Graham Caldersmith's free plate and assembled violins data - Correlations

[Anders Buen]

Graham Caldersmith was an Australian instrument maker. He made both violins, violas, celli and guitars. He passed in 2019, but his website is still there with an obituary: https://www.grahamcaldersmith.com.au/ I think he also was a scientist, and there are a few articles by him on wood and wood testing, I think in the CASJ, or Newsletter. He was enthusiastic about and probably used local Australian wood. 

I recently got a database of his via Dr. Jesus A. Torres in Mexico, with free plate weights, arch heights, tap tones in steps for the free plates and data for the signature modes in the assembled violins. There are 64 violins in there. This is a "spin off" of an other project where I collect data for predicting plate properties from wooden parameters and arch-height.

Torres gave permission to share information from this, after informing him on the preliminary results. I thank him, both for the generosity with sharing the data, and for letting me share findings from it. He is one of the guys we may find interesting on the violin acoustics scene now. 

I enclose the correlation matrix where bold numbers are significant on the 1% level and the green ones on the 5% level, after Boneferroni-corrections, as we are asking the dataset "many questions", one for each number, and the limits thus has to be more strict. The matrix is symmetric, so the lower and upper part contain the same information. 

There are significant correlations between the free back plate modes 1, 2 and 5 and the three signature mode frequencies T1 (B1-), C3 (B1+) and the C4 (ring mode in back plate)
There is also a significant correlation with the same signature modes and the top plate mode 5 and somewhat weaker with mode 2 of the free top. 
Thickness does not appear to give significant correlations. I think the graduation data might be few.

The arch height data are also not complete, only 17 for the tops and 12 for the backs. Larger correlation coefficients can appear with fewer data, but higher numbers will not make them more significant. The weights does not show significant correlation either, somewhat surprising.

If the correlation coefficient is squared, it should give an estimate for the "prediction power" of the given pair. A r = 0,61 will be 0,372 = 37,2% prediction power for Tuned top plate mode 5 and B1+ frequency. That is: 63% of the other influences are not explained by this parameter.   

I haven't figured out his making "patterns" yet, but he must have been a "tuner" in "Hutchins tradition", although his plates are way lighter than hers. The backs are around 100g, very normal. The top plate mode 5 frequency is average 305 Hz, which is low. Average top plate weight with sealer and cooked (linseed oil?) is 62,1 g. One Hutchins top I've gotten data for weighs 80 g. Maybe he was fond of a rich low end? Or the climate could be humid.
 

 

 

240316 Rev 1 Caldersmith Lokk_ bunner og sammenlimt engl.pdf

Edited March 16 by Anders Buen
Correction of the correlation matrix and added average thickness data

[TZEENTCHAU]

Some of his violins used Australian timber (some of what you see on his website) and some used traditional European timber (i saw one of his violins was for sale recently and that was made of European timber).

For Australian timber he most likely used king billy pine for the top and tasmanian blackwood for the back (   https://www.google.com/amp/s/amp.smh.com.au/national/luthier-was-in-tune-with-australian-woods-20191011-p52zt4.html).  

I havent heard any of his instruments (at least not announced as such)- outside of short documentaries 

Thanks for the info.

[Don Noon]

Very impressive project and undoubtedly very tedious to gather and enter all of that data.

I suppose it is not surprising that there is some correlation between free plate taptones and signature mode frequencies.  What HAS been surprising is that I have found much weaker correlations in my own data.  Perhaps my data analysis skills are lacking, or I make stuff that varies too much.  I would suspect that a more consistent maker would have better correlation, but between different makers there could be much worse correlation.

In any case, the main issue I have is that, within a fairly broad range, I don't see that signature mode frequencies are much of an indicator of whether a violin is any good or not.  Many violins that sound like crap have the same signature mode frequencies as great concert violins, and concert violin signature modes can vary.  It is not difficult to get signature modes within the acceptable range.  What IS difficult is to figure out how to make a great concert violin.

[Andreas Preuss]

7 hours ago, Don Noon said:

Many violins that sound like crap have the same signature mode frequencies as great concert violins, and concert violin signature modes can vary

Isn’t the correlation of amplitudes of the signature modes more relevant, if anything? 
 

But yup, the high frequencies above 2khz are what makes significant differences how the sound is perceived and how the instrument feels under the bow. Strange that so little research is done on that.

[Don Noon]

6 hours ago, Andreas Preuss said:

Isn’t the correlation of amplitudes of the signature modes more relevant, if anything? 

"More" relevent, but not a critical thing.  Evenness I think is nice, but a lot of violins considered "good" have an overly strong B1+ verging on (or actually) wolfy.

6 hours ago, Andreas Preuss said:

But yup, the high frequencies above 2khz are what makes significant differences how the sound is perceived and how the instrument feels under the bow. Strange that so little research is done on that.

