How does a violin reproduce overtones? - Theorizing a model

[Carl Stross]

9 hours ago, Carl Stross said:

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

 

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.  

 

7 hours 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?

No, they do not. Not to my ear. Tuned to same pitch and driven by same tuning fork they don't sound the same, in particular in the decaying region of the sound.

I addressed your initial question. If you modify it and bring the results of said modification in argument then we are lost. Things change drastically when you "load" the bridge with a heavy piece of metal and some weight from your hand. Play LIGHTLY an open A and touch the scroll - the sound will change.  Increase bow pressure /speed and the difference will vanish.

Violins do lots of very interesting  things at low levels of input. 

[Marty Kasprzyk]

11 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. 

The wings vibrate widely at their resonance frequency but they are too small to produce sound.  However due to a conservation of momentum if the wing is going up and down some thing else is going down and up at the same time.  If this other place is big enough such as a node of the top plate at this frequency it will produce some sound.

Placing a weight on the wing tip will lower its resonance frequency and some plate region will vibrate at this frequency and produce more sound at this lower frequency and the change can be heard.

                

[GeorgeH]

15 minutes ago, Marty Kasprzyk said:

The wings vibrate widely at their resonance frequency but they are too small to produce sound.

I have always been curious if fluting the lower wings was done purely for aesthetics or for improving tone or for both.

It is also curious to me that the upper wings are only very rarely fluted.

[uncle duke]

1 hour ago, GeorgeH said:

It is also curious to me that the upper wings are only very rarely fluted.

Grain tear out comes to mind first along with how to make the overall area look well with some having more texture than the surrounding areas. 

I almost reach around from the lower wing to the upper part of the hole area but not quite to the top.

[GeorgeH]

58 minutes ago, uncle duke said:

Grain tear out comes to mind first along with how to make the overall area look well with some having more texture than the surrounding areas. 

Here is a picture of one of the ffs of the only violin that I have ever owned with 4 fluted f wings. It looks different, but well-done.

[Don Noon]

On 5/24/2021 at 8:23 AM, Andreas Preuss said:

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?

On 5/24/2021 at 8:36 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.

17 hours ago, Carl Stross said:

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

Most of the attention in modal analysis seems to be on the lower frequencies, where it's easier to analyze, but acoustically less  important IMO.  Very little exists on the higher frequencies, where it is extremely important acoustically.  It is unfortunate that the Strad3D mode animations are blanked out under the fingerboard area, where I think a lot of the real action happens.  I say that based on a couple of observations:  1) Listen.  It is hard to put your ear close to the instrument when someone is playing it, but you can use a voice coil bridge driver to either play music or a sine wave into the instrument, and listen closely to where the sounds are coming from.  It is very clear to me that the dominant source of the higher frequencies is the upper bout.  2)  Close-mike mapping of sound intensity and location, at various frequencies.  This confirmed to me what my ears heard.

Explaining why and how this happens is another (and far more complicated, naturally) matter.  The best I can offer is arm-waving semi-logical theories.  My current thought is that the tighter arching curvature in the upper bout creates larger antinode areas, thus more efficent sound radiators at the higher frequencies.  Tweeters are usually dome-shaped for similar physics reasons.

How the vibration energy gets from here to there is even another level of complexity.  Try scraping a fingernail on the scroll of a violin, and you won't hear sound coming from the scroll at all, but from the body far from where the energy is put into the system.  Similarly, I think that the body will radiate sound from where it does so most effectively, and the the energy will come in from the bridge and circulate around the structure until it finds that place.  IMO the whole structure should have low damping to avoid absorbing energy, but that is most critical where movement is highest.

3 hours ago, GeorgeH said:

I have always been curious if fluting the lower wings was done purely for aesthetics or for improving tone or for both.

I can't imagine that fluting is anything other than aesthetic.

[Anders Buen]

It is not possible to determine the high frequency radiation from near field measurements. The recorded sound levels can just as easily be air-particle movements in the same plane as the plate.

We (the acoustics comany I work for) do have an "acoustical camera" with 255 mics in a disc. This kind of array can analyse this, from some distance.

Modal analysis requires mode fitting. When the modes are well spread apart, that works well. When the modal density gets higher, it becomes more difficult, and in reality we cheat a little to get fitted vibration modes there. In reality the method is not valid there. That also applies to FEA. Pretty much useless above the signature modes and a little higher in frequency. 

[Don Noon]

1 hour ago, Anders Buen said:

It is not possible to determine the high frequency radiation from near field measurements. The recorded sound levels can just as easily be air-particle movements in the same plane as the plate.

While that might be true to some degree in theory, I sure as heck can put my ear close to a 3-way speaker and tell where the tweeter is located.  The effect is similar to what I have found with violins.  And a VERY close (<1mm from the surface) directional microphone I think can give a reasonable idea where active areas are.

