing" making one "think" it's coming from there, when in fact it is the entire proximity of the "face" of the instrument, the entire "blanket of air" around it , including the back.and in all that, it very well may seem like amplitude is "pooling" there, but it's somewhat of an auditory illusion in my experience. 

you do bring up very important "thinks" as far as "zones" in graduations that may be thicker or thinner that are carved that way in order to influence the dynamic states of an entirely different region of the top or instrument, these can be used to "direct" energy elsewhere where it will be better used, or to absorb energy. 

the thing is that based on the inherent differences in material I have never found any "cookie cutter" short cut to help carving one way or another, every instrument seems to be an individual endeavor that like any construction project is somewhat the same yet always different and will always involve custom decision making throughout the process to hopefully achieve satisfactory results 

edit; to "see" or hear how much the air around the violin has to do with the entire thing is to get a powerful yet quite fan, like a Dyson blade-less one, and blast it on high and blow it right onto the violin as it's being played by someone else, you can literally hear the sound get blown away. In this case we changed nothing on the violin but the sound sure does change as they move around and air is more or less directed right at them and the instrument.

 

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Vibrations travel quickly and whatever is presented to the bridge will rapidly present to all masses in the instrument.

All these presentments of vibrations will include the overtones and harmonics presented by the strings.

Each mass will respond to principal and partials as well as it can.  This will depend on which if any resonant modes of the mass are near enough in frequency to the signal vibration.

This will depend on the Q and frequency of each resonance.  If the frequencies of resonance and near enough, and the Q low enough, then the resonance will accumulate energy from the signal.

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The violin body reproduces overtones the same way it produces tones: each natural mode of vibration of the body vibrates at the string frequencies.

The amplitude and phase of each string overtone that is echoed by the body varies by how much the string frequencies differ from the natural body frequencies.

So you need a string that can produce a lot of strong overtones.

And you need a violin body that has lots of natural modes with frequencies throughout the overtone region.

The phase of the body vibrations to the string/bridge vibrations is an additional complication. As a general rule, a string overtone whose frequency is lower than a natural mode frequency, will make that violin mode vibrate in phase with it. If the string overtone frequency is higher than a natural mode frequency,  the two vibrations may occur out of step with each other and can cause unexpected tonal changes.

For example, as once plays up the G string towards the very strong air body mode frequency, A0, (around 270Hz or B to D range), the amplitude of vibration of the violin becomes strong because the frequency of the string is getting close to the frequency of the mode. Once you get a little past A0 frequency, the vibration will still be strong but the phase can suddenly become out of sync with the bridge/string. 

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If a bridge and neck is put on a massive body, it would still radiate some sound. Some may arrive from the bridge, some from vibrations in the massive body. Maybe some radiates from the bow hair as well? Possibly a little from the tailpiece and neck/fingerboard.

Regarding the body, it probably is difficult to determine which part of the body contributes most to the radiation. The signal comes from the bowed string, and the bridge is probably the most sensitive part regarding the highs. Adding mass there has a clear effect on the sound. More clear, in my experience, than adding masses to the inner f-hole wings.

The whole body vibrates more or less and the resonance density increases with the frequency. The adding mass thing can probably be used for calculations of effective masses (see Janssons book), but not to determine where the largest contribution to the radiated sound is. As the plate divides up into smaller portions of in phase and put of phase patterns, the radiation direction and strength becomes more complex and "beam like". The behaviour in this region is not really "modal" but are rather clusters of modes.

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6 hours ago, Andreas Preuss said:

If we play any note, presumably the overtones from the strings are transmitted to the body. (1) It seems that the center and upper part of the top then play the most active role in the reproduction of overtones. But how have we to see this?  Why does it happen in the upper part of the top and not in the lower part?

Best would be to find a mechanical / civil engineer specialized in dynamics with an interest in violin making. 

 

7 hours ago, Andreas Preuss said:

(1) Or, if we excite the bridge with a sine wave generator, the body wouldn't add by itself any overtones. (Wondering if this is really correct)

Yes it is, as long as the sine wave is pure, the "excitation" is kept small and the violin is not strung up. It is easy to create a very pure sine wave ( any sound card will do )  but it is difficult to maintain the purity ( linearity ) when it's being coupled to the violin.  

