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How does a violin reproduce overtones? - Theorizing a model


Andreas Preuss

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52 minutes ago, Don Noon said:

My lightest top is 48g including varnish, and it too does not sound like a bluegrass fiddle.  But neither does it sound or play like a normal violin.  Not terrible, but not normal either.  Players often talk about "resistance", but I think it's more about "inertia"... where mass matters.  I also think that light tops (beyond a point) don't help the high frequencies as much as some of the middle ones, giving a loud but unrefined tone.

Well, I actually see a pinch of ‘loud and unrefined’ as the spice I am looking for. Not saying this should be everyone’s goal as there is certainly more than one solution to the sound good players want to have. 

My point was however that traditional solutions in the rib construction set certain limits to how thin and light you can go on the top. I would bet that I could make your 48g top work to sound more normal (if not pretty good) with reconstructing the ribs re calibrating the string angle and eventually use the x shaped bass bar. 
 


 

i would be really interested to see a graph of your 48g top for comparison. And it would also be interesting to know how you made the rib structure for that instrument.

If I see any shortcomings on my current top, there are three:

1. The relative weight was .38 and could eventually a bit lighter.

2. What bothers me more is that it was not split wood.

3. Because I have done the bending process of the top the first time, I couldn’t control some details on the arching the way I imagined it. 
 

What the combined corrections will do is hard to say. I only know that trying to minimize the top weight and thickness is a kinda of the ‘pure art of violin making’ for whatever tonal goal you have.

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1 hour ago, Anders Buen said:

Ok, this was an impact test. The impact roloff is related to your stick and bridge properties, I belive. The contact physics there play a role I think. Im not able to tell where the rolloff comes in relation to the contact time but they are in some way inversely related. The roloff may even depend a bit on the humidity level in the bridge and the spruce stick.

I think the theory behind it is described in one of the references I gave under my thread on radiation from orthtropic plates. 

I think I have a similar mic to the one you use, a mic that came with my first computer and fine soundcard then. I do think it is a little directive. I used it until I bought finer ones for the Curtin rig. 

The impact hammer impulse is dependent upon the hammer tip hardness--a soft tip hammer bridge impact will produce a violin frequency response curve with a rolloff at a lower frequency than a hard one.  So you don't know how much the violin's frequency response curve  is affected  by the impact hammer's tip hardness.

The violin's FRC is also dependent upon the direction of the hammer impact on the bridge-- a vertical impact will produce higher amplitudes at high frequency than a horizontal impact.  Many researchers now do both (averaged ?) to better represent the bowing angle on the strings.

I therefore use repeated bowed glissandos on the outer E and G strings for a violin with my computer's microphone and Audacity software.  I think this is a more realistic violin test but it has the disadvantage of having poor repeatability of the amplitudes of the frequency response curve because my bowing (force, speed, distance from the bridge) is inconsistent despite efforts to control it.

As a result I can reliably see the overall shape of the FRC and can determine the frequencies of the various peaks but their amplitude measurements is questionable.  So if I make violin construction changes I can't reliably know if the violin's loudness changes.

I should buy one of Curtin's rigs. 

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On 8/12/2021 at 12:49 AM, Andreas Preuss said:

Here I made with audacity a graph from a live stereo recording I have on a CD. Its a violin solo piece and the performer is using a golden period Strad. 

So even with the mic at some distance I think we can see what matters.  The strongest peak is around 2700Hz and we have peaks slowly ascending to it on one side and slowly descending from it on the other side covering easily one octave. 887135804_Stradivariinliverecording.thumb.png.f7566e69718820c0d2dabd60d5609317.png

The violin simply sounds brilliant. 

(Picking this recording was just a lucky guess, I think I am going to dig out more live recordings to get a better picture.)

I would be willing to bet that an Audacity plot of a full orchestra playing would have a very similar high frequency fall-off

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On 8/13/2021 at 10:53 AM, Don Noon said:

It is interesting to see the process of experimentation leading to theorizing about why the results are what they are.  I have often come across writings by well-regarded, experienced makers who will expound upon something they think works well... and then go into an explanation of why it works that makes no sense whatsoever in terms of physics/acoustics.

I'm not saying anything about the current thread... I can't tell anything for sure one way or the other.

But a incorrect explanation doesn't matter, in the end.  Something that WORKS is what matters.  

