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How does a violin reproduce overtones? - Theorizing a model


Andreas Preuss
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1 hour ago, David Burgess said:

I think of the violin as producing an "impact spectrum" (though a very small one) every time the string kink hits the bridge.

That's kind of what I was thinking, when I starting the question, followed with some tests.

I also thought that the notes/string motion by themself could contribute, but it does that only when a note is very near a mode.

 

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13 hours ago, David Burgess said:

What is your impression from this slow-motion video?

The bridge isn't moving AT ALL. (Because it is not sitting on a violin?)

Interesting to see it visualized. Unfortunately it doesn't give any idea how overtones are transmitted to the bridge.

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7 minutes ago, Andreas Preuss said:

 

Interesting to see it visualized. Unfortunately it doesn't give any idea how overtones are transmitted to the bridge.

It's my understanding that there are also numerous harmonic, smaller kinks hitting the bridge (too small to show up easily in this demonstration), since the string is simultaneously vibrating in sub-sections of one half, one third, one quarter etc. of the main string length.

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19 minutes ago, David Burgess said:

It's my understanding that there are also numerous harmonic, smaller kinks hitting the bridge (too small to show up easily in this demonstration), since the string is simultaneously vibrating in sub-sections of one half, one third, one quarter etc. of the main string length.

The string in the video is nowhere near correct tension. It's not representative of an open G.

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19 minutes ago, David Burgess said:

It's my understanding that there are also numerous harmonic, smaller kinks hitting the bridge (too small to show up easily in this demonstration), since the string is simultaneously vibrating in sub-sections of one half, one third, one quarter etc. of the main string length.

Right, otherwise there wouldn't be overtones. 

But I leave those problems to the manufacturer of strings. I am much more interested in how a good violin can pick up the 'overtone information' best.

From all what I know by experience, a bad setup can destroy a lot, or the other way around it is not only the construction of the body itself which makes a the overtone spectrum really work best. Therefore all measurements in physiscs lab might give to some degree a distorted image if the setup of the examined violin was not at its optimum.

If I would put it in one word I think 'balance' is the best description. So to me it looks like the ideal balance between the 'driving system' (strings, string angel, fingerboard tilt, bridge, tailpiece and tailgut) and the resonating system (the violin body itself). What are the necessary pre conditions from the violin body and how the 'balance' can be achieved is the real question.

There was a violin maker in Germany in the 1970s who tried to balance forces and could show in experiments that he improved the playability of flagolet harmonics on an instrument. While this might be not really a solid proof, I think this is the correct direction to search for answers.

 

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55 minutes ago, David Burgess said:

It's my understanding that there are also numerous harmonic, smaller kinks hitting the bridge (too small to show up easily in this demonstration), since the string is simultaneously vibrating in sub-sections of one half, one third, one quarter etc. of the main string length.

14 minutes ago, Andreas Preuss said:

Right, otherwise there wouldn't be overtones.

Wrong.

If the string is plucked, then you'd have the string harmonics doing whatever they want (even out of tune with the fundamental).  But a bowed string, with Helmholtz motion, will have any other kinks  (and out-of-tune frequencies) damped out by the bow hair.  You can see some startup extra kinks in the video, but once it gets going, there's only one kink circulating.

The "kink" gives a sawtooth input to the bridge, sortof like a periodic impact, and that's all you need to provide the full spectrum of overtone energy into the body.

 

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1 hour ago, Don Noon said:

Wrong.

If the string is plucked, then you'd have the string harmonics doing whatever they want (even out of tune with the fundamental).  But a bowed string, with Helmholtz motion, will have any other kinks  (and out-of-tune frequencies) damped out by the bow hair.  You can see some startup extra kinks in the video, but once it gets going, there's only one kink circulating.

The "kink" gives a sawtooth input to the bridge, sortof like a periodic impact, and that's all you need to provide the full spectrum of overtone energy into the body.

 

If that were so, wouldn't you hear the impact spectrum of the violin itself, rather than the harmonic series of a string?

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Reading all the text I do not any about how the sound is produced. Yes the string produce frequency and overtones but where on the structure is the sound produced. This comes from a vibrating structure on the both bout shapes of the belly. If the shape of the arching hold a specific condition with a specific graduation of thickness in relation to the wood quality we may accept that these conditions will produce a vibration that transform the input on the bridge feet. Why is the shape of arching and the dynamic behavior of the bout shapes not discussed?

 

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37 minutes ago, David Burgess said:

If that were so, wouldn't you hear the impact spectrum of the violin itself, rather than the harmonic series of a string?

The "impacts" are tiny and periodic to the note being played.  If a body resonance is not at the frequency of the note or a harmonic, the energy from the string will give it a kick during one pass of the kink, but the next kick will be out of phase with the body resonance, with the net result that the body mode does not get pumped up.  

If you could isolate one kink pass and just feed that into the body, then you'd see something more like an impact spectrum.  But that would be very quiet and not at all like what happens in a real played note.

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18 minutes ago, Don Noon said:

The "impacts" are tiny and periodic to the note being played.  If a body resonance is not at the frequency of the note or a harmonic, the energy from the string will give it a kick during one pass of the kink, but the next kick will be out of phase with the body resonance, with the net result that the body mode does not get pumped up.  

 

Granted, for the fundamental. But why does a bowed violin emit a "perfect" harmonic series above the fundamental, if this is not generated and communicated by the string? The body of the violin doesn't have this property on its own. It must come from the multiple vibrational modes of the string.