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8 hours ago, Andreas Preuss said:

(1) Or, if we excite the bridge with a sine wave generator, the body wouldn't add by itself any overtones. (Wondering if this is really correct)

I think it would in some cases also excit overtones.  

If you look at motion studies of the plates, in many ways the violin responds like a low Q driven soundboard.  In this way, maybe harmonics would much be driven if they weren't in the signal.

Bu that isn't the whole story.  The violin also responds by having the resonances of its masses stimulated.  The air body in thw cavity is a good example.  When such resonances are stimulated, I don't see how their harmonics wouldn't also be stimulated.

 

 

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4 hours ago, David Beard said:

Each mass will respond to principal and partials as well as it can. 

If you are saying 'as well as it can' this implies that there are masses which can respond better than others, or not? 

For me it looks like that under the condition the top plate is properly framed masses on the top can respond better to the presentments. 

If you remove wood from the back plate of a violin there are not so dramatic changes. The most sensitive zones are at the C-bouts and I interpret this in my model as modifying the stiffness of the frame.

Then some experiments (not made by me) seem to indicate that removing wood from the center of the top ca change a lot. I interpret this as changing the properties of the membrane. What we hear is a dramatic change in the overtones. 

 

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1 hour ago, Carl Stross said:

Yes it is, as long as the sine wave is pure, the "excitation" is kept small and the violin is not strung up. It is easy to create a very pure sine wave ( any sound card will do )  but it is difficult to maintain the purity ( linearity ) when it's being coupled to the violin.  

If I take two strung up violins and excite the bridge with a tuning fork (not quite a a sine wave generator) both violins sound the same. The major difference is the loudness. You could presumably even recognize in a blind test that a tuning fork was used. So it does make not a difference if the violin is strung up, or not?

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4 hours ago, Anders Buen said:

The signal comes from the bowed string, and the bridge is probably the most sensitive part regarding the highs.

I look on the bridge only like a transmitter. So impairing its functonality will of course have a dramatic effect. However, the bridge itself can't radiate enough sound because its surface is too small. (Correct me if this is wrong)

That's why I am more interested in the question why can we dramatically change the sound with placing small weights on the wings of the f holes and only there. 

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I think stringing and tuning the strings matter greatly.

 

* The 'membrane' or soundboard response should happen as long the materials aren't too thick and stiff.

* Some of resonance responses depend on enough mass being present.  Mostly I'm thinking of the extra back mass.  If that is significant enough it can contribute response to some playing imputs that are other wise unavailable.    

* Coupling of respnses also matter.  The more heavy and stiff the overall building, I think it can interfere with things like the body and air responses coupling up and influencing each other.

I believe there's a famous rock and roll guitar maker that says something like 'a good playing instrument is just on the verge of falling apart'.  I think this largely has to do enabling responses to couple readily.

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6 hours ago, Peter K-G said:

The question is: 

Does the soundbox only amplify and filter

Or does it add inherit, by design sound (modes)

The thing is that I don't think the violin body can add harmonics. 

Different strings produce different harmonics (overtones) and are used eventually to equalize the the sound of a given violin where it has too much filtering.  Or a string which makes particular strong overtones in that range can counterbalance the filtration.

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11 minutes ago, David Beard said:

Would you mind summarizing your observations on this?

Its a simple as taking two small supermagnets of 1.2g (just measured them again, each is 0.6g) and placing them on all thinkable locations on the violin body. I made this once in a more systematical way like moving them over an invisible grid some thing like 2cm apart. I did this on back top and ribs and regardless the violin the most audible changes are actually at the bass side upper f wing. It seems as well that a thicker top is less sensitive.

With heavier weights the effect is of course more audible

With 'dramatically' I meant that you can hear clearly the damping. It is however not as strong as on the bridge. 

 

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1 minute ago, Andreas Preuss said:

If I take two strung up violins and excite the bridge with a tuning fork (not quite a a sine wave generator) both violins sound the same. The major difference is the loudness. You could presumably even recognize in a blind test that a tuning fork was used. So it does make not a difference if the violin is strung up, or not?