Definitely a topic worthy of investigation.  The obvious player, bridge rocking frequency, I have tested... but in test and theory, is is a slow rolloff at best, or about -6dB/octave for a 1st order lowpass filter... far less than what I actually measure.  At the moment, I haven't looked all that deeply into higher order filters and how a structure might perform higher order filtering... but it is a very intriguing idea.

This is a response plot of one of my violins, showing a steep dropoff corresponding to about a 4th order (-24 dB/octave) filter.

rolloff.jpg.99d45fdb5751865524bea3bda949c8f3.jpg

 

Plate arching doesn't seem to be necessary to have a steep drop-off .  The size of a plate's vibration nodes decrease with increasing frequency so the arching of the span they cover decreases and it approaches a flat plate.

This is even more apparent at the plate edges where the arching is already nearly flat.

Attached is a frequency response curve of one of my flat top plate violas which shows a similar dB/octave drop-off.  The frequency of the start of the drop-off is dependent upon the thickness of my plates--thicker:higher frequency.

This might show that the thickness near the plate edges of traditionally arched plate violins is also important in determining the drop-off frequency.

Screen Shot 2021-08-13 at 12.18.33 PM.png

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48 minutes ago, Andreas Preuss said:

i would be really interested to see a graph of your 48g top for comparison. And it would also be interesting to know how you made the rib structure for that instrument.

1854138422_Spectrum6210712.jpg.b6aee942028ce0e751eebc49cb2ec5c8.jpg

Compared to a violin considered "good", this has a lot of power in the less-than-desirable 1-1.4kHz band, and a skinny/anemic bridge hill.  Loud but not bright.  Top wood is .31g/cc torrefied Engelmann.  

The rib structure is just the usual, nothing special.

If you want "loud and crude", I'd suggest low density / high RR wood, low arching, and light plates (but still relatively thick due to the low density).

 

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50 minutes ago, Don Noon said:

The rib structure is just the usual, nothing special.

Thanks for the graph. Interesting. 

Can you be more specific about the ribs? Thickness of ribs and dimension of linings? I would guess strad type construction with 1.0mm ribs and rather thick but light wood linings. 

 

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Seems to me the drop off is much more of a by product of the type of oscillation that the bowed string inputs into the body, primarily a side to side motion vrs a plucked up and down motion which translates a different type of directional motion into the plate which results in much less cut off...or?

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1 hour ago, Andreas Preuss said:

Can you be more specific about the ribs? Thickness of ribs and dimension of linings? I would guess strad type construction with 1.0mm ribs and rather thick but light wood linings. 

I built this over 10 years ago, and don't have photos or notes on rib details... but generally I have been using 1.1mm thick ribs with 7x2mm spruce linings.  The maple on the back and sides (untorrefied Bigleaf) measured fairly light (.57) and low stiffness (3600 m/s speed of sound), and is likely a major factor in the low signature modes.

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Rather than start a new topic, this experiment was cooked up as a result of this thread, and is relevant, so I'll tack it on and drag this thread out some more.

The idea is based on the notion that the upper bout, and more specifically the central area (or slightly to the treble side) is where a large portion of the high frequency energy comed from.  At higher frequencies, there are multiple antinodes in different phases, so the second notion is that attenuating the antinodes that are out-of-phase with the central one might result in more overall output.

If any of this is correct, then the idea would be to keep the central area of the upper bout light, and go thick everywhere else (i.e. extreme "reverse graduation").  The bass bar is part of the attenuating mass, at least for this experiment.  The scalloping is to keep mass, but allow flexibility to retain low frequency power, and I didn't do anything outside of my usual in the center or lower bouts.

210814.JPG.aff24326dd3dbda727f546fb4ebe90f6.JPG

The plate is a CNC'd one that sortof fits my old Frankenfiddle testbed beater.  I ripped off the MDF back that was on it and put the maple one back on, ripped off the strange trapezoidal arched top, and put this one on.  The specifics of the new top plate:

16mm arch

.42 density torrefied Sitka, 5972 m/s measured speed of sound in the wedge.

2.2mm center of upper bout, 3-3.5 around the edges in a wide band.

W/o bass bar:  67.5g, M5=332Hz   With bar:  72.5g, M5=350Hz

In spite of the fairly high speed of sound, the plate characteristics fall more in my "clunker" range of heavy and floppy.  Some of it is undoubtedly due to extra-thick edges, but I also suspect wood properties as measured do not translate with high accuracy into what happens in the plate.  I have seen this happen many times.

