Violin Forum/Message Board

[John Schmidt]

I am trying to either verify, or debunk the idea that the stiffness of the back, represented by kback, compared to the stiffness of the top, ktop, is a useful number to know.

To wit: The John Masters formula

kback = (mass_back*(M5frequencyback)^2)/10,000,000

range of the above is recommended to be 1.2-1.4

ktop = (mass_top*(M5frequencytop)^2)/10,000,000

recommended value of the above is 0.8

stiffness ratio = kback/ktop

recommended 1.5 to 1.75


I have data for 2 good violins and 2 poor ones. Don Noon's and mine.

I would like to have 12 data points to help me decide to pursue the idea further or give up.

So, I would appreciate frequency of M5 and mass for tops and backs, along with a statement about the tone of the finished violin. ... poor, mediocre, very good, etc.

I will share the results, once I get 12 data points.

jpschmidt44[atsign]gmail.com

[DonLeister]

Hi John, if I recorded that kind of data I would share it with you.

[John Schmidt]

[John Schmidt]

I have my 12 data points from people I trust. The best fit line for the good violins is

kback = 0.81*ktop + 0.68

The graph is here http://jpschmidtviolins.com/images/violin_stiffness_good_vs_poor.jpg

[kjb]

thanks for sharing john

[John Schmidt]

[williamwalsman]

Hi John,

I use a formula attributed to Nigel Harris of the U.K. I won't get into the details here but if you google him you should be able to get his doctoral dissertation which explains it thoroughly. My latest violin which is the most vibrant and open sounding violin to date has the following specs. Back plate is 112 grams pre varnish with a mode 5 of 355 hz. Mode 2 is 177 +/- 5hz. This gives it a stiffness factor (Harris method) of 1.09. The top plate is 65 grams pre varnish with a mode 5 of 357hz and mode 2 of 178hz. Once again the Harris stiffness factor for top is 1.09. I don't think this formula or any other is the holy grail but I've got good results following it.

The masters of century's past probably judged proper stiffness by bending the plates in several places and listening carefully for recognizable tap tones. Not having a feel for proper stiffness obtained over decades of experience I use Dr. Harris' method to get good results. I do try to stay consistent when selecting the Spruce for the top. Very straight grain within a certain number of grain lines per inch. Why not keep as many variables consistent as possible especially when in relates to the pliable/ vibrant top plate.

[John Schmidt]

William,

Thanks for the data. I have added it to the graph. The new equation for the line of best fit is kback = 0.77*ktop + 0.72

The graph is found here: http://jpschmidtviolins.com/images/violin_stiffness_good_vs_poor2.jpg

At some point I will have to separate "good" into excellent and good.

Yes, I know about Harris. In fact, that is what got me started on this path. Currently I am using the equation by John Masters

kback = massback * (M5^2)/10,000,000

ktop = masstop * (M5^2)/10,000,000

Although I have not tried a Harris violin, the PRELIMINARY guess, from the graph, would be that Harris violins, in general, are not soloist violins. But that is only a guess. I would love to have data from Harris. At this point, I only have his "average" violin. Not a real one.

My violin #16 is the best one yet. I followed Masters, so naturally, I am converted, until my next "best" violin.

Do you have any data for "bad" violins? That would be useful.

[williamwalsman]

John,

I'll give you two more sets of numbers.

For an early violin (in state of disrepair) with unremarkable tone, mass of back=131g. with a mode 5= 330hz. mass of front = 69g. with a mode 5 = 319. Using Masters formula I get a k(back) of 1.43 and a k(top) of .702. Ratio = 2.02 if my figuring is correct.

For a later violin with a very desirable tone though not as open and vibrant as my latest, numbers are as follows: mass(back) = 124g with a mode 5 = 346hz. mass(top) = 71g with a mode 5 = 346hz. Using the formula I get k(back)= 1.48, k(top) = .85. K ratio = 1.74

Hope this helps. Bill

[Ken Pollard]

Hi John,

Thanks for posting the graphs.

I don't understand much about the stiffness ratios, but I have some understanding of lines. Is your line fit for all the data, or just the 'good' violins?

Your graphs show two 'poor' violins that seem to lie on the line extended to the right, assuming you are not restricting the domain (the horizontal axis). Any comments on that?

I haven't measured any of this data for any of my few instruments, but I assume they would be all over the graph, as with the rest of the red diamonds!

Thanks,

Ken

[John Schmidt]

[williamwalsman]

Hi John,

As I'm sure you are aware you can reach desired plate stiffness numbers for both top and back a couple different ways, reaching good relationship numbers top to back regardless of the approach. And I wonder if one way might be preferable than the other? The target numbers can be reached either by having somewhat heavier plates with lower mode 5 frequencies or slightly higher frequencies and relatively lighter plates. Or the numbers for the back reached one way and the top the opposite.

For my latest two violins, both back plates are about 12 grams +/- lighter and top plates about 7grams +/- lighter than previous violins. Yet each plate has significantly higher mode 5 hz numbers than the corresponding plates on previous fiddles. Of course one could attribute that to varying wood densities one violin to the next. But I'm very careful selecting wood, trying to maintain reasonable material consistency one instrument to the next.

But what I have changed slightly is the arching. Not the long arch or its overall height but rather somewhat pulling in the horizontal arching toward the center line of the violin at the "c" bouts.

We know that the mode 5 frequency predominantly represents the vibration running down the length of the violin. By slightly pulling in the arching at the "c" bouts it stands to reason that that might make each plate longitude-ally stiffer and thus providing higher hz numbers in spite of the reduced mass.

So that brings me back to my original question. If we are shooting for certain ratio stiffness numbers and can get there a number of different ways (higher m. lower mode 5 hz.; lower m. higher hz, perhaps going one way for the back plate and the opposite for the top, any idea which combination might be preferable? Thanks Bill

[John Schmidt]

William,

Thanks for you thoughts. I have a new plot. Your data is included. One of your data points near 0.85 , 1.48, which is a green dot, because you thought it was a good violin, is right next to a red dot, which someone else labeled a "bad" violin.

So, either both of you are correct in your tone assessment, which makes the hypothesis invalid (that the relationship between top and back plate stiffness need to be within certain limits), or one, or both of you is incorrect in your tone assessment.

I would ask that you re-consider your tone evaluation for that point. I don't mean delete it. I mean just think a little more about your definition of what a good violin is. The point right next to it was labeled poor by a very experienced violin maker. So if you are correct, it will really tell a lot.

The new graph is found at http://jpschmidtviolins.com/images/violin_stiffness_good_vs_poor3.jpg

You can email me privately with your result, if you wish.

And the data from your latest violins with the different arching would be very significant as well.

Thanks a lot.

John

[John Masters]

[John Schmidt]