If the tuning fork pitch is the same as the frequency of one of the violin's resonance peaks the sound will be loud.  If it is the same frequency as one of the valleys between the peaks the sound will be much much less loud.

A bowed string has many harmonics which are integer multiples of the fundamental pitch f:  1f, 2f, 3f, 4f, 5f, 6f.....  the amplitudes of each of these harmonics follows a decreasing sequence 1/1, 1/2, 1/3, 1/4, 1/5, 1/6....  This forms a "saw tooth wave" form.

Each one of those harmonics can fall on a violin's bridge resonance peak, valley, or some where in between.  So some of the harmonics might be high amplitude while others low and the resultant note will be a summation of all of these different amplitude harmonics.  Thus the bridge's frequency response curve acts as a filter which changes the shape of the bowed string saw tooth wave.

The violin's body acts as another subsequent filter with its frequency response curve changing the amplitudes of all of the note's harmonics which further changes the shape of the bowed string's saw tooth curve.  This is shown in the attached diagram taken from   one of Colin Gough's presentations https://acousticstoday.org/wp-content/uploads/2016/06/Gough.pdf

Thus a filtered bowed note for example can sound "boomy" and loud if its fundamental frequency and its second harmonic happen to have a high amplitudes and conversely the note can sound "tinny" and weak if the first few harmonics have low amplitudes.  

Every note has a different series of harmonics and it is apparent that the sound character and loudness of each of these notes depend upon how their harmonics are filtered by the bridge and violin body.

 

If you are a serious student of the support I suggest doing a Google search on "Colin Gough, violin" and read many of his free publications and watch his Youtube presentations.

 

Screen Shot 2021-05-24 at 9.02.55 PM.png

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5 hours ago, ctanzio said:

And you need a violin body that has lots of natural modes with frequencies throughout the overtone region.

That's what I am interested in. 

So far I can only say that the frame around the top (under condition that the top is pretty thin) largely influences the strength of the overtone spectrum and I am looking for an explanation.

5 hours ago, ctanzio said:

The amplitude and phase of each string overtone that is echoed by the body varies by how much the string frequencies differ from the natural body frequencies.

If I understand this correctly you see it as a resonator model. 

 

5 hours ago, ctanzio said:

For example, as once plays up the G string towards the very strong air body mode frequency, A0, (around 270Hz or B to D range), the amplitude of vibration of the violin becomes strong because the frequency of the string is getting close to the frequency of the mode. Once you get a little past A0 frequency, the vibration will still be strong but the phase can suddenly become out of sync with the bridge/string. 

Yes, for this the resonance model is correct. But my question I am asking myself is how does this resonance simultaneously produce overtones? Does the resonance itself vibrate differently comparing violin A with violin B?

 

 

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21 minutes ago, Marty Kasprzyk said:

Every note has a different series of harmonics and it is apparent that the sound character and loudness of each of these notes depend upon how their harmonics are filtered by the bridge and violin body.

So this is a filter model and the body can by no means add anything to the 'information' given to it.

 

22 minutes ago, Marty Kasprzyk said:

If you are a serious student of the support I suggest doing a Google search on "Colin Gough, violin" and read many of his free publications and watch his Youtube presentations.

Yes, I am a serious student. Thanks for the material.

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5 hours ago, Andreas Preuss said:

I look on the bridge only like a transmitter. So impairing its functonality will of course have a dramatic effect. However, the bridge itself can't radiate enough sound because its surface is too small. (Correct me if this is wrong)

That's why I am more interested in the question why can we dramatically change the sound with placing small weights on the wings of the f holes and only there. 

Put your weight on the bridge and listen, the effect there is going to be more dramatic than on the inner f-hole wings. An interesting twist is Joe Curtins «super light», where he has differeent weights to be screwed on the right foot (?) of the bridge. A variable sound concept. A violinist use a mute, as you know well.  

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6 hours ago, Andreas Preuss said:

The thing is that I don't think the violin body can add harmonics. 

Are you sure, the lower modes if near a note shows up on spectrum. What's to say that that's not the case with higher modes too.

If you can call them harmonics is another question, but the lower body modes are added as extra that aren't coming from bowed strings.

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