My expectation for this radical experiment, as formed by the results of most of my experiments, is that there will be nothing conclusive, or perhaps conclusively not good.  How I build my instruments now has somehow ended up with arching and graduations well within the bounds of what we see from Strad and Guarneri, not much from experiments except sometimes as an indication of what NOT to do.  But you never know.  

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Two thoughts on high frequencies:

First, to make a kettle drum sound higher you don't replace the skin with a one inch board just because stiffer objects vibrate at higher frequencies. This might accomplish the job, but the result would be much quieter, less efficient and wouldn't compete with the other drums' sound volume. I think the same with violin tops: you don't get high freqs EFFICIENTLY by making the top thicker where you think the highs will appear. To make a drum sound higher you make the drumhead area smaller and still thin. If I were thinking of stimulating highs, I'd think of thinner wood, not thicker, in smaller sized areas in the most critical locations.

With that in mind. . .
Second, Kinberg (famous Chicago maker of the 50s and 60s) violins are unusual in their spectrum in that they have a lot of crunchy bright highs. Where the normal E string might only sound the first four harmonics of the note loudly, on a Kinberg six or more are loud before the response drops off. The only difference I have found in his grad pattern is that the widest parts of the upper and lower bouts of the top are as thin as 2 mm or less (only in the area outside the respective corner's longitude--a very narrow band of wood) on an otherwise 2.8 mm or thicker top. Not saying that's how he does it, but it's the only oddity I've noticed in his work. I don't like this sound quality, so I haven't attempted to replicate it. Needless to say, this spectrum isn't at all like what a classical Cremonese shows, nor is the sound similar. But since AP seems to want nasty. . .

One additional thought: a lot of the ideas I see in this thread seem to rely on old ideas that are passed along without proof. I think you might get farther if you thought wayyyy outside the box, as in the example above. LIke in the opposite direction. Those familiar with working with players have probably observed that you get the best results if you give them the opposite of what they think should be done. If they say the sound is tight, for instance, tighten the post, don't loosen it. Etc. I find that model useful, myself.

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4 hours ago, Michael Darnton said:

But since AP seems to want nasty. . .

I said I want to have roughness like a spice in a dish. Only loud and rough is NOT my goal.

I imagine it like some North African dishes where the combination of sweet and chili adds the little extra over the otherwise interesting blend of different spices. 
 

 

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6 hours ago, Michael Darnton said:

I think the same with violin tops: you don't get high freqs EFFICIENTLY by making the top thicker where you think the highs will appear. To make a drum sound higher you make the drumhead area smaller and still thin. If I were thinking of stimulating highs, I'd think of thinner wood, not thicker, in smaller sized areas in the most critical locations.

Completely agree with this. 
 

But since the activation mechanism is not like a drum it is not as easy as thinning down areas where you think they must be thin.

i made experiments with a.violin string up in the white and scraped the top from the outside on the upper bout under the fingerboard. (I used a fingerboard shortened to the neck length and a special narrow scraper for this) The results were the sort of thing where you start to talk yourself into changes which are not really there and sound graphs just stood there unchanged. 

So, I as m not going too much for local areas to trigger sound effects though too thick is certainly not a good idea for the top. 
 

We need to think as well how the vibrations in those areas are getting activated and there I see the real trigger mechanism. I have seen some graphs which show how the bridge activates the top in the first few milliseconds and this gives me some ideas. 

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8 hours ago, Don Noon said:

Rather than start a new topic, this experiment was cooked up as a result of this thread, and is relevant, so I'll tack it on and drag this thread out some more.

The idea is based on the notion that the upper bout, and more specifically the central area (or slightly to the treble side) is where a large portion of the high frequency energy comed from.  At higher frequencies, there are multiple antinodes in different phases, so the second notion is that attenuating the antinodes that are out-of-phase with the central one might result in more overall output.

If any of this is correct, then the idea would be to keep the central area of the upper bout light, and go thick everywhere else (i.e. extreme "reverse graduation").  The bass bar is part of the attenuating mass, at least for this experiment.  The scalloping is to keep mass, but allow flexibility to retain low frequency power, and I didn't do anything outside of my usual in the center or lower bouts.

