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How does a violin reproduce overtones? - Theorizing a model


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46 minutes ago, ctanzio said:

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.

 

A perfect saw tooth wave has all of the overtones.  A triangular wave has only the odd numbered ones

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24 minutes ago, ctanzio said:

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.

 

Yes. As ctanzio says, vibrations add.

The OP asks how harmonics/overtones are reproduced in a violin.

One thing that doesn't happen is they don't travel as separated sine waves.    Instead, vibrations add together and travel with the shape of their summed totals.

This means that when we hear a sound, we aren't very good at distinguishing between a sound composited from many separate sources versus a single source that produces total of that composite in one complicated wave shape.

This is why we aren't great at distinguishing a speaker reproduction from an orchestra of seperate sound sources.

We can separate harmonics mathematically, but in a medium they are combined.  

We can also isolate and stimulate separate harmonics on a string, as we all know.

For these reasons, it's easy to make the mistake of talking and thinking about overtone harmonics as if they somehow did exist as independent sine wave shapes in a string or an instrument.

But mostly they are more just mathematical artifacts of a non-sinewave wave shape.  They are the simple sine waves that add up to the shape of the actual physical wave present.

When we strongly pull a string to the side in a triangle shape and then let go, the distortions shooting back and forth along the string have shape related to the initial triangle shape we pulled.  Nothing much looks like sine waves.

But when we hear that, our ears and brain process the cyclic shape of the presure distortions reaching us as a sum of sine waves.  So we hear harmonics.

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Using an online tone generator I found:

https://www.szynalski.com/tone-generator/

pure sine waves are less audible (to me, anyway) at higher frequencies (above 10000Hz) than the synthesized sawtooth waves. There is a sum of a LOT of something in the “violin sound wave.“

Does a sawtooth wave at 440Hz also contain all the upper partial tones?

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On 5/24/2021 at 10:36 AM, David Burgess said:

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.

I read what Andreas says reproducible overtones.  All I can say from experience is once they present themselves they're there - don't know about phasing in or phasing out, if it's alright to call it that.

I also can't say if one can detect the overtones through testing.  One way maybe is to put the violin through your testing procedure right after a hot hand gets through putting the fiddle through the rigors of a thorough playing session.  

Things needed for the mostly wanted overtones are good fittings, i.e., pegs, fingerboard and and the rest.  Good, not so supple, varnish along with a decent working belly arching at least can help things along too, imo.  

So what is good arching?  Some know but a lot of others don't know or ever will know.

About overtonage presenting itself while playing.  First question would be is it really necessary for overtones to show up.  Not really for the average joe but if the average joe just happens to be able to pick up upon what the overtone sound/wavelength is about their playing and possibly enthusiasm for playing can or will be enhanced.  I've been there, makes one just a little bit more confident in what one is doing. 

Why?  Because overtones sound well as long as they're not overpowering during music reading/playing instances along with fingerboard note stopping and bow work.

Again, are they needed?  No.  Are they nice to have?  Yes.

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2 hours ago, Rothwein said:

Using an online tone generator I found:

https://www.szynalski.com/tone-generator/

 

Using that generator under 100hz for mode 1 plate tuning through headphones my dog could hear the low tone and just start growling non stop - he'd be outside about 15ft. away and could hear from the headphones being used indoors.

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After all No one of you seem to understand that the function of the violin consist of two DYNAMIC conditions acting simultaneously. One is the vibration of the bridge providing the frequency the other is the dynamic behavior of the violin body that produce buckling on the belly and bending on the back. The stress condition that arise on the buckling belly bouts consist of a big number of very smal beams the vinter grown wood. The beams are forced to bend (buckle) and they are all different. The quality is that such one beam ort a couple of beams hold the same stiffness condition needed producing a vibration. They only need to bee "informed" by the vibrating string and the input of the frequency under the bridge feet. The bridge thus has a special function. This function in some FEA take place with a probe hold somewhere on the surface. No dynamic movement in the FEA is produced by the action of the vibrating string. The reults found of such FEA thus give us not the information comparable with the played instrument. As long as YOU ALL do not accept that we deal with TWO differnt action YOU Never will understand the function of the instrument and YOU will never be able improving in relation the the double dynamic system working on the instrument. Its nice what is shown earlier on recorded frequency but NO ONE explain where the vabrating location happens on the bout structure. WHY IS THAT???

 

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5 minutes ago, reguz said:

 Its nice what is shown earlier on recorded frequency but NO ONE explain where the vabrating location happens on the bout structure. WHY IS THAT???

 

Perhaps because ultimately it's not productive in the real world to analyse the violin according to scientific first principles.

