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Wood properties, plate mass, and the final violin


Wm. Johnston

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Lately I've been continuing my experiments on how to control the body modes of assembled violins. In the past these were done with a 1/2 size violin body but now I'm doing some work on a 4/4 violin body with a neck. Here's a quick summary of what I am doing. I have a violin body with a back, ribs, neck, and fingerboard. Onto these I glue different top plates. Since the rest of the body is left unchanged throughout the tests I will be mostly looking at the effects of the different top plates.

The back plate is carved from Bigleaf maple. Usually Bigleaf is low density but this piece is as heavy as rock maple but not as stiff. I left the graduations like a heavy del Gesu, ~6.5mm at the center. I did this because in my earlier experiments I found that a thick back produces a louder violin than the same violin but with the back thinned.

The topic of this post are some tests that I've made with two different top plates, one of Douglas Fir and one of Hemlock, on this 4/4 violin body.

The properties of the Douglas Fir top (with bar) are,

density 0.41 g/cm^3

radiation ratio 11.5

thickness of plate ~2.5mm fairly uniform

weight 82g

arch 16mm high

Tap tones

mode 1 83Hz

mode 2 133Hz

mode 5 319Hz

The properties of the Hemlock top (with bar) are,

density 0.45 g/cm^3

radiation ratio 9.22

thickness of plate ~3.0mm and fairly uniform

weight 100g

arch 17mm high

Tap tones

mode 1 96Hz

mode 2 146Hz

mode 5 317Hz

The arches of the two plates are very similar except that the Hemlock is a little bit higher.

In a recent thread people were talking about the 3g or so that can be saved by thinning around the endblock of a violin. Well here I have plates that are 18g different. How different would the assembled violin bodies be? I would expect them to be very different but were they?

If you look at these two plates based on a stiffness number, say mass times tap tone frequency squared, the plates are pretty different. What would you expect this to do to the modes of the assembled bodies?

Anyways, how different do you think the violin body would be with these two tops? On paper they look very different to me but does that translate in to a vastly different assembled violin? The materials used for each are pretty different, should that show up?

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I know these are just experiments, and I applaud anyone who takes the time to do these things and share what they have found.

Assuming you could ultimately control the modes of assembled violins 1. do you think this is the "key" to a good sounding violin and 2. If you could do this, do you think that even though all the violins are from dissimilar wood that they would all basically sound the same?

I do not think this is the case. Personally I feel there are far too many quantum interactions to put all the eggs in one basket related to modes being "it" and that the "key" is wood choice and wood "marriage", along with a whole bunch of other stuff.

To me, choosing the wood is probably the best way to ensure a good sound, assuming you do all the other stuff right. I do not think you can turn "sheet into shinola" regardless of how you carve it. I think we can do radiation tests,dampening, mass and such and get good characteristics ideas from this, but to me, using "machines" to in essence verify what I can do with my hands, eyes and ears on the spot seems useless.

Yet still, i appreciate the foot work and hope you keep us posted. I'm not a big fan of Hemlock{its got a "wet" feel to usually} so I think that one will sound rope'y

What is the moisture content? are you creating a "chart"? I would measure the moisture every time you do test, prior to varnish and after with a pinless meter.

I feel that one must account for moisture content, and do several base readings over the course of tests in order to be able to factor in how that may be effecting things.

Good luck

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No formulas or correlation equations, just a guess:

Fir: B1- 440Hz, B1+ 545Hz

Hem: 460Hz, 550Hz

These low modes are just a small fraction of the stuff that determines what it sounds like, but my guess is that they'll both sound relatively dead, with the hemlock being deader.

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No formulas or correlation equations, just a guess:

Fir: B1- 440Hz, B1+ 545Hz

Hem: 460Hz, 550Hz

These low modes are just a small fraction of the stuff that determines what it sounds like, but my guess is that they'll both sound relatively dead, with the hemlock being deader.

Would'nt that be...more dead, or is it more deader....but really, once something is dead, can it be more dead? hmm, deep thoughts, I suppose we could shoot it once more, just to make sure. :lol:

I agree, I don't think I would use either for a "real" violin. But I suppose for experiments and such, why not, nothing ventured and all.

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The properties of the Douglas Fir top (with bar) are,

density 0.41 g/cm^3

radiation ratio 11.5

thickness of plate ~2.5mm fairly uniform

weight 82g

arch 16mm high

Tap tones

mode 1 83Hz

mode 2 133Hz

mode 5 319Hz

The properties of the Hemlock top (with bar) are,

density 0.45 g/cm^3

radiation ratio 9.22

thickness of plate ~3.0mm and fairly uniform

weight 100g

arch 17mm high

Tap tones

mode 1 96Hz

mode 2 146Hz

mode 5 317Hz

The arches of the two plates are very similar except that the Hemlock is a little bit higher.

Well here I have plates that are 18g different. How different would the assembled violin bodies be? I would expect them to be very different but were they?

If you look at these two plates based on a stiffness number, say mass times tap tone frequency squared, the plates are pretty different. What would you expect this to do to the modes of the assembled bodies?

