This site has something for you if you are either making a violin or you want to improve a low cost violin or viola.

By tuning the top & back plates you can get a good instrument that responds well to the bow and that can sound like a £1500 instrument.

Making or modifying a violin for good tone

 In making or modifying a violin or viola for good or better tone you can choose one of a number of methods as follows:

The basic methods are, in historical sequence:-

• The Traditional method : Tune Mode 5 (Ring tone) and let Mode 2 ‘float’, and ignore the plate’s weight. Allied with good practice and experience it can work well, but gives no clues about any cases that require the back to be tuned below the front’s Mode 5 ring tone, as normally it is a semitone or tone above. Heron-Allen and Harry Wake describe how to tune the plates quite well in their books.
• Then there’s the ‘CAS’ method: Tune Mode 5 and Mode 2, but ignore the plate’s weight. This is Carleen Maley Hutchinson’s (or the CAS**) method. It works well if you are choosing the best wood with low or standard density and therefore plate weight. Or
• use Dr. Harris’s method: Tune Modes 5 and Mode 2 and take the plate’s weight into account by making the ‘plate stiffness’ proportional to the plate’s weight. The method is described below. It seems to work well with any spruce or maple, and especially well when the wood of the plates is less than optimum, such as a particularly heavy front plate***, or a light maple back.

  Looking at the weighs of plates given below maybe you can see just how much plates can vary in weight: e.g. a belly can be about 54 grams right the way to 103 grams - nearly a 100% range, so we really do need to take weight into account in choosing tap tone frequencies.

  A Charles Davis ( and I hope he doesn’t mind me using his name!) has been in touch to tell me (Jun08) about Joseph Curtin’s Strad magazine article on Stradivarius front plates: the article can be found here at the Strad magazine website. All of the Stradivarius bellies mentioned in the article have low ‘stiffness figures’ as defined by Dr. Harris below (in fact 15 to 20% below ‘standard’ on average), and one, the ‘Kreutzer’ is 27% below ‘normal’! For one of the world’s great violins to have a belly that is this far below ‘normal’ front stiffness means I think that there is a need to reconcile Carleen or CAS work with Dr. Harris’. I’m starting to think this through: it seems that we need a relationship where the plate’s weight has a smaller effect on ‘stiffness’ than direct proportionality ......... but for the moment, Dr. Harris’ work may be the best we have !

Dr. Nigel Harris’s figures.

  In his paper Dr. Harris gives Stiffness Factors * of

• 7,255,000 for backs, and
• 4,247,000 for fronts (bellies), with the back unvarnished, and the front raw, i.e. with neither ‘ff’ holes, bassbar or varnish.

 This figure, the “Stiffness Factor” is a simple product. It is the average of the Mode 2 and 5 frequencies (in Hz) squared, multiplied by the plate’s weight (in grams), and is explained too in Joseph Curtin’s Strad article.  So for instance, a good belly or front plate of spruce might have a Mode 2 of 172 Hz, a Mode 5 of 327.8 Hz, and a weight of 68 grams in the raw with no ff’s, bassbar or varnish. So the average frequency is (172 + 327.8) / 2 = 249.9 Hz, squared (multiplied by itself) gives 62,450, x 68 grams = 4,247,000.

Similarly, a back, unvarnished with Mode 2 of 171 Hz, a Mode 5 of 345 Hz and weighing 109 grams would have stiffness factor of (171 + 345)/2 = 258 Hz, squared = 66,564, x 109 grams = 7,255,000.

If you’re not for the maths, then here is a chart (left) I have created for the ‘Stiffness Factor’ to be read off for both front and back plates before the ff’s are cut, the bassbar added, or plates varnished.

This simple chart allows the Stiffness Factor to be read off directly from

1. the average tap tone, i.e. the average of Modes 2 & 5, typically = 262.5 Hz, and
2. the plate’s final weight: 61.6 grams for a belly before the ff’s are cut and bass bar added, and 105 grams for a back.

Note: David Langsather gives low plate weights of 54 gm front with bass bar, and an 86 grams back. Stradivarius’ bellies, with bass bar & varnish, are typically low too at 58 - 70 gm. Dr. Harris uses heavier plates, typically 65 gm front and 109 gm. back before ff’s and varnish.

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.

To use it, just use a ruler’s edge to connect the average frequency of Modes 2 & 5 at the bottom, and the plate’s weight at the top. Read off the stiffness factor on the middle line scale. A Stiffness Factor of 1.0 on the middle line is equivalent or is scaled to 4.25 x 10E6 (4,250,000) for a belly, and 7.25 x 10E6 (7,250,000) for a back.

It is very important to note that the “Stiffness Factors” of the front and back plates must match for a good instrument. I can’t tell you yet just how close they have to be, but I suspect it should be within 5% or so.

* Just where this formula is derived can be found in Dr. Harris’s paper here.

** CAS = Catgut Acoustical Society, now part of the Violin Society of America, the VSA.

***   I have one good violin with a finished front of 101 grams! The third fiddle I worked on had such a belly, and although heavy, it produced an excellent violin tone. In fact it is one of the oddities that set me on the road to tap tones (!): why should such a belly with a tap tone (Mode 5) at only 316 Hz (final) make such a good sounding fiddle that projects well? A standard front is nearer to 75 grams with ff’s, bassbar and varnished, and even as low as 57 grams.

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:- 

1. the average tap tone, i.e. the average of Modes 2 & 5, typically 270 Hz,  and
2. 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.