The violin is a traditional recipe, and like a good Spaghetti Bolognese, it's best learnt in the kitchen from your mother, not by analysis of its molecular content.

With violin sound there is no objective measure of quality, so there is no philosophical basis for your approach.

You may be on a path which helps you personally to understand the mechanisms, but it's the most absurd arrogance to tell professional violin-makers that they must all understand it your way.

 

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No Martin its not understanding my way. Its about understanding the function. I'm open for any discussion and you may start letting us know what you "believe" is the function. Hope you will do this.

 

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11 minutes ago, reguz said:

No Martin its not understanding my way. Its about understanding the function. I'm open for any discussion and you may start letting us know what you "believe" is the function. Hope you will do this.

 

The "function" of a violin is to sound and perform like other violins that are generally regarded as good examples. Therefore to follow the techniques and copy the style and material properties of those other violins is as far as it all needs to go.

A violin is a traditional cultural artifact, not a scientific instrument like for example a telescope, where your kind of approach might allow us to see further into the universe ...

 

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"the "function" is to sound and perform" Yes that's right but the question I like you to give an explanation on is HOW does it function? Not a lot of other talk please. No the violin is not a scientific instrument but the telescope has a function that is well described in order to do what we like it to do. So the function of the violin is based on the structural shape producing the sound we like it to make. That is what I like to read your opinion on. If you cannot just say I don't know. I accept that. You are not alone that's for sure.

 

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58 minutes ago, martin swan said:

... ultimately it's not productive in the real world to analyse the violin according to scientific first principles.

I mostly agree.  The science and analysis thus far is just barely scratching the surface of the infinite complexity of how a carved wooden box vibrates and produces sound.  It is far too easy to take what we have and imagine it to be important and meaningful when (IMO) it is not... at least in a way that can be used directly in creating a new instrument.

29 minutes ago, martin swan said:

The "function" of a violin is to sound and perform like other violins that are generally regarded as good examples. Therefore to follow the techniques and copy the style and material properties of those other violins is as far as it all needs to go.

Material properties is the area I'm most interested in, and unfortunately the properties of the wood in "good examples" (if that means Cremonese, with several hundred years aging) are not completely known.  Sure, we can get density, and maybe a vague notion about the main stiffness properties... but there are still many relevant properties that are totally unknown.  

 

All of this might seem like I'm giving up on science, but that's not happening.  I still think modern tools and materials can be helpful... as long as the limitations are recognized.  I'm still finding out what the limitations are, and how much we don't know, with the latter category increasing as I find out more.

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25 minutes ago, Don Noon said:

I mostly agree.  The science and analysis thus far is just barely scratching the surface of the infinite complexity of how a carved wooden box vibrates and produces sound.  It is far too easy to take what we have and imagine it to be important and meaningful when (IMO) it is not... at least in a way that can be used directly in creating a new instrument.

Material properties is the area I'm most interested in, and unfortunately the properties of the wood in "good examples" (if that means Cremonese, with several hundred years aging) are not completely known.  Sure, we can get density, and maybe a vague notion about the main stiffness properties... but there are still many relevant properties that are totally unknown.  

 

All of this might seem like I'm giving up on science, but that's not happening.  I still think modern tools and materials can be helpful... as long as the limitations are recognized.  I'm still finding out what the limitations are, and how much we don't know, with the latter category increasing as I find out more.

I agree with all of this

My statement was a bit disingenuous, obviously there's a lot of room for research, and material properties are the grey area. But I think a lot of the scientific and pseudo-scientific pissing in the wind is fuelled by contemporary makers' envy of the price tags attached to old Italian instruments, rather than to a well-founded belief or personal experience that they work better ...

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12 hours ago, uncle duke said:

I read what Andreas says reproducible overtones.  All I can say from experience is once they present themselves they're there

Long time I was just working with the principles you are presenting here.

But one day a violinist of the top class made a comment on one of my instruments I could absolutely not understand. He tested an unfinished instrument I thought didn't have a good sound at all and said 'THIS has resistance!' in comparison to another instrument I thought was much better.

This became the starting point to question many things I believed to be correct and useful. I started to inquire and on the way experienced many things I couldn't understand from the beginning. 

I am seeking now a very particular sound, and need to understand for this goal more things. But 'understanding' is not pure theory, it simply boils down to set things into practice based on a sort of model. And I am not shy any more to walk into undiscovered territory of building instruments which don't follow well established rules or models. 