210814.JPG.aff24326dd3dbda727f546fb4ebe90f6.JPG

The plate is a CNC'd one that sortof fits my old Frankenfiddle testbed beater.  I ripped off the MDF back that was on it and put the maple one back on, ripped off the strange trapezoidal arched top, and put this one on.  The specifics of the new top plate:

16mm arch

.42 density torrefied Sitka, 5972 m/s measured speed of sound in the wedge.

2.2mm center of upper bout, 3-3.5 around the edges in a wide band.

W/o bass bar:  67.5g, M5=332Hz   With bar:  72.5g, M5=350Hz

In spite of the fairly high speed of sound, the plate characteristics fall more in my "clunker" range of heavy and floppy.  Some of it is undoubtedly due to extra-thick edges, but I also suspect wood properties as measured do not translate with high accuracy into what happens in the plate.  I have seen this happen many times.

My expectation for this radical experiment, as formed by the results of most of my experiments, is that there will be nothing conclusive, or perhaps conclusively not good.  How I build my instruments now has somehow ended up with arching and graduations well within the bounds of what we see from Strad and Guarneri, not much from experiments except sometimes as an indication of what NOT to do.  But you never know.  

Yes, somehow to me the further you get away from "what they did" the less likely you are to get "that" tone, but garsh darn it lets find out anyway

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8 hours ago, Michael Darnton said:

Two thoughts on high frequencies:

First, to make a kettle drum sound higher you don't replace the skin with a one inch board just because stiffer objects vibrate at higher frequencies. This might accomplish the job, but the result would be much quieter, less efficient and wouldn't compete with the other drums' sound volume. I think the same with violin tops: you don't get high freqs EFFICIENTLY by making the top thicker where you think the highs will appear. To make a drum sound higher you make the drumhead area smaller and still thin. If I were thinking of stimulating highs, I'd think of thinner wood, not thicker, in smaller sized areas in the most critical locations.

With that in mind. . .
Second, Kinberg (famous Chicago maker of the 50s and 60s) violins are unusual in their spectrum in that they have a lot of crunchy bright highs. Where the normal E string might only sound the first four harmonics of the note loudly, on a Kinberg six or more are loud before the response drops off. The only difference I have found in his grad pattern is that the widest parts of the upper and lower bouts of the top are as thin as 2 mm or less (only in the area outside the respective corner's longitude--a very narrow band of wood) on an otherwise 2.8 mm or thicker top. Not saying that's how he does it, but it's the only oddity I've noticed in his work. I don't like this sound quality, so I haven't attempted to replicate it. Needless to say, this spectrum isn't at all like what a classical Cremonese shows, nor is the sound similar. But since AP seems to want nasty. . .

One additional thought: a lot of the ideas I see in this thread seem to rely on old ideas that are passed along without proof. I think you might get farther if you thought wayyyy outside the box, as in the example above. LIke in the opposite direction. Those familiar with working with players have probably observed that you get the best results if you give them the opposite of what they think should be done. If they say the sound is tight, for instance, tighten the post, don't loosen it. Etc. I find that model useful, myself.

So you mean it's like reverse psychology and children :lol:

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The sound radiation from eg a window mainly comes from the corners and the border, because there the «vibration balance becomes» unbalanced. The window vibreates and the wall does (almost) not.

A violin is sort of a baffled plate too as the inside only is open through the holes. I speculate that the main region for radiation at given frequencies above the monopole region or 0,8-1kHz is along the borders, because nothing counteracts the radiation outside while it may inside. 

A drum is a membrane. A plate has bending stiffness, and the wave velocity is frequency dependant. For a membrane the wavespeed is independant of the frequency. This does have the consequence that a membrane usually not becomes an efficient sound radiator. Still they produce much sound, becuse they are so thin and light. If a plate vibrated equally much it would radiate way more sound, at least in the highs.  

In some way a membrane is like a 2D version of a string. A Banjo has a membrane and there is much, quite recent, literature now on them. 

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16 hours ago, Michael Darnton said:

Two thoughts on high frequencies:

>

>

One additional thought: a lot of the ideas I see in this thread seem to rely on old ideas that are passed along without proof. I think you might get farther if you thought wayyyy outside the box, as in the example above. LIke in the opposite direction. Those familiar with working with players have probably observed that you get the best results if you give them the opposite of what they think should be done. If they say the sound is tight, for instance, tighten the post, don't loosen it. Etc. I find that model useful, myself.