[jezzupe]

4 hours ago, GeorgeH said:

I have always been curious if fluting the lower wings was done purely for aesthetics or for improving tone or for both.

It is also curious to me that the upper wings are only very rarely fluted.

It is to counteract distortion curling or lifting. 

[Anders Buen]

24 minutes ago, Don Noon said:

While that might be true to some degree in theory, I sure as heck can put my ear close to a 3-way speaker and tell where the tweeter is located.  The effect is similar to what I have found with violins.  And a VERY close (<1mm from the surface) directional microphone I think can give a reasonable idea where active areas are.

Sure you get "active areas" but not radiating areas. Most of the vibrations in a violin dores not radiate perticularly efficiently. 

I am syre you hear the tweeter when you know were it is ;-) 

A tweeter is not the same as a vibrating plate. You will need 255 mics for that purpose. You already have one. :-)

[David Burgess]

10 hours ago, Peter K-G said:

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.

Are you referring to the lower body modes which emit almost no sound?

[Don Noon]

54 minutes ago, Anders Buen said:

Sure you get "active areas" but not radiating areas. Most of the vibrations in a violin dores not radiate perticularly efficiently. 

I am sure you hear the tweeter when you know were it is ;-) 

A tweeter is not the same as a vibrating plate. You will need 255 mics for that purpose. You already have one. :-)

I have listened for a tweeter when I thought I knew where it was behind the grille cloth, but I heard it elsewhere.  Turns out, I didn't really know where it was to start with.  It's really easy to hear, though, if you put your ear close to the grille.

In using a voice-coil driver, I listen from a bit far away, in different positions, and use my built-in stereo imaging to locate the apparent source, and then nearby (as in locating a tweeter)... all of that is consistent with the near-mic measurements that say the upper bout is the strongest source of high frequencies.

I would be most happy if anyone has fancier measurements to map the source of the high frequency radiation, even if (or especially if) it conflicts with what I think I know.

 

[Peter K-G]

11 minutes ago, David Burgess said:

Are you referring to the lower body modes which emit almost no sound?

Obviously I was, and if the violin is lying on a shelf they emit nothing.

If they are excited they do emit quite a lot of sound if near a mic (long distance I don't know)

If they are nearby a played note, they can show up on the FFT spectrum, with equal db to the played note. So the question was does the violin body add harmonics!?

They also amplify nearby notes, that would fall into the amplyfing filtering that Marty posted on Colin's work.

[Don Noon]

17 hours ago, Andreas Preuss said:

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

True

9 minutes ago, Peter K-G said:

So the question was does the violin body add harmonics!?

No

As yet I have seen no evidence that the violin produces any significant harmonic distortion, where you can input one frequency, and get out something other than the input frequency.  Sure, the amplitude response will be different at different frequencies, but no new frequencies are created by the body... unless there is a loose glue seam or something similar that can create a buzz, which is basically an impact with lots of associated noise.

[David Burgess]

8 minutes ago, Peter K-G said:

Obviously I was, and if the violin is lying on a shelf they emit nothing.

If they are excited they do emit quite a lot of sound if near a mic (long distance I don't know)

If they are nearby a played note, they can show up on the FFT spectrum, with equal db to the played note. So the question was does the violin body add harmonics!?

They also amplify nearby notes, that would fall into the amplyfing filtering that Marty posted on Colin's work.

The east-west thin sides of the bridge also emit quite a bit of sound, if they are mic'd closely enough, so my question would be if tiny things like this matter. If they do, should we be attaching sails to the thin bridge edges to give them more radiating power?

[Don Noon]

2 minutes ago, David Burgess said:

should we be attaching sails to the thin bridge edges to give them more radiating power?

The "sails" would have modes of their own, and change the sound completely.  You'd have to keep the "sails" small and well-controlled, then have a sound tube to prevent front/back pressure cancellation, and, viola, you now have a Stroh violin. 

[Marty Kasprzyk]

8 minutes ago, Peter K-G said:

Obviously I was, and if the violin is lying on a shelf they emit nothing.

If they are excited they do emit quite a lot of sound if near a mic (long distance I don't know)

If they are nearby a played note, they can show up on the FFT spectrum, with equal db to the played note. So the question was does the violin body add harmonics!?

They also amplify nearby notes, that would fall into the amplyfing filtering that Marty posted on Colin's work.

The violin body is not an amplifier--it is an energy transducer.  It converts the vibrating energy of the string into the vibrating energy of the violin's body, which converts this energy into the vibration of air which is sound.  Nothing is amplified--no additional energy is added.

A vibrating string produces nearly no sound because the narrow width of the string is too narrow to move much air.  The violin body merely adds more surface area to efficiently move air. 