Anyways, how different do you think the violin body would be with these two tops? On paper they look very different to me but does that translate in to a vastly different assembled violin? The materials used for each are pretty different, should that show up?

I guess the Hemlock topped violin body should have a weaker A0, slightly higher frequencies (4-5Hz ish) for the B1- mode and possibly the B1+ than the Douglas Fir top. Both the higher weight and higher stiffness number (and the higher arch height) points toward a body with a weaker A0. I would guess the douglas Fir topped body has about 4 dB higher sound level of the A0 and that the region between the A0 and B1- will be a few dB stronger than for the Hemlock topped body.

I think the B1- frequencies are below 444Hz for both violins, but that the B1+ is rather high because of the back plate thickness. The wood is softer than normal, so maybe not extreme, but above 550Hz would be a possibility.

Since the questiaon is asked in this manner, maybe the results are very similar. The tap tones are quite low for the weight. So maybe the outline or the border thickness is rather high?

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Are you sure your scale is properly calibrated? These masses seem extremely high for the dimensions.

I haven't checked it too carefully but now that you bring it up the masses do seem to be pretty high. It's just a cheap Harbor Frieght scale so I don't ask too much from it except that it gives me the same number each time I place the same thing on it.

I did measure the density of my wood samples by flotation as well as by size and weight, the measured densities were in good agreement so for weights of ~50g the scale should be alright. I'll check the scale against some quarters and pennies when I have time. It's also possible that my old homemade calipers aren't working well but the thicknesses it measures look right by eye. The difference in mass between the two plates seems reasonable based on the wood densities and thicknesses.

The Hemlock plate in particular does feel quite heavy.

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These low modes are just a small fraction of the stuff that determines what it sounds like, but my guess is that they'll both sound relatively dead, with the hemlock being deader.

The violin body with the Hemlock top definately feels more dead in my hands when I tap on it with my fingers, overall it feels quite heavy and not too lively.

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The tap tones are quite low for the weight. So maybe the outline or the border thickness is rather high?

Yes, the overhang is generous and the edges are fairly thick. There is a scoop around the edges so the graduations are continued fairly close to where the plates are glued to the ribs but the edges themselves are heavy. Since the Hemlock top is still on the violin I might thin the edges and overhang down to normal tonight and see what changes. The reason that the edges have been left heavy is because I'm also going to do tests on several different spruce tops (with specific gravities down to less that ~0.35) to see how more traditional woods of various materials properties compare. These spruce tops are then going to be reused on other violins so the overhang and edge thickness has been left generous so they can be trimmed to size as needed.

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I know these are just experiments, and I applaud anyone who takes the time to do these things and share what they have found.

Assuming you could ultimately control the modes of assembled violins 1. do you think this is the "key" to a good sounding violin and 2. If you could do this, do you think that even though all the violins are from dissimilar wood that they would all basically sound the same?

'Good' is a matter of opinion and human opinions are tricky things to deal with. I think that controlling the modes of an assembled violin could be one way of achieving consistant violin tone, whether it is a good tone or not is a different question.

I do not think this is the case. Personally I feel there are far too many quantum interactions to put all the eggs in one basket related to modes being "it" and that the "key" is wood choice and wood "marriage", along with a whole bunch of other stuff.

To me, choosing the wood is probably the best way to ensure a good sound, assuming you do all the other stuff right. I do not think you can turn "sheet into shinola" regardless of how you carve it. I think we can do radiation tests,dampening, mass and such and get good characteristics ideas from this, but to me, using "machines" to in essence verify what I can do with my hands, eyes and ears on the spot seems useless.

Yet still, i appreciate the foot work and hope you keep us posted. I'm not a big fan of Hemlock{its got a "wet" feel to usually} so I think that one will sound rope'y

I'm not a big fan of it either, too unstable, but I had some laying around so it was good for some cheap experiments. The cheap experiments are mostly done so now I'm moving on to my spruce stash.

What is the moisture content? are you creating a "chart"? I would measure the moisture every time you do test, prior to varnish and after with a pinless meter.

I feel that one must account for moisture content, and do several base readings over the course of tests in order to be able to factor in how that may be effecting things.

Good luck

I'm not too concerned with how the moisture content of the wood affects things because that is where I draw my line in terms of the size of the effects that I'm interested in. In principle just about anything you do to a violin should change its tone but I don't want to chase after everything, there's only so much time for these things after all. I'd rather focus on the large effects.
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Are you sure your scale is properly calibrated? These masses seem extremely high for the dimensions.

I checked the scale and it is good to within about 1g. Some of the extra mass is due to the generous edge overhang mentioned earlier. I trimmed back to edges on the Hemlock violin top last night and this removed 7g, I'll post the results of the edge trimming later.

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Since the questiaon is asked in this manner, maybe the results are very similar.
I was hoping that the answer wouldn't be too obvious. The violin was very similar with the two tops, not identical but more similar than I was expecting. Attached are the spectra of the low frequency body modes as well as the response over all frequencies but averaged over 250Hz intervals to make to overall output more obvious.