 

String.gif

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Look at the spectrum of the sawtooth wave.  The string is being driven not only at the fundamental frequency, but also at all the overtone frequencies.  The body doesn't need to create the overtones, it simply responds to drive force of the bridge at the overtones in the sawtooth as you would expect of any approximately linear system.  Again, look here: https://en.wikipedia.org/wiki/Sawtooth_wave.  Again, I will accept my flogging gracefully if wrong.

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43 minutes ago, David Burgess said:

Granted, for the fundamental. But why does a bowed violin emit a "perfect" harmonic series above the fundamental, if this is not generated and communicated by the string? The body of the violin doesn't have this property on its own. It must come from the multiple vibrational modes of the string.

 

String.gif

to me it seems something is happening in the motion transition, meaning the string only moves side to side with a bowed instrument, but this side to side motion starts the bridge rocking side to side, once the side to side motion happens it starts a "mock" up and down motion that is being transferred back from the body to the string, and or any up and down energy in the body is initially coming from the strings side to side motion.

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3 hours ago, Andreas Preuss said:

The bridge isn't moving AT ALL. (Because it is not sitting on a violin?)

Interesting to see it visualized. Unfortunately it doesn't give any idea how overtones are transmitted to the bridge.

But it must be moving, just very tiny motions

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2 hours ago, David Burgess said:

Granted, for the fundamental. But why does a bowed violin emit a "perfect" harmonic series above the fundamental, if this is not generated and communicated by the string? The body of the violin doesn't have this property on its own. It must come from the multiple vibrational modes of the string.

David, your diagrams are for a string showing how they vibrate at the pure overtones.  Helmholtz bowed motion is essentially all of those overtones (and more) all at once.  If you add all of the string pure overtones together, in the right phase and the right amplitude, you'll get a rotating kink just like the Helmholtz movement.  A side effect of the Helmholtz motion is that all of the overtones are forced to be precise overtones of the fundamental, otherwise they would migrate out of the kink and be damped by the bow hair. 

An extreme exception would be a wolf note, where the non-fundamental disturbance from the body is so strong that it screws up the stick/slip physics of the string... but that's really something a bit different.  More applicable might be a string where some of the windings have unravelled and broken off, making the free string harmonics way out of tune.  I think that could smear out the kink into something ugly and unplayable.

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6 hours ago, reguz said:

Reading all the text I do not any about how the sound is produced. Yes the string produce frequency and overtones but where on the structure is the sound produced. This comes from a vibrating structure on the both bout shapes of the belly. If the shape of the arching hold a specific condition with a specific graduation of thickness in relation to the wood quality we may accept that these conditions will produce a vibration that transform the input on the bridge feet. Why is the shape of arching and the dynamic behavior of the bout shapes not discussed?

 

Robert,

I hope that you will continue on this forum, dispite all!

I have got my fair share of "what ever you call it". It's a harsh, funny and condescending place this MN. But some really, really smart people are posting too (that does not include David B. he told long time ago, he is a Hillbilly, took me a long time to figure out, that it's a definition of not smart, so don't listen to him ;))

If ones ideas doesn't fit your "model", you are probably on to something, I have studied your website for years, but only after I found the STL on my own violins. (this after Patrick's super insights, he really did crack some eggs)

If you look through this thread, I had some thoughts. I was both right and wrong. I knew that there was something about the fundamental modes that I saw and did not fully understand.

This time especially Marty and ctanzio helped me crack the question. Anders, Don (and surprise David B. not a Hillbilly after all?),  confirmed in the direction to get the answers I was looking for.

However, this is Andreas thread and I hope he got what he was looking for!

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2 minutes ago, Peter K-G said:

Robert,

I hope that you will continue on this forum, dispite all!

I have got my fair share of "what ever you call it". It's a harsh, funny and condescending place this MN. But some really, really smart people are posting too (that does not include David B. he told long time ago, he is a Hillbilly, took me a long time to figure out, that it's a definition of not smart, so don't listen to him ;))

He pretends to be a Hillbilly, but he's actually a Redneck working undercover. Don't be fooled.

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10 hours ago, Peter K-G said:

That's kind of what I was thinking, when I starting the question, followed with some tests.

I also thought that the notes/string motion by themself could contribute, but it does that only when a note is very near a mode.

 

Yes.  The bow can pull the string only when it's velocity and the strings are similar.  

That will tended to be cyclic, but won't be strickly so.  

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5 minutes ago, David Beard said:

But that ignores it's driven aspects.

I've discussed another aspect in a different post.

A third aspect which isn't often discussed is the more direct side force exerted on the bridge when the string is pulled to the side by the bow hair, similar to that which would be exerted by pulling the string to one side near the bridge with a finger.

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7 hours ago, David Burgess said:

Granted, for the fundamental. But why does a bowed violin emit a "perfect" harmonic series above the fundamental, if this is not generated and communicated by the string?

If you add the fundamental and the overtones together for a vibrating string, you get what looks like a single kink traveling up and down the string. IOW, the vibration of the string is not symmetrical as one might expect for a perfect sine wave. 

Although it is common to refer to the shape of the wave as "sawtooth", it is actually pretty far off from that shape. A perfect sawtooth would only generate odd numbered overtones. Because of the complex shape of the kink, it is the sum of all the overtones, not just the odd ones.

Your description of how the bow is actuating the string is correct. It constantly tugs the string to one side, and the kink traveling up and down the string periodically increases the force against the motion of the string to kick it loose until it slows down enough for the string to grab it again. It is during the kick loose and sliding phase where I would expect noise, or small vibrations, to be introduced into the string.

 

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