How does a violin reproduce overtones? - Theorizing a model

[Andreas Preuss]

8 hours ago, Don Noon said:

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

My general observation on this theme looks like this:

Thicknesses in lower archings reduced to the bare necessary minimum seem to be slightly thicker, not very much though. I count in this category GDG and some Poggis I have seen and played. The sound is on the rougher side you could also say 'it has texture'.

If a high arching is made in its thickness to the bare minimum you get a richer sound a sort of very dense, compact and 'plastic'. There we find many Strads, and early Guads.

9 hours ago, Don Noon said:

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.

You can in theory press spruce  to any form especially in the thickness of 2.5 - 3.0mm. I think @Evan Smithmade some daring experiments bending the top with bass bar installed.

I think bending wood combines several very practical aspects which can simplify things (maybe) to a great degree.

1. The spring-back-effect brings stiffer wood to lower archings than soft wood. Something which seems logic. Likewise arching curves on softer wood are rounder. Maybe at the end of the process minimal thickness corrections are needed
2. Heating done in a controlled way doesn't have a negative effect.
3. Keeping the grain and medular rays running throughout the arching seems to be better for the general stability. Actually it might be more important for cross grain stiffness.

All needed is to develop the mould and test it with wood of VERY different properties.

9 hours ago, Don Noon said:

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.

Yes, I think the first weeks do in fact play an important role. I almost dare to say that a good instrument can't sound from the beginning because it absolutely needs to stretch-in. 

[ctanzio]

The generic term "filter model" is used in too imprecise a context in this case, and suggests that it might be significantly different or mutually exclusive from a "resonance model". This is not the case.

The violin uses a resonance model. When that model is applied to the "wave shape" of a vibrating string, it transforms that periodic energy into sound with its own unique "shape".

From that perspective, it is "filtering" of a sort, but it is more like a conversion of energy. But is is not the same as taking an audio recording, say, and running it through a spectrum equalizer to change the audio.

The violin follows a "resonance model" in that it is constrained, by its geometry and physical properties like mass, stiffness and damping, to vibrate in certain shapes called natural modes. The frequency at which these shapes vibrate are defined by the frequencies of the vibrating forces being applied.

To the extent that that a simple sine wave input will cause ALL the mode shapes to vibrate, one might be tempted to think of them as overtones because the shapes are so dramatically different from one another. But that is not what is meant by an overtone.

They are all vibrating, more or less depending on damping, at the same sine wave frequency. So they are all producing the same fundamental tone with damping adding "color" or "filtering".

The relative amplitudes of vibration of each mode will vary. That adds more "color" or "filtering" to the tone.

Many will be vibrating out-of-phase with each other. So that will add additional "color" or "filtering" to the tone. This is why extracting the amplitudes from a sound response spectrum of a violin playing, say, a D, and then numerically combining sine saves using these amplitudes, fails to adequately simulate a violin tone. The phase shifting is an important part of the "filtering".

To the extent that two violins will differ in geometry, density, stiffness and damping, they each will color or filter the tone differently.

 

 

[David Beard]

I violin is primarily a soundboard, with secondary resonantors added.

It isn't just a 'resonator model'.

[Evan Smith]

3 hours ago, Andreas Preuss said:

You can in theory press spruce  to any form especially in the thickness of 2.5 - 3.0mm. I think @Evan Smithmade some daring experiments bending the top with bass bar installed.

Daring to say the least,,

Yes I have bent them with the bars in them and the bars bend also and hold, (for decades so far) but not bent from fully flat. Like you,,, I have many experiments that live here with me permanently that I can keep an eye on.

But what ever is wrong with my curious mind got the best of me one day, out of many days,,,

I figured that about 5mm of side ways push will give a 16mm arch, so I built flat plates, graduated with purfeling,,, completely finished edges,, f-holes and all.

I glued the plates onto the ribs, then stuck in several posts to get the arches started out instead of in,, and squeezed,,, piece of cake. The only cracks were from the lower holes to the edge,,,, there was too much sideways bending there. A cross grained patch inside and out would have prevented it though. Of course some of the edges came loose,,as was expected.

This was so extreme that I left the bar out and installed it later. There were many difficulties involved, as it gets narrower and taller, it also gets shorter,,, some places have not enough wood, whereas, some places have too much. After much coaxing, boom! a truly bent violin was born.

I have a special small curved hot Iron to form things out into a shape,, after some adjustments to the arching, and a bar and a neck,, it was good to go.

It resembles a DaSalo type arching.

[Evan Smith]

4 hours ago, ctanzio said:

Many will be vibrating out-of-phase with each other. So that will add additional "color" or "filtering" to the tone.  The phase shifting is an important part of the "filtering".

I believe that this is the major difference between a great violin and a bad one, why thick can work, as well as thin can work. Why there are no certain numerical formulas that can dictate anything, no recipies for a good violin other than the rules of weight, stiffness, and functional shape. Copying specific graduations will never sound like what is being copied. A violin is more like a moving machine with many parts moving around simultaneously on many differently levels, if it is working together, it will work well. The arching gives it the possibility of it's basic voice, the parts working together as they should, give it the quality that makes it a delight to play.

