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 Last updated:

1st.. Jan. 2021

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 www.platetuning.org

        This page has been updated with revised data 30th November 2017 and June 2020.

  I  hope this page will help those making or improving their first violins: everything is new and so how can can tell good from bad?

Priorities.

  If I had to name priorities on how to make a violin I would  say you will need a coffee and a “L. A. TT. E.” :-

‘L'  stands for    Light-weight plates,
‘A' stands for     Arching, it has to be right!
‘TT' stands for  Tap-Tone,so the violin will sound good, and
‘E' stands for     Edgework.    Tap-tones do not measure the   edges well, so edges need to be right too.

 What is ‘TT'? Tap tones, or plate tuning?

    Just as a violins are made to standard dimensions, plate tuning allows the stiffness, density and peculiarities of the particular wood of each back and front plate to be taken into account and compensated for: every piece of wood is different!

  What a tap tone is, how to measure it and how to thin the wood to set or tune each one to get the Modes 2 and 5 where you want is shown in the Modes and tuning plates page.

What does plate tuning offer the violin maker?

   Measuring tap tones and plate weights keeps us on the right track as they can enable you to create a violin with the 5 key body resonances in the right places.

  The ‘model' described in the right hand column of this page offers a way of predicting, with reasonable accuracy, where these resonances that largely define a violin's tone will be. So a maker can select a particular model and tone that they want, seeking after that elusive consistency, where every piece of wood is different.  So if the wood you use (spruce for bellies, maple for backs) is not the best then that plate will turn out heavier than the plate reference weights.

Does it matter how heavy the violin plates are?

   In general the data on the best violins shows that they have light plates, and often very light plates indeed. They are made of the best wood: so often the wood of factory violins is mediocre, so your plates will be heavier ... but they can still make a very good violin indeed! You will just need to leave the centre section of the back rather thicker, and therefore somewhat heavier.

  The ‘radiation ratio' of plates improves dramatically if they are light, so there is a virtuous circle here: the best light-but-stiff belly means and excellent radiation ratio, and so much better with a light back too.

The Mode 2 (and Mode 5) ring tones of both front and back plates.

 Just as you make a violin with standard sizes, the plates need to have standard tap tones.

  The method is :-

   (1) to cut the plate outer archings first and then

   (2) remove wood inside the plate so that there is (say) 1 mm more than the standard thicknesses all over the plate. Then

  (3) Tune the Tap Tones: remove wood from inside the plate until you have the tap tones you want - while respecting the need to keep near the standard thicknessing pattern for the plate.

     It is best to start with the belly:-

 The Belly Plate.

      Mode 2: crossways stiffness. The belly plate with its bass-bar needs to have a Mode 2 that is in the range 155 Hz (the absolute minimum) up to 180 Hz:  160-165 Hz is ideal.
         A high figure achieves little but increases the plate weight.
     Mode 5: longways stiffness. This should be in the range 310 Hz to 385 Hz (abs. max.): ideal is 340-350 Hz.
It is better to keep the Mode 5 down below 385 Hz to keep the back plate weight down, and a normal belly will be 80 grams or less.  60 grams is exceptional.
 
 The Back Plate.

      Mode 2: The very important back plate Mode 2 ring tone needs to be in the range 160 to 190  Hz.  If it is below 160 Hz start again: it is unusable as the area between the C-bouts is too thin.
      Mode 5: This needs to be in the range 310 to 390 Hz: ideal is 360 Hz, and a normal back plate weighs about 105 -110 grams. Under 100 gms. is very good wood, good thicknessing and good arching.

 Dr. Nigel Harris' and Evan Davis' work.

       Research by Dr. Harris at Cambridge UK and Evan Davis of Boeing  in the USA have shown that the weight of a violin plate and its key Mode frequencies (2 and 5) yield a “Stiffness Figure” for a plate. This work allows a trade off between the plate weight and it's tap tones: no two plates are the same - all wood is different!

   In essence a heavy plate needs to have lower tap-tone frequencies (10% extra weight needs 5% lower frequencies) and the two violin plates, the belly and back, should also have matching “Stiffness Figures”.

   To save us all from the maths I have put the data we have into table form and into these two tables below, the first for the belly plate and the second for the back plate.

    They are shown below: just click on them. Depending on your choice of spruce and maple woods and how the arching goes then you can  then use cutting plate thicknesses to tune both plates to give matching Stiffness Figures. This also will also give an idea of the kind of tone the violin will have: so you can choose ‘chamber', ‘orchestra' or ‘solo'.  Orchestral is recommended.