All the original harmonics of the vibrating strings are converted into harmonics of the sound produced.  No new harmonics are produced.

Some of the string's harmonic energy conversions are more efficient than others due to the violin body's various resonance peaks and valleys. This makes the sound output of a note's harmonics louder or softer.

A note from a bowed note does have some non harmonic noise from various sticking and sliding of the bow hair on the string.  If you play a single note and do an Audacity plot you will see some random noise between the harmonic series.  For example if you play an A note with a frequency of 220hz, its next harmonic will be 440hz, and the next one 660 etc.  In between these peaks there will be many much lower random noise peaks between the 220 and 440 peaks etc.

But this noise is not created by the violin body--it is produced by the string/bow interaction.  The violin body merely converts this random string vibration energy into sound noise energy.  

[Peter K-G]

31 minutes ago, Marty Kasprzyk said:

The violin body is not an amplifier--it is an energy transducer.  It converts the vibrating energy of the string into the vibrating energy of the violin's body, which converts this energy into the vibration of air which is sound.  Nothing is amplified--no additional energy is added.

A vibrating string produces nearly no sound because the narrow width of the string is too narrow to move much air.  The violin body merely adds more surface area to efficiently move air. 

All the original harmonics of the vibrating strings are converted into harmonics of the sound produced.  No new harmonics are produced.

Some of the string's harmonic energy conversions are more efficient than others due to the violin body's various resonance peaks and valleys. This makes the sound output of a note's harmonics louder or softer.

A note from a bowed note does have some non harmonic noise from various sticking and sliding of the bow hair on the string.  If you play a single note and do an Audacity plot you will see some random noise between the harmonic series.  For example if you play an A note with a frequency of 220hz, its next harmonic will be 440hz, and the next one 660 etc.  In between these peaks there will be many much lower random noise peaks between the 220 and 440 peaks etc.

But this noise is not created by the violin body--it is produced by the string/bow interaction.  The violin body merely converts this random string vibration energy into sound noise energy.  

Great explenation!

Amplifying is for sure the wrong word, that implies added energy.

Using a realtime FFT, it's pretty clear what happens and you can see visually what you wrote.

Still the question is how to explain  the body modes showing up on the spectrum, even from recordings you can sometimes find them.

 

[Anders Buen]

Some near field holography patterns around a normal size Hutchins violin. The article is written by Lily Wang and Courtney B. Burroughs in JASA in 2001. Acoustic radiation from bowed violins . They had a bowing machine. 

[Andreas Preuss]

14 hours ago, Marty Kasprzyk said:

Placing a weight on the wing tip will lower its resonance frequency and some plate region will vibrate at this frequency and produce more sound at this lower frequency and the change can be heard.

 

For sure the F-wing surface is not big enough and I was speculating if 'some plate region' is not by any chance the upper half of the top which is mechanically connected to the wings.

How could we prove this argument with an experiment?

(thanks for the Colin Gough reference, I am trying to understand now the paper on the Wilmotte Strad. With my background in physics like a housewife, not so easy.)

[Andreas Preuss]

12 hours ago, Don Noon said:

Explaining why and how this happens is another (and far more complicated, naturally) matter.  The best I can offer is arm-waving semi-logical theories.  My current thought is that the tighter arching curvature in the upper bout creates larger antinode areas, thus more efficient sound radiators at the higher frequencies.  Tweeters are usually dome-shaped for similar physics reasons.

I suppose 'tighter' is 'flatter'.

But on this equation I see the wood thickness as a big factor. I would simply assume that a less flat arching can be counterbalanced with thinner thickness to some degree. 

12 hours ago, Don Noon said:

IMO the whole structure should have low damping to avoid absorbing energy, but that is most critical where movement is highest.

Does stress on material influence its damping properties? 

12 hours ago, Don Noon said:

Similarly, I think that the body will radiate sound from where it does so most effectively, and the the energy will come in from the bridge and circulate around the structure until it finds that place. 

Hmmm, 'circulate around the structure' is a kind of surprising expression from you, Don. IMO there must be ways to channel high frequencies efficiently in the right spot. And because 'things are complicated' when we analyze them I rather try to go around that and develop methods and procedures which simply bring the result I want. 

My current thoughts are to continue tests. If I start with a violin which has a 'bad' overtone spectrum (whatever you define as such) and make alterations to it to improve it, it should give answers where we need to work with diligence in calibrating the whole structural system of the violin. And this is the goal, isn't it? Knowing the successive steps of calibrating the sound to bring it to the point we want to have it.

 

[Andreas Preuss]

6 hours ago, Anders Buen said:

Some near field holography patterns around a normal size Hutchins violin.

I hope I am not annoying you with a question.

Does this looks the same for all violins? 