Now, for me it was a total surprise that just the linings on a violin can change so much. It was at another stage very surprising that the rib height can change overall so much, it was surprising that a flat arch did not change so much, it was surprising that a top with a very unusual arching was better than a top with a normal arching. So putting out some topics on MN I am a sort of thinking loud. 

 

 

 

 

 

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15 hours ago, David Beard said:

One thing that doesn't happen is they don't travel as separated sine waves.    Instead, vibrations add together and travel with the shape of their summed totals.

I am interested in this 'travel' part.

On the way of this travel' it seems a lot of things can happen. And maybe it is more instructive to get an understanding what can absorb or filter overtones. So instead of looking at the peaks in a graph focus on the valleys.

I see the outcome of a rich overtone spectrum just as the result of a well functioning mechanism. Something which is in a perfect balance. And this mechanism puts a real good player in the position not to play just 5 colors but many more subtle shades. 

 

 

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3 hours ago, martin swan said:

With violin sound there is no objective measure of quality, so there is no philosophical basis for your approach.

Absolutely.

But still, the really good instruments seem to have something in common despite their obvious differences.. It is not all about overtones, but I think they play a major role.

(I am not trying to defend Reguz here)

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3 hours ago, martin swan said:

>

With violin sound there is no objective measure of quality, so there is no philosophical basis for your approach.

>

 

One objective measure of violin quality is the evenness of the all of the note's loudness.   Some players go up and down the chromatic scale or play music passages to find overly loud or weak notes which are generally not liked. 

The loudness of each note can also be measured with a sound meter.

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4 minutes ago, Marty Kasprzyk said:

One objective measure of violin quality is the evenness of the all of the note's loudness.   Some players go up and down the chromatic scale or play music passages to find overly loud or weak notes which are generally not liked. 

The loudness of each note can also be measured with a sound meter.

I haven't found this to be a reliable measure of quality - for instance, many really great instruments have notorious wolf problems which people are prepared to tolerate because the rest is so good.

Apart from wolfnotes, significant discrepancies in volume between one semitone and another are quite rare, and are usually easily modified by set-up tweaks.

 

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26 minutes ago, Anders Buen said:

Do anybody know what theoretical drop of harmonic levels one may expect from bowing the string? That is what you get before the bridge and body "shape" the sound. It may depend on bowing position, I guess. 

It does. The extremes are “sul tasto“ and “sul ponticello.“ or “am Steg“ and “am Griffbrett“ (auf dem Griffbrett?) 

A violin that does not have good variation between is not ideal for classical music.

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17 minutes ago, martin swan said:

I haven't found this to be a reliable measure of quality - for instance, many really great instruments have notorious wolf problems which people are prepared to tolerate because the rest is so good.

Apart from wolfnotes, significant discrepancies in volume between one semitone and another are quite rare, and are usually easily modified by set-up tweaks.

 

I didn't say note evenness was the only measure--I said "One objective measure..."

Note loudness unevenness is quite common (see attachment) even in great instruments.  

Screen Shot 2021-05-16 at 9.44.43 AM.png

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1 minute ago, Marty Kasprzyk said:

I didn't say note evenness was the only measure--I said "One objective measure..."

Note loudness unevenness is quite common (see attachment) even in great instruments.  

Screen Shot 2021-05-16 at 9.44.43 AM.png

Is the Titian in there?

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12 minutes ago, Marty Kasprzyk said:

I didn't say note evenness was the only measure--I said "One objective measure..."

Note loudness unevenness is quite common (see attachment) even in great instruments.  

Screen Shot 2021-05-16 at 9.44.43 AM.png

OK so we can agree that the one objective measure of violin quality we can think of turns out to be very unimportant in player preference?

Besides, I don't think anyone playing any of those instruments would relate to what the graphs tell us, which is that the open D is more than twice as loud as the open G ...

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15 minutes ago, Anders Buen said:

Is the Titian in there?

I don't know.  The loudness graph is from Saunders' 1937 report:

 F. A. Saunders, "The Mechanical Action of violins", J. Acoust. Soc. Amer., 9, 81-98 (Oct 1937) reprinted in Musical Acoustics, Part           I, Benchmark Papers in Acoustics/5, 1975

I loaned my Benchmark book to a friend so I can't see if Saunders used the 1715 Titian in this graph.  But I do know he measured the Titian later in 1946:

Screen Shot 2021-05-29 at 1.01.24 PM.png

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1 hour ago, Anders Buen said:

Do anybody know what theoretical drop of harmonic levels one may expect from bowing the string? That is what you get before the bridge and body "shape" the sound. It may depend on bowing position, I guess. 

Is this what you wanted?:

Screen Shot 2021-05-29 at 1.35.17 PM.png

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