Most of the violin's low frequency sounds (<1000Hz) come from internal cavity volume changes which cause sound to come through the f holes whereas the high frequency sounds come directly off of the outside surfaces.

So I try to think both inside the box and outside the box.

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1 hour ago, Marty Kasprzyk said:

Most of the violin's low frequency sounds (<1000Hz) come from internal cavity volume changes which cause sound to come through the f holes whereas the high frequency sounds come directly off of the outside surfaces.

So I try to think both inside the box and outside the box.

Does this mean for a frequency below 1000 hz that the fundamental frequency is from air compression and simultaneously higher partials or overtones of the same note are radiated from the surface?

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The radiated sound energy is the same outwards and inwards from the plates of a hollow radiator. So if all sound energy that goes inward came out the f-holes, it would give about 3 dB higher sound level in average. Around the A0 and the signature modes it may be some more.

Lord Rayleigh made a theorem that it is possible to determine the sound power of a sound source by measuring it inside the source. However, I think this breaks down due to the resonances in there, or one must take special precautions because of the resonances like many measurement points. I do have two of his books and can look it up.

Colin Gough have made an attempt at using it. Hutchins used it as it is a simpler method of doing measurements on larger instruments. 

Bissinger have done near field holographic measurements of the sound coming out of the f-holes and compared that to the radiated part from the outside of the plates. I am sure his abstract on that JASA article does give a clue as to what the numbers were measured to. 

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22 minutes ago, Anders Buen said:

Bissinger have done near field holographic measurements of the sound coming out of the f-holes and compared that to the radiated part from the outside of the plates. I am sure his abstract on that JASA article does give a clue as to what the numbers were measured to. 

The whole Bissinger paper can be read here. (click on the READ FULL TEXT button)

My reading of it:  the air resonance contribution to sound drops off above A0, but is still fairly strong at B1-.  Above that (500 Hz and above), F-hole radiation is pretty weak... except for a specifc peak or two, notably around 1 kHz.  I suspect the peaks in the upper frequencies have something to do with higher air modes and/or relation between where the active plate areas are vs. F hole location.

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27 minutes ago, Don Noon said:

The whole Bissinger paper can be read here. (click on the READ FULL TEXT button)

My reading of it:  the air resonance contribution to sound drops off above A0, but is still fairly strong at B1-.  Above that (500 Hz and above), F-hole radiation is pretty weak... except for a specifc peak or two, notably around 1 kHz.  I suspect the peaks in the upper frequencies have something to do with higher air modes and/or relation between where the active plate areas are vs. F hole location.

Thanks for posting the link and giving a condensed abstract.

There are some losses inside the violin body like it is in a regular room. A little radiates through the plates and mainly the f-holes. I haven't tried to make assessments, but it can be done using classic room acoustics and radiation methodes. The modes inside makes it a bit complex.

One part of it would be to measure the reverberation time of the volume. Knowing that and the volume, an assessment of the radiated power out the f-holes can be made. The sound level in there is quite a bit  higher than outside.

I have a cheap violin filled with cotton. It is heavy and does not radiate much from the f-holes. :-)

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20 hours ago, Don Noon said:

I built this over 10 years ago, and don't have photos or notes on rib details... but generally I have been using 1.1mm thick ribs with 7x2mm spruce linings.  The maple on the back and sides (untorrefied Bigleaf) measured fairly light (.57) and low stiffness (3600 m/s speed of sound), and is likely a major factor in the low signature modes.

I see now all measurements against other parameters . Top measurements alone don’t tell us anything without looking at the rib dimensions. 
 

Getting a stiffer frame for that top would definitely help. If you   want to make a quick experiment you can glue linings from the outside on the ribs (like some double bases).

19 hours ago, Don Noon said:

My expectation for this radical experiment, as formed by the results of most of my experiments, is that there will be nothing conclusive, or perhaps conclusively not good.

So nothing conclusive or is the experiment not finished ?

Hmmm, it seems that the wood is not the best and this might destroy a conclusive result. 
 

Sometimes I follow the logic to change something, even if in a negative direction to see if it matters. You could also glue a cross grain bar in that area. I don’t know if this can be regarded as an artificial nodal line, but supposedly something must change. 
 