I suppose you posted it more with the intent to give a general visual idea of what is going on. 

---------------------------------------------------------------------

If I read this correctly the top is mostly involved at 'low' frequencies. I am saying 'low' because it goes up to quite high notes on the E string. 

And then I would interpret the first three pictures at frequencies above 2000Hz that the back becomes more active for overtones. (Makes me scratch my head because I could improve 'clarity' with stabilizing the frame around the top with 3 lining layers glued together.)

My pretty rough observations from carving a flat walnut back from the outside were as follows. 

I tried to create a central 'island' between the C bouts and therefore thinned down step by step the upper and lower region with the goal to make the island smaller and smaller and at the same time increase the difference between thickest and thinest zones.

Somehow it seemed that the strongest overtone spectrum was descending during the process and by making the island smaller the overall range seemed to get broader but maybe weaker too.  Unfortunately I didn't make a detailed documentation on that, but might repeat the same experiment with a new arched maple back. 

 

[Andreas Preuss]

9 hours ago, David Burgess said:

The east-west thin sides of the bridge also emit quite a bit of sound, if they are mic'd closely enough, so my question would be if tiny things like this matter. If they do, should we be attaching sails to the thin bridge edges to give them more radiating power?

Interesting to know, but we have probably to accept the fact that there are many 'radiating zones' which are simply unable to contribute to the sound.

I remember having read somewhere that 95 percent of the energy input on a violin is lost. (Or my father told me after he had read  Lothar Cremers 'Die Physik der Geige') Shows us how efficient this is, but teaches at the same time how carful we have to be in using the remaining 5 percent as efficient as possible.

 

 

[Don Noon]

7 hours ago, Anders Buen said:

Some near field holography patterns around a normal size Hutchins violin. The article is written by Lily Wang and Courtney B. Burroughs in JASA in 2001. Acoustic radiation from bowed violins . They had a bowing machine. ...

I only see one plot of the top surface above 2 kHz, which I think of as the start of the high-frequency range for a new violin (I would have preferred these tests be done on a good reference instrument, rather than a Hutchins one of unknown quality).  In that one plot, it does appear that the output is stronger in the upper half of the instrument.  There are 3 plots of the back radiation above 2 kHz (why?), and they show most activity in the upper bout.  If we presume the  back is reacting to top plate movement, then the top plate should also show most activity in the upper bout.

Seems awfully complicated to extract these kinds of frequency-specific plots from a bowed instrument where there is a pile of frequencies going on all at once.

47 minutes ago, Andreas Preuss said:

(see below)

I suppose 'tighter' is 'flatter'.

No, I meant smaller radius, sharper curve.

But on this equation I see the wood thickness as a big factor. I would simply assume that a less flat arching can be counterbalanced with thinner thickness to some degree. 

Arching and thickness can have different effects at different frequencies.  I'll just leave it at that for now (it's really complicated).

Does stress on material influence its damping properties? 

No... unless you're including the few weeks when an instrument is first strung up, or after a long period of unstrung, or after some major repairs.

Hmmm, 'circulate around the structure' is a kind of surprising expression from you, Don. IMO there must be ways to channel high frequencies efficiently in the right spot.

With enough work, you might be able to get efficient transfer of energy from the bridge to an efficient radiating spot... for ONE FREQUENCY.  At a different frequency, the "right spot" will be elsewhere, and the efficient channel would be something else too.

And because 'things are complicated' when we analyze them I rather try to go around that and develop methods and procedures which simply bring the result I want. 

I think that's kindof what I've been saying... it's so dang complex, you can't really analyze it fully, so you might as well use trial-and-error to find out what works closest to the way you want.  Some acoustics and physics might help in guiding in a useful direction or avoiding dead ends... or maybe not if the assumptions are not correct.

My current thoughts are to continue tests. If I start with a violin which has a 'bad' overtone spectrum (whatever you define as such) and make alterations to it to improve it, it should give answers where we need to work with diligence in calibrating the whole structural system of the violin. 

It's a good system (trial-and-error), but it's hard to alter wood properties and arching on an existing instrument, and I think those are huge factors in the overtone production.

[Anders Buen]

13 hours ago, Andreas Preuss said:

Does this looks the same for all violins?  

 

For the low frequencies up to about 800 Hz, probably yes. Basically omnidirectional radiatation. Then it may be differences. In principle one may expect similar things. In the high frequencies we may expect some kind of «beamforming». Directive radiation.

Bissinger also made directivity plots from a series of instruments. I do not know if he made patterns for the finest violins he had in his lab. Jim Woodhouse show one of these patterns as a movie on his «acoustics book website»: https://euphonics.org/4-3-sound-radiation/

Edited May 26, 2021 by Anders Buen
Added link to Jim W’s violin radiation demoes and explanations.