It's not so strange.  Because it's so complicated, and nearly impossible to get experimental results that prove anything.  If you can't show results, you don't write a paper.

There are logical arguments for damping being a strong factor, and probably arching as well for the middle frequencies (Sam Z. has mentioned this as well).  It seems apparent in some of my results, but nowhere near paper-worthy.  And writing papers isn't something I'm interested in.

[Anders Buen]

14 hours ago, Andreas Preuss said:

Isn’t the correlation of amplitudes of the signature modes more relevant, if anything? 
 

But yup, the high frequencies above 2khz are what makes significant differences how the sound is perceived and how the instrument feels under the bow. Strange that so little research is done on that.

making correlation on amplitudes takes a a stable measurement system and cosistency that is much more difficult to achieve. I do have such a dataset on my own work, both bowed response and impact hammer tests. However, the soundcard I used would drift in level for the piezoelectric impulse hammer. So I do not trust that the recoridngs over 10 year are done under similar conditions.

In Caldersmiths data there are no levels. Working with frequencies are simple. Everyone can do that with simple means.

There are quite a bit research on the high frequency part. E.g Woodhouses article on the bridge. Janssons work with Niewzyk on the bridge and f-hole properties. Bissingers articles on the radiation efficiency. I have some article drafts on it too related to the radiation efficiency which is a classic architectural acoustics issue. 

In the higher frequencies we have to work more with clusters of resonances rather than single ones, except for the bridge and f-hole wings maybe. 

I think the simple idea with balance in violin sound is that you can always get a good high frequency output from a rather stiff and heavy violin. You loose somewhat of that while the lows are strengthened by thinning down the plates and possibly the bass bar. The thinner and more pliant the top central region becomes, the less firm grund you have for the bridge and the flatter the bridge hill becomes. 

The bass bar stiffness determines at which frequency the bridge starts to become more active on the spoundpost side, in the "transition hill region". A stiffer bar will make a stiffer ground for the left bridge foot in that region and probaly push it up somewhat. 

I have heard Sam Z indicate that they see a trend in their data that the wood may have more of an influence in the highs. I think that makes sense also theoretically.  

[Don Noon]

1 hour ago, Anders Buen said:

I think the simple idea with balance in violin sound is that you can always get a good high frequency output from a rather stiff and heavy violin.

In my experience with regrads, the 2000+ Hz frequencies stay about the same in amplitude, but with less dips.  The 800-1500 Hz range is where I see strong peaks with a thick top, and these are reduced with thinning.  Naturally, it's the low frequencies where you see the largest differences.

1 hour ago, Anders Buen said:

I have heard Sam Z indicate that they see a trend in their data that the wood may have more of an influence in the highs. I think that makes sense also theoretically.  

The few non-torrefied instruments I have made seemed to lack something on the high end, which agrees with this.  The largest difference in torrefied wood is the lower damping.  Any violin will display the difference with low humidity vs. high humidity environments, which is primarily a damping effect.

[sospiri]

On 3/12/2024 at 11:52 PM, Don Noon said:

Very impressive project and undoubtedly very tedious to gather and enter all of that data.

I suppose it is not surprising that there is some correlation between free plate taptones and signature mode frequencies.  What HAS been surprising is that I have found much weaker correlations in my own data.  Perhaps my data analysis skills are lacking, or I make stuff that varies too much.  I would suspect that a more consistent maker would have better correlation, but between different makers there could be much worse correlation.

In any case, the main issue I have is that, within a fairly broad range, I don't see that signature mode frequencies are much of an indicator of whether a violin is any good or not.  Many violins that sound like crap have the same signature mode frequencies as great concert violins, and concert violin signature modes can vary.  It is not difficult to get signature modes within the acceptable range.  What IS difficult is to figure out how to make a great concert violin.

Surely the biggest difference is the player?

[Anders Buen]

10 hours ago, sospiri said:

Surely the biggest difference is the player?

Gestures is very important for the resulting sound and experience. Its the 10000 hours of talent training. But it also probably takes its 10000 hours of talented training to be able to produce a violin, on a regular basis, that a violinist trained like that is willing to play over time. We all may be lucky at times. 

[Don Noon]

I'd say that a good violinist can get the maximum potential out of any violin, but a good violin has more potential.  Listeners might not be able to tell the difference too easily, but the violinist sure can.

[Marty Kasprzyk]

On 3/11/2024 at 12:46 PM, Anders Buen said:

>

If the correlation coefficient is squared, it should give an estimate for the "prediction power" of the given pair. A r = 0,61 will be 0,372 = 37,2% prediction power for Tuned top plate mode 5 and B1+ frequency. That is: 63% of the other influences are not explained by this parameter.   

>

 

240302 Caldersmith Lokk_ bunner og sammenlimt engl.pdf 41.19 kB · 21 downloads

Is it correct that If I add up all the "prediction power"s of each variable it should add up to 100%?