I still think about the ‘ignition’. We know that a violin doesn’t function without sound post. Never made a graph in this condition but I guess the frequencies above 1khz will be completely diffferent because the sound is without sound post hollow and dull.  So what happens without sound post? Do we have a sound cancellation. effect right at the bridge feet moving in opposite direction?
 

This seems to me the reason too why the thickness of the back at the c bouts  matters because it makes the springiness of the area where the sound post stands. 

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First iteration of the latest Frankenfiddle test (detailed previously) is done.  As predicted, results are not hugely conclusive or good... but that almost always happens with radical experiments.  However, there might be something to be learned.

Here is the impact response.  The bowed response is similar, but impact is clearer and easier to repeat.

2132975802_210815ImpactResponse.jpg.b24273184e75fcd7a4958d78bf376ec0.jpg

Generally it is very loud, on the buzzy/woody/nasal side, but not obnixiously so.  High frequency seems fairly strong.  Feels a bit stiff to me.

BH - the Bridge Hill zone was the main focus of the test, to see if a fairly radical idea might work.  While there are strong sub-hills, it's not a solid, even response, with weak zones.  Also, I'd prefer to see the hill starting at lower frequencies.  It appears to be pushed into the higher frequencies.

TH - Transition Hill - looks typical to me of something that's too thick.  Several very strong peaks and dips.  Likely the cause of the loud/buzzy/nasal character.

C4 - I usually don't see a clear peak of this resonance.  Not a big deal one way or another, just curious.

B1+  Abnormally low frequency (507 Hz), especially for a thick-ish torrefied top.  The center-heavy bass bar contributes to lowering this frequency.  Amplitude looks relatively low... also an effect of center-heavy bar.

B1-  Looks about normal

A0  Looks relatively weak.  Since A0 amplitude is very strongly related to absolute stiffness under the bass foot, I suspect the thick, dense top is the controlling factor here.

While this test did not produce spectacularly good results, thus shooting down the concept of trying to get one small controlled area to radiate super-efficiently, the test is not quite over yet.  Now to rework the top into something more normal, and see if the wood/arching is totally in control, or if going to more normal grads and bass bar improve things.

I expect that getting rid of the super-thick graduations around the border of the top bout will increase modal density and smooth out the Bridge Hill, as well as extend the response into lower frequencies.  Thinning out the center of the top and putting in a lighter, stiffer bar should balance the B mode frequencies and amplitudes (mostly getting B1+ frequency and amplitude up a bit).  Overall thinning should help A0 amplitude.

To be continued.

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2 hours ago, Andreas Preuss said:

>

I still think about the ‘ignition’. We know that a violin doesn’t function without sound post. Never made a graph in this condition but I guess the frequencies above 1khz will be completely diffferent because the sound is without sound post hollow and dull.  So what happens without sound post? Do we have a sound cancellation. effect right at the bridge feet moving in opposite direction?
 

This seems to me the reason too why the thickness of the back at the c bouts  matters because it makes the springiness of the area where the sound post stands. 

You're right. The soundest prevents its side of the top plate from vibrating much thereby reducing out of phase far field sound cancellations. The sound post increases the sound output.

If you like a more detailed explanation I recommend  John McLennan's 2017 book "The Soundest in the Violin"

I've never met him but he's an inspiration to me now that I'm getting older.  He got his PhD at the age of 84 (!) with his thesis "Violin Acoustics from Baroque style to Romantic style instruments".  He along with Oliver Rogers. Norman Pickering and Carleen Hutchins have shown that actively doing violin research increases your life span. 

 

 

 

 

 

 

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9 hours ago, Marty Kasprzyk said:

You're right. The soundest prevents its side of the top plate from vibrating much thereby reducing out of phase far field sound cancellations. The sound post increases the sound output.

If you like a more detailed explanation I recommend  John McLennan's 2017 book "The Soundest in the Violin"

I've never met him but he's an inspiration to me now that I'm getting older.  He got his PhD at the age of 84 (!) with his thesis "Violin Acoustics from Baroque style to Romantic style instruments".  He along with Oliver Rogers. Norman Pickering and Carleen Hutchins have shown that actively doing violin research increases your life span. 

From Amazon

https://www.amazon.com/Soundpost-Violin-John-Ph-d-Mclennan/dp/1543403107

"This book dispels the mystery that the position of the sound post in determining the sound quality of the violin is critical."

 

This tells me all I need to know about his ability to discriminate sound quality...............

 

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