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David Langsather gives low plate weights of 54 gm front with bass bar, and an incredible 86 grams back. Stradivarius’ bellies, with bass bar & varnish, are also typically low at 58 - 70 gm. Dr. Harris uses heavier plates, typically 65 gm front and 109 gm. back before ff’s and varnish.
A Charles Davis has been in touch to tell me (Jun08) about Joseph Curtin’s Strad magazine article on Stradivarius front plates: found at the Strad magazine website. Based on these (obviously) finished Italian violin bellies I suggest the front’s target ‘stiffness figure’ is 4.5x10E6 (i.e. just 5% or nearly 1 semitone above raw plates of Chart 1) for a finished belly or violin front plate. Chart 2 (see right) incorporates these figures.
Matching the plates: Matching Stiffness Factors!
It’s important that the “Stiffness Factors” of the front and back plates match for a good instrument. The general rule seems to be that the front ‘s stiffness factor should be equal to or not more than 15% less that of the back.
Finished plates: the front or belly with ff holes bassbar & varnish, and the back varnished.
Based on the good old Italian fronts of Joseph Curtin’s Strad article then final violin fronts should have a ‘Stiffness Factor’ some 5% or nearly 1 semitone higher than the raw plate of Chart 1, and this is shown in Chart 2 below.
Cutting the ff holes lowers Modes 2 & 5 frequencies. Then adding the bassbar and varnish raises them again. If there were no “final tuning”, i.e. thinning the belly a little from the ‘raw plate’ tuning, then typically the plate stiffness would be 15% - 20% higher than the ‘raw plate, implying that the Stiffness Factor of a raw belly plate (no ff’s, bassbar or varnish) can be as low as 3,800,000.
Final tuning will reduce either or both Modes 2 & 5. Varnish will then increase Modes 2 & 5 by about 5 Hz each, and also increase the weight slightly. Varnish will harden too over the first year an more, raising Modes 2 & 5 slightly with time. The back is only slightly affected by varnish.
As before for the ‘raw’ plates before the ff’s are cut and bassbar put in, a similar relationship applies:-
The average of the Modes 2 and Mode 5 tap tones (in Hz) still needs to be modified somewhat to take account of the plate’s weight, and what sort of ‘tone’ you want from the instrument.
So for an ’orchestral’ tone (see below) the final plates need to have a stiffness factor of :-
- about 4,500,000 for the front, with its ff’s, bassbar & varnish, calculated, or a Stiffness Factor of 1.0, and
- 7,580,000 for a good maple back plate that is varnished, calculated as above.: a Stiffness Factor of 1.0 again.

To avoid the maths, use the chart (left) that allows the ‘Stiffness Factor’ for both a front (belly) and back plates in final varnished state to be derived directly from:-
- the average tap tone, i.e. the average of Modes 2 & 5, typically 260 Hz, and
- the plate’s final weight: e.g. 112.1 grams for a back, and e.g. 66.6 grams for a belly with bassbar, ff’s and varnish.
I use a pocket calculator to derive the average plate freq. from the Modes 2 and 5 figures, and the average (corrected) plate weight using the plate weight data of Table 1 left. The two Mode frequencies can be read off the one tap tone recording and its FFT, made with mic & computer as shown here.
The chart above has log graduations on the scales#. To save and print it , just right click it, select ‘Save Link As...’ and save to ‘My Pictures’. Then open it in any picture/photo program and print it out from there.
As before, this chart above has log graduations on the scales#. To use it, just use a ruler’s edge to connect the average freq. (Mode 2 + Mode 5)/2 at the bottom scale, and the plate’s weight at the top, to read off the stiffness factor relative to 1.0 off the middle scale.
The figure 1.0 on the middle line is equivalent to or is scaled to 4.5 x 10E6 (4,500,000) for a belly in finished form, and 7.58 x 10E6 (7,580,000) for a back.
Different ‘Stiffness Factors” for different tones.