If that is true and if they don't add up to 100% does that mean there are some other variables we haven't measured and included in our analysis?

[Anders Buen]

11 minutes ago, Marty Kasprzyk said:

Is it correct that If I add up all the "prediction power"s of each variable it should add up to 100%?

If that is true and if they don't add up to 100% does that mean there are some other variables we haven't measured and included in our analysis?

We often get more than 100% because some of the the variables are not independent, like the free plate tap tones of the different modes, and the plate weight. The one or two of them may be used in an analysis. Or the dependence can be accounted for by cross terms.

In multiple regression using a pr tool for this, there will be suggestions for what input parameters to use, or you try and fail until the best model has been achieved. There is non linear regression available in the tool I use (Minitab) and it is a wizard for it. I choose the input and the wizard tell me how well these perform in the modeling.

Sometimes the data may need a transformation before entering linear regression, which is the safer method. Out of nonlinear models one can get strange results if the input is outside the region of the input parameters. Ad the faults can become very large.

Statistics is kind of a handicraft. My best models this far is models for prediction of absorption of slatted panel sound absorbents. The best octave bands have over 95% prediction power.  However the modeling does not account well for resonances passing through different bands, so the Helmholtz resonance band at 250 Hz is not so good 75% ish. So I guess there is something to learn in dealing with that. 

I have tried to make models like that for panel absorbers, which also are "resonance driven". And it has not been as successful as for the slatted panels, although the dataset behind is huge.

[Anders Buen]

I have revised the correlation table in the first post as I found a couple of errors from the transfer process in the dataset. I have also added average graduations there for both for the top and back. I think they may be rather coarse.  

[Anders Buen]

Caldersmith appear to have been matching the top and back plates. At least there are strong correlation between the free plate to and back plate mode 2 and 5 frequencies in the tops and backs. However, it doees not look like he has been using "octave tuning" as proposed by Hutchins. 

Maybe matching of the plates give a stronger, or some, control with the signature modes than not doing it?

[Don Noon]

1 hour ago, Anders Buen said:

Maybe matching of the plates give a stronger, or some, control with the signature modes than not doing it?

Highly doubtful. 

I would suspect something more along the lines of:  "This client prefers a stiffer instrument, so it seems like a good idea to make both plates on the stiff side."  Or maybe a Guarneri model vs. Strad.

I would probably tend to do that, although I have absolutely no real evidence that this kind of matching results in anything better than highly mismatched plates.  Maybe some other maker has evidence?

[Andreas Preuss]

1 hour ago, Anders Buen said:

Caldersmith appear to have been matching the top and back plates. At least there are strong correlation between the free plate to and back plate mode 2 and 5 frequencies in the tops and backs. However, it doees not look like he has been using "octave tuning" as proposed by Hutchins. 

Maybe matching of the plates give a stronger, or some, control with the signature modes than not doing it?

Some scattered thoughts on your post:

Control. 

What needs to be controlled? 

How much control is really needed? 

When we think a certain control is absolutely necessary we must also do the crash test on it. 

  ———————-

I personally got away from the idea that this kind of control is necessary. Each parameter in a controlled scheme must follow a theoretical idea which explains only one isolated aspect.

Observation guided alterations are in my view better even though they can’t be theorised. 

[LCF]

1 hour ago, Andreas Preuss said:

Observation guided alterations are in my view better even though they can’t be theorised. 

I can't quite put my finger on the semantics here, but I think you still must have some theory about things when you are making an observation followed by an action. You might not think of it it a scientific theory but on many levels it is. It's your 'what if?'. 

[Peter K-G]

15 hours ago, Anders Buen said:

Maybe matching of the plates give a stronger, or some, control with the signature modes than not doing it?

Yes, but there is also a straight forward correlation between:

Top   M5 and B1- (back not altered)

Back M5 and B1+ (top not altered)

[Andreas Preuss]

1 hour ago, LCF said:

I can't quite put my finger on the semantics here, but I think you still must have some theory about things when you are making an observation followed by an action. You might not think of it it a scientific theory but on many levels it is. It's your 'what if?'. 

With observations you see imo rather the total. You may call it a theory knowing which alteration has which effect, I don’t there a theory because it is too imprecise. 
More discussion about this would lead to far away from the original post. I am simply sceptical about trying to control things too much. 

[Don Noon]

3 hours ago, Peter K-G said:

Yes, but there is also a straight forward correlation between:

Top   M5 and B1- (back not altered)

Back M5 and B1+ (top not altered)

For an already completed instrument, sure... you can get some decent correlation between a change in the plate modes and a change in the assembled instrument modes.  You're just changing one thing, and everything else is the same.  Starting with the free plates on a new instrument, the correlation becomes poor.  Perhaps if you only used wood from one tree and pathologically controlled everything in the entire build, you could get signature mode frequencies closer to some target.  The purpose eludes me; I have never seen evidence that precise signature mode frequencies correlate with desirable tone.