Choice of violin tone.

 green,          (easier-playing chamber and amateur tone),

blues,           (orchestral tone),

     ... and  ....

 red               (solo tone, requiring expert bowing).

    The two tables above should give you enough to be able to make a violin that will sound really good! What is so important about these tap tones is they tell you when to stop thinning plates: light is better, but too much wood removed is a disaster!

The key body resonances.

       By setting yourself targets for B1-, B1+ body frequencies and the ‘Delta' or difference between body modes A1 and ‘B1+' then you can select the kind of tone you want from the violin. These ‘tones' are shown in Table 2 in the next column.

  The higher ‘B1+' frequencies shown as ‘ideal' on the page ‘Resonances of the Violin body' give solo grade instruments.  But selecting lower target frequencies for ‘B1+'will give a violin that is much easier to play and suitable for orchestral or chamber music.

 Note that the A0 and A1 frequencies are mostly fixed by the dimensions of the violin body.

 Tuning the body modes after assembly.

     Once the violin is put together ‘in the white', that is before varnishing, Stradivarius and many other makers used a technique of tuning the body resonances to what he wanted by finishing the channeling and purfling after the violin was assembled as it affects these key resonances a lot.

   You can also make the plates a little too thick and then thin them ‘in the white' by scraping or sanding the outside of the plates to get those resonances just where you want them, but this is not for your first violin! This is very hard to do. Start by walking before you run!

   Alternatively I use the tables given here to estimate how much to take off the belly and back when I remove the belly for adjustments! (Use weakened glue to glue on the belly then!)

Limitations.

  It is worth noting that there are limitations to this method because wood is organic, and because tap tones do not measure edge properties well.

(1) Moisture content (MC).

     The violin plates measured here have low moisture content (MC) which is normal for wood in a heated workshop in winter.  So tap tones change all the time (!) with the moisture content (MC) of the  wood.

   In a heated workshop in winter wood will have an MC of ~6% and the figures given on this website will apply. However in summer the wood MC will rise to ~12%, and the Mode 5 tap tone frequencies I give will need to be reduced by as much as 15 Hz! The plate weights also increase slightly with higher MC too!

(2) The plate edges ² 

     Unfortunately plate tap tones are hardly affected at all by the thicknesses of the plate edges, and yet these very edges matter a great deal because the plate is held firmly by the bouts and linings in the assembled violin ² and the edges contribute a lot to the plate's weight.

    So take care with your choice of edge thicknesses, especially between the C-bouts on the back plate, and complete the edge thicknessing before tuning the plates. Never make the edges thin around the C-bouts.

   I recommend thicknesses of 2.7-3.0 mm an all edges (just before the plate meets the linings) and 3.5 mm around the C-bouts ⁴ for both belly and back plates. Better wood needs thinner edges.

 If you are making the plates from scratch

    Cutting the f-holes on a belly reduces the Mode 5 by about 2 semitones (2 x 6% = 12%, about 38 Hz), but the original Mode 5 frequency is then restored to the same (or to a slightly higher frequency) by installing the bass-bar.

         [continued in next column]       ------------------------------------- 

Footnotes:

¹   This data also includes the data published in Patrick Kreit's book and website that gives the ‘deltas' between these (A0), A1, B1-, B1+ body resonances we should look for in a first rate violin.  You may need to get Patrick Kreit's book to get details.

2.  See “The Art of Violin Making”  by Courtnall and Johnson and the chapter on plate tuning.   Tap tones do not measure everything about a plate!

Making or modifying a violin for good tone.

   I will now show how to get an estimate of the key body frequencies of a finished violin from the weights and tap tone frequencies of the plates that go to into making it.

 A ‘model' that uses weights and tap tones to predict key body resonances¹.

    By concentrating on the very important  B1- ,  B1+ and A1 violin body resonances I have derived a model to predict the B1- and B1+ violin body resonances and hence help you make what can be a fine-sounding violin.

   With regard to accuracy of the model, the prediction for the frequency of B1+ has a Standard Deviation (sigma) of 10 Hz.  So there is a 68% likelihood that the actual ‘B1+' frequency will fall within +/- sigma (+/- 10 Hz) of the predicted frequency.

     The model described here predicts ‘B1-' and ‘B1+' body mode frequencies from the characteristics of the plates. It is derived by extending the work suggested in a paper by Alonso Moral (1984) outlining these relationships. My data looks for (assumed linear) relationships between ‘B1-', ‘B1+' and 7 aspects of the violin plates: Modes 2 and 5 in belly and back, their respective weights and the bass-bar