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Humidity
It is worth noting that the Stiffness Factor 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.
Finished plates: bellies with ff holes bassbar and varnish, and the back varnished.
I have found that a good finished violin front plate with ‘ff’ holes cut, with a good bassbar fitted, and varnished will have a ‘Stiffness Factor’ some 20% higher than the raw plate, i.e.
- front, with ff’s, bassbar & varnish: a stiffness factor of 5,108,000 calculated just as above.
A good maple back plate that is varnished
- back, varnished: a stiffness factor of 7,577,000 calculated just as above.

To avoid the maths, use this 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 270 Hz, and
- the plate’s final weight: 104 grams for a back, and 70 grams for a belly with bassbar, ff’s and varnish using good spruce.
I use a pocket calculator to derive the average plate freq. from the Modes 2 and 5 figures. These two frequencies can be read off the one tap tone recording and its FFT made as shown on 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. of Mode 2 with Mode 5 at the bottom, 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 scaled to 5.1 x 10E6 (5,100,000) for a belly, and 7.58 x 10E6 (7,580,000) for a back.
Different ‘Stiffness Factors” for different tones.
Using Carleen Maley Hutchinson’s figures now for higher or lower tap tones for a range of violin tones, she found that plates (both front and back) with tap tones of Modes 2 & 5 of 170 & 340 Hz gave a ‘Student 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. Other tap tone frequencies in between gave ‘amateur or ‘Orchestral’ tone.
This gives us a range of Stiffness Factors. A ‘Student tone’ violin may go as low as 15% below the standard plate stiffness figures of 1.0 on the chart scales. 15% below is equivalent to 0.85 on the chart scale. I certainly can’t recommend any lower than that. A violin I did with plates 18% below the figures above (a factor of 0.82) played well and is easy under the bow, but has quite a a weak tone, not carrying much.
On the other hand by taking the plate Stiffness Factors higher than the figures above by ~10% to ~12% (1.1 to 1.12) should give a ‘Solo’ tone, projecting very well, but harder to bow. I have not tried a factor this high yet, so I can’t report any results.
I have found that for half a dozen violins so far, using a Stiffness Factor between 90% and 100% (0.9 to 1.0 on the charts) of the figures above gives a very good, playable instrument.
So I reckon you can go up to +10% above 1.0 i.e. to 1.1 for a ‘solo’ violin tone (based on Carleen’s findings, but not yet verified by any fiddles I’ve altered), or no lower than 15% below or 0.85 for an easily-bowed ‘student’ tone fiddle that’s good as a ‘chamber’ instrument. In fact I can see no strong reason to go more than 10% below, or no lower than 0.9.
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 - at every single stage. Back & front have to match, and I try to keep them quite high too for a better ‘orchestral’ or 'solo' tone as the remaining wood allows. I set the same target factor for both plates and work towards it.
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 to do calculations at every step (!), but they are simple: find the average of the plate’s Mode 2 and 5 frequencies, and keep a watch on the weight too. Record the details, including the factor at each step for each plate. I mostly use a 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: some people don’t get on with spreadsheets - they can be rather intimidating.
It is easy to create a spreadsheet that will do all the calculation for you: I will put one here shortly to show how straightforward it is. Use OpenOffice for a good free spreadsheet.
# I created it using using the ‘SmallBasic’ language on a PC.
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