To summarise Carleen Maley Hutchinson’s figures for higher or lower tap tones for a range of violin tones, she found that both front and back plates with Modes 2 & 5 of 170 & 340 Hz gave a ‘Student or Chamber instrument tone’ that is easy to bow, but doesn’t carry all that well. She also says how to make ‘Solo’ instruments with tap tones of 190 & 380 Hz shown in Table 1 left. Other tap tone frequencies in between gave ‘amateur, ‘Orchestral or teacher’ violin tone.
So start with the ‘Stiffness factor’ of the back. This should be at about 1.1 for a ‘Solo’, 1.0 for an ‘Orchestral’ and about 0.9 for a Student’ tone. The relative ‘Stiffness factor’ is read off Charts 1 or 2 above or found with a spreadsheet.
I’ve found it better that the stiffness factor of the front should match the back or be below it: this a similar to what Carleen (CAS) recommends. Never take too much wood off the back plate - it’s better to leave it with a Stiffness Factor not less than 0.95, even for a student instrument.!
You can choose to take the front’s ‘stiffness factor’ anything up to 10% below that of the back for a good tone, but I would not generally recommend more then 5% - 8% below the back. This uses the data from the Strad fronts Joseph Curtin wrote about in his Strad Magazine article. I have modified some instruments with final belly Stiffness Factors of as low as 0.85 (3,800,000), (and indeed many Strads etc. have bellies with a stiffness factor as low as this), and the modified instruments are an absolute delight to play under the bow, but need top quality spruce to have good solo or carrying power as well.
I have found that in a dozen violins so far a Stiffness Factor between 90% and 100% of the figures above (0.9 to 1.0 on the charts) for both front and back plates makes a good violin with Student, Chamber to Orchestral tone.
Plotting the Stiffness Factor for a plate as you go along.
The method I use is as follows: I keep a constant watch on the calculated 'Stiffness Factors' of front and back all the time as I evenly thin the plates from the inside. Back & front have to match subject to the rules above, and don’t take the back too thin!
The wood you have may limit your choice of ‘tone’ perhaps, but you can put in a rather high new bassbar to raise the stiffness factor of the front, and graft (i.e. glue) in a round or oval maple patch (~45 x ~50 mm across) into the middle of the back to raise its stiffness factor.
It took me a week or two to get used to the method, but now I don't really have to think about it: it's just habit.
I have do calculations at every step (!), but they are simple: find the average of the plate’s Mode 2 and 5 frequencies, and watch the weight of the plate too.
Spreadsheets.
Record the details and the stiffness factor at each step for each plate. I mostly use a simple spreadsheet to do all the calculation on the same PC I'm measuring the Mode frequencies, but you might prefer the charts I’ve given above if you don’t like spreadsheets. Here is an example I created for a JTL ‘Steiner’ violin with finished, varnished plates to show how easy it is. The screen looks like this:
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Ssheet Steiner violin SFs V1.0.xls
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8 Jan '10
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Table 3
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Stiffness Figures are for fully finished plates with varnish
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Belly Reference Weight (gms.)
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64.7
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Back Stiffness Figure for Reference
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4,500,000
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Belly Reference Weight (gms.)
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109.3
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Back Stiffness Figure for Reference
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7,580,000
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Weight (gms.)
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Mode 2 (Hz)
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Mode 5 (Hz)
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Stiffness Factor
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Belly
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78
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162.5
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351
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1.05
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Back
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100
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164.5
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374
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1.00
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Italics = estimated figures
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relative to Stiffness Figures above
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Only the cells shaded yellow need to have your measured figures entered, and the Stiffness Factor can then be read out from cells E7 and E8. It is easy to create a similar spreadsheet that will do all the calculation for you. Use OpenOffice for a good free spreadsheet.
A note on humidity
It is worth noting that the Stiffness Factor of plates and the final violin changes with humidity. What I have noticed however is that as the weight of a plate increases with water content (high humidity) then the tap tones decrease to compensate, so the effects of changing humidity are significantly reduced if you derive the Stiffness Factor for a plate and use it rather than just the tap tones, Modes 2 & 5.
# I created it using using the ‘SmallBasic’ language on a PC.
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