I tapped the top in a vertical manner, as descibed in Joseph Curtin's recent Stard article, because that is the only way you can do it without fitting a bridge. The attached spectra have been averaged over 100 taps with 5 different soundpost locations, I put a mark on the back so that the post would be in a similar spot for both of the top plates. Since there could be several days between testing different configurations of the violin I made a simple microphone calibration system out of a sheet of acrylic. I used this to adjust the overall microphone levels between runs. This worked very well at frequencies below 1500Hz but not so good at higher frequencies. I'm still trying to make this amplitude measurement better, right now I think room acoustics are messing with the measurements at high frequencies.

The Douglas Fir top was louder in the low frequency region while the Hemlock top was better in the 2000 to 5000Hz region which is generally associated with good carrying power. I was expecting the Hemlock top to have horrible high frequency response but that doesn't seem to be to case. The body modes below 700Hz are in the same places for both of the violins but the D.Fir top has a 'peakier' response. This could mean that the response would be more uneven note-to-note or it could be more prone to wolf notes but also notes with vibrato could sound more interesting on it. The mode frequencies are not low, at least some of this is due to the thick back.

So, the violin wasn't the same with the two tops but concidering how different the masses of the free plates were I was surprised that the resulting violins weren't extremely different. If I were to slowly adjust these two top plates over several days I think that I would be able to get these two tops to produce extremely similar results, but that would be very tedious to do.

post-24240-0-71547100-1307553615_thumb.jpg

post-24240-0-55991900-1307553622_thumb.jpg

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Ok, interesting results. I have extracted some signature mode data from the low frequency figure of curiousity. The B1- modes are rather low, and may drop a little with the strings on. The B1+ modes are not as high as I guessed, but the distance between the b1+ abd b1- are, as expected, a bit on the high side (Old Italian average ca 95Hz).

For fun I have plotted the B1 mode data into the regression data from Don Noons and Wilkins data set I have presented before here. The green and red data points are from Wm's experiment and lie a little above the regression lines.

The level differences are rather large, if the differences are as large as this in reality, the sound will be very different, I think. 10dB is a lot. The damping is indeed smaller for the douglas Fir top as the peaks are higher and the valley is deeper as well. Is the fixture slightly different in these two cases? The glue is equally dry? (at least a day and night?)

I am not quite sure if hammering straight down and sideways will give similar results for the Dünnwald L parameter. If they do, both these fiddles may be shallowish. The differences in the high frequency region is indeed large.

[Edit] The numbers given for the frequencies in this post are incorrect.

post-25136-0-50621500-1307573529_thumb.jpg

post-25136-0-88221900-1307573540_thumb.jpg

Edited by Anders Buen
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I went back to the original plots, they are saved in a format that allows me to pick the values directly off of the plot. Your amplitude estimates seem right but the frequencies are a little low. This is what I get,

Hemlock top

A0 277Hz 7.2dB

B1- 459 15.4

B1+ 565 18.9

D.Fir top

A0 281Hz 9.5dB

B1- 446 21.3

B1+ 560 27.0

Both of these violins were supported in the same manner, suspended from a string running under the fingerboard.

I'm not too familiar with the effects of the amplitudes of these resonances yet. I need to go back and do some reading on this subject. I also want to play with simulating violin tones with various response curves to see how the amplitudes of single modes affects things.

The reason that I said I was surprised at the similarities of these two spectra is because I have compared them to a normal spruce topped violin that I have and it was very different than these two. The spruce violin had the same amount of high frequency response but much less low frequency response. This was likely due to its back plate being thinner. In my previous tests on a 1/2 size violin I found that thick backs resulted in louder violins. Compared to the spruce topped violin, I don't see anything here that would make me say that the D.Fir or Hemlock topped violins were 'dead' sounding, just not as harsh or bright as the spruce violin.

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I went back to the original plots, they are saved in a format that allows me to pick the values directly off of the plot. Your amplitude estimates seem right but the frequencies are a little low. This is what I get,

Hemlock top

A0 277Hz 7.2dB

B1- 459 15.4

B1+ 565 18.9

D.Fir top

A0 281Hz 9.5dB

B1- 446 21.3

B1+ 560 27.0

Both of these violins were supported in the same manner, suspended from a string running under the fingerboard.

Ok, in my fitting plot I had not matched the upper scale correlctly, so all fitted frequencies became too low. Thanks for sharing the numbers directly.

I replot the regression data.

post-25136-0-47472500-1307599228_thumb.jpg

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And the fitted mode data. Might be fun to see how well the fit is. I also enclose the figure with the fitted points.

The B1+-B1- distance is large as assumed by the thick back plate. The regression data lie higher for the modes than the data in Dons and Wilkins data. Maybe the back plate thickness does influence the modes a bit? If the effect was idependant of the effect from the top, the effect should be at a right angle to the regression lines. Strings and bridge will reduce them a bit. High B1+ modes are also a trait of thick backs, I think.

post-25136-0-35692700-1307647976_thumb.jpg

post-25136-0-76616700-1307648089_thumb.jpg

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