2 hours ago, Andreas Preuss said:

With observations you see imo rather the total. You may call it a theory knowing which alteration has which effect, I don’t there a theory because it is too imprecise. 
More discussion about this would lead to far away from the original post. I am simply sceptical about trying to control things too much. 

We seem to be dancing around the term "trial-and-error".  Theory might suggest something that might be worthwhile, but the violin is too complex to what will really happen across the full spectrum.  This is especially true for things like arching shape, where it's close to impossible to predict much of anything useful from basic principles.  

In the end, it's humans who evaluate the final result, and we know how wildly unpredictable they are.

[Anders Buen]

32 minutes ago, Don Noon said:

The purpose eludes me; I have never seen evidence that precise signature mode frequencies correlate with desirable tone.

I bought a couple of series of instruments made in Weihai, China some years ago. It is on the east coust and I think it is pretty humid there. It is humid in Cremaona too. My frends cello cracked when it came home to our dry winther climate, after a few months, I think. So for the customers from Scandinavia, Cremona is not really a agood place to run a workshop from.

Now to the case. I bought these violins because I needed data points for my «data mining project». The prices were reasonable and the quality quite good. You can choose of course, related to the price. I bought some finsihed and varnished and some white. The finished ones can be played before regreaduation, and it is easy to get the signature modes on FFT, «mobility» or SPL/F.

I have done this over many many years, along with a small business in the same, where instruments came in for repair etc. Doing so mapping instrument properties, you see trends after a while.

In general the chinese violins are relatively solid built (not all of them) and tend to have high lying signature mode frequencies. A few out of say 20 are great as they are. But the regraduated ones get more low frequency punch and, possibbly looses a bit of the highs.

I think there is plenty of evidence that thick mass produced or just thick solid built insturment do sound stiffer and may benefit from being thinned a bit. There is evidence also in Moral and Janssons work on this from the 80ties. At least they manged to get «rules» that would separate the winners from the «loosers» in the FIOL 80 or whatever year competition. 

Players prefer different instruments, so a competition resiult will be the preferences from the judges, and not a universal judgement. It is all subjective, but with different degrees of objectiveness. Absolute objectiveness does not exist. 

[Don Noon]

48 minutes ago, Anders Buen said:

I think there is plenty of evidence that thick mass produced or just thick solid built insturment do sound stiffer and may benefit from being thinned a bit.

And then there's the Vieuxtemps Guarneri...

I think it's lots other things, not the signature mode frequencies that make the difference.  You thin the plates of an instrument to get power balance across the range, which is primarily an amplitude issue.  Signature mode requency by itself is minor, although often related to ampliutde.

With good stiffness/density wood, I find that my signature modes tend to be a bit higher than "normal".  To get the frequencies down, I'd have to go so thin that the low end would get overly strong, and bow resistance would be too low.  It's just fine with high-ish signture mode frequencies.  No player has yet commented on that.

[Anders Buen]

I do not think the Vieuxtemps del Gesu is a particularly interesting instrument. 

[Anders Buen]

10 hours ago, Andreas Preuss said:

Some scattered thoughts on your post:

Control. 

What needs to be controlled? 

How much control is really needed? 

When we think a certain control is absolutely necessary we must also do the crash test on it. 

  ———————-

I personally got away from the idea that this kind of control is necessary. Each parameter in a controlled scheme must follow a theoretical idea which explains only one isolated aspect.

Observation guided alterations are in my view better even though they can’t be theorised. 

If you run a business and have success in some way, you would probaly try to repeat success. How to do that? Many solutions may work. I onserve that e.g. Schleske and Von derLippe uses the same model. Von der Lippe also uses the same wood trunk, at least that is my impression. This must be atttemts at being more consitent than pure chance at making sucessful instrumnets.

The attitude is probaly different if you do not need to sell the instruments to keep going. If making is the second job or a hobby, and you are edxperimentally oriented, then experiments may be the solution. Part of the thrill is top learn and experience new things. Then cosistency is not what one look for. 

Personally I think there are a lot of ways to make instruments that may lead to some kind of sucess. And as my rose painting (and HF player) father say about an original outcome: «Somebody is going to like, and buy, this one too».

What you think is good quality is highly personal. And if you are stubborn and idependant enough to stand for your choice, you may be a fairly happy maker no matter the outcome. Somebody will like the instrumet eventually. Maybe only yourself. Then keep it and use it. 

[Marty Kasprzyk]

6 hours ago, Don Noon said:

>

I have never seen evidence that precise signature mode frequencies correlate with desirable tone.

>

That's correct. Precise 2.0 ratios (octave) of mode frequencies should be avoided.