Once this concept is understood, any violin with enough wood left,, can be made to preform well, it will always have the voice it was born with, but it will be balanced, with no weak strings, it will bow nicely, no screechy annoying E strings, no tubby rubbery G strings. I think that the phase shifting is everything, all the modes are just standard physics,, the phasing is the adjustment so they work like they should, and work together. The secret's in the sauce,,, no special wood, no special varnish, and if you make them thin enough so there is not a lot of weight to sling around, they sound pretty good, no need to understand anything. If it works, do it again, if it doesn't try something else. I've tried it all.

Main thing is to have fun and enjoy the journey,,

[Evan Smith]

2 hours ago, David Beard said:

I violin is primarily a soundboard, with secondary resonantors added.

It isn't just a 'resonator model'.

 The back is absolutely as important as the top,,,,someone besides me and Andreas,, needs to do some real in depth experiments someday, there's more to it.

I would rather have a Strad back rather than a top without question.

[Carl Stross]

On 5/25/2021 at 5:10 PM, Anders Buen said:

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. 

KIndergarten FEA, maybe. Big boy's FEA don't need modes. 

It's  worth remembering that the fact a function accepts a series approximation doesn't mean those terms actually exist. Sometimes they do, sometimes they don't. Mostly don't.

[Anders Buen]

4 minutes ago, Carl Stross said:

KIndergarten FEA, maybe. Big boy's FEA don't need modes. 

Big boy FEA combine FEA at low frequencies with SEA at mid and high frequencies.

[Don Noon]

2 hours ago, Evan Smith said:

 The back is absolutely as important as the top,,,,someone besides me and Andreas,, needs to do some real in depth experiments someday, there's more to it.

I would rather have a Strad back rather than a top without question.

I'd say my recent test replacing a normal maple back with one made of MDF convinced me that the top is definitely the most important, as the general tonal character remained, although the signature modes changed significantly.

When someone parts out a scrapped Strad, you can keep the back and I'll take the top.

[ctanzio]

4 hours ago, Carl Stross said:

It's  worth remembering that the fact a function accepts a series approximation doesn't mean those terms actually exist. Sometimes they do, sometimes they don't. Mostly don't.

If by "actually exist" you mean give an insight into what is actually happening physically, then I agree with you. I encountered a disturbing trend among young physicists starting about 30 years ago where the math was mistaken for the physics. 

Modal analysis is a bit stronger than a series expansion with a set of orthogonal functions. It starts with functions where EACH term in the series is a solution to the governing equations. So each term does have physical meaning.

This is probably going beyond what MNers would be interested in reading. So if anyone wants a more expanded explanation, feel free to send me a private message.

 

[Rothwein]

I for one am interested; it's fun to read while glue dries.

[Peter K-G]

6 hours ago, ctanzio said:

This is probably going beyond what MNers would be interested in reading. So if anyone wants a more expanded explanation, feel free to send me a private message.

It's beyond what a lot of people even begin to understand (including me)

I read your posts, but I hesitate to respond, because I would just look silly, with my basic engineering physics degree.

I'm a software architect. Once I worked with a really intelligent senior software architect and when difficulty level were discussed, he sayd - if you want difficult you should study physics.

[Peter K-G]

On 5/25/2021 at 8:57 PM, 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.

 

On 5/25/2021 at 9:34 PM, 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.  

 

On 5/25/2021 at 10:14 PM, Peter K-G said:

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.

 

 

18 hours ago, ctanzio said:

The generic term "filter model" is used in too imprecise a context in this case, and suggests that it might be significantly different or mutually exclusive from a "resonance model". This is not the case.

The violin uses a resonance model. When that model is applied to the "wave shape" of a vibrating string, it transforms that periodic energy into sound with its own unique "shape".

From that perspective, it is "filtering" of a sort, but it is more like a conversion of energy. But is is not the same as taking an audio recording, say, and running it through a spectrum equalizer to change the audio.

The violin follows a "resonance model" in that it is constrained, by its geometry and physical properties like mass, stiffness and damping, to vibrate in certain shapes called natural modes. The frequency at which these shapes vibrate are defined by the frequencies of the vibrating forces being applied.

To the extent that that a simple sine wave input will cause ALL the mode shapes to vibrate, one might be tempted to think of them as overtones because the shapes are so dramatically different from one another. But that is not what is meant by an overtone.

They are all vibrating, more or less depending on damping, at the same sine wave frequency. So they are all producing the same fundamental tone with damping adding "color" or "filtering".

The relative amplitudes of vibration of each mode will vary. That adds more "color" or "filtering" to the tone.

Many will be vibrating out-of-phase with each other. So that will add additional "color" or "filtering" to the tone. This is why extracting the amplitudes from a sound response spectrum of a violin playing, say, a D, and then numerically combining sine saves using these amplitudes, fails to adequately simulate a violin tone. The phase shifting is an important part of the "filtering".

To the extent that two violins will differ in geometry, density, stiffness and damping, they each will color or filter the tone differently.

 

 

 

With some courage from PM exchange with a MNetter I will give this another try. It might just be misunderstanding and wrongly used words/terms.

The question: Does the violin body add harmonics!?

The answer has been NO - to that I agree, it would not be called harmonics, but I still think it's kind of an addition

Quick test yesterday on 

The Soil "copy" 2014

Bridge tap

 

Open G-String bowed 193 Hz, 386 Hz harmonic is the strongest, with the other strings damped

(There is also another interesting phenomenon, B1+ actually has it's own harmonics)

 

 

 

[Peter K-G]

And that was a long post...

[sospiri]

1 hour ago, Peter K-G said:

And that was a long post...

The Harmonic Series of open G plus the Hemholtz. So, what's your point?

[Carl Stross]

10 hours ago, ctanzio said:

If by "actually exist" you mean give an insight into what is actually happening physically, then I agree with you. I encountered a disturbing trend among young physicists starting about 30 years ago where the math was mistaken for the physics. 

Modal analysis is a bit stronger than a series expansion with a set of orthogonal functions. It starts with functions where EACH term in the series is a solution to the governing equations. So each term does have physical meaning.

This is probably going beyond what MNers would be interested in reading. So if anyone wants a more expanded explanation, feel free to send me a private message.

 

Yep. But I think it started in the '60s with Landau & Lifshitz . Whichever way one looks at it L&L does encourage that sort of approach.

[Carl Stross]

3 hours ago, Peter K-G said:

Quick test yesterday on 

The Soil "copy" 2014

Bridge tap

Which software is that ?

[ctanzio]

3 hours ago, Peter K-G said:

...Quick test yesterday on The Soil "copy" 2014...

All the major peaks are just overtones of the G. But it is interesting that one can still detect the presence of the fundamental modes, but they are a tenth to a hundreth of the intensity of the main G overtone.

I suspect this is due to a certain amount of "noise" the bow hairs feed into string during the release in the catch and release cycle. I can hear the low level scratching of the bow when I play if I focus on that.

[Andreas Preuss]

@Peter K-G

If your point is that the first harmonic (overtone) is stronger than the fundamental frequency, this might come already from the string. (I think low piano strings work actually like that) 

Physics people here can certainly give an answer on that.

 

[uncle duke]

7 minutes ago, ctanzio said:

All the major peaks are just overtones of the G. 

 Since it is just a non stopped string being bowed couldn't another adjacent string be activated to do a little too?

Maybe remove the other three strings and try again.

[Peter K-G]

5 minutes ago, ctanzio said:

All the major peaks are just overtones of the G. But it is interesting that one can still detect the presence of the fundamental modes, but they are a tenth to a hundreth of the intensity of the main G overtone.

I suspect this is due to a certain amount of "noise" the bow hairs feed into string during the release in the catch and release cycle. I can hear the low level scratching of the bow when I play if I focus on that.

This is the general explenation I have got so far yes.

I think it's a combination of that and bridge rocking (like when you tap the bridge)

In any case, my view is that their relative Hz and db strength gives the violin its fundamental base sound, mostly to G & D strings.

I find I can hear their "chord" when playing (ignore the word chord, it's not what I mean)

[Peter K-G]

2 minutes ago, Andreas Preuss said:

@Peter K-G

If your point is that the first harmonic (overtone) is stronger than the fundamental frequency, this might come already from the string. (I think low piano strings work actually like that) 

Physics people here can certainly give an answer on that.

 

Not my point, that is the case with violins open G, the second harmonic is stronger at a certain distance from the mic and what type of mic is used. Violins are weak at 194 Hz

[sospiri]

17 minutes ago, Andreas Preuss said:

@Peter K-G

If your point is that the first harmonic (overtone) is stronger than the fundamental frequency, this might come already from the string. (I think low piano strings work actually like that) 

Physics people here can certainly give an answer on that.

 

The notes on the G string first position, below the Hemholtz frequency are an aural illusion. We actually think we hear a strong fundamental.

I think I've got that right? 

[Peter K-G]

30 minutes ago, uncle duke said:

 Since it is just a non stopped string being bowed couldn't another adjacent string be activated to do a little too?

Maybe remove the other three strings and try again.

 

As I wrote:

Open G-String bowed 193 Hz, 386 Hz harmonic is the strongest, with the other strings damped

 

 

 

[ctanzio]

16 minutes ago, sospiri said:

The notes on the G string first position, below the Hemholtz frequency are an aural illusion. We actually think we hear a strong fundamental.

This is a specific example of the resonator model in action.

The G string is vibrating strongly with a 196Hz fundamental.

But the first major mode of the violin, A0 around 262Hz or a C, also known as the Helmholtz frequency, does not respond strongly to the G string's fundamental because the fundamental of the G (196Hz) and the natural frequency of A0 (~262Hz) are so far apart.

The air inside the violin is vibrating at 196Hz, just not very strongly compared to the other overtones of the G string.

It does sound strong for a good part of the population because of the ability of the brain to "hear" a tone which is the lowest frequency that is common to all the overtones. But not everyone can fill in a completely missing or weak fundamental. I have wondered if that could be a reason some people think certain tones on a violin are weak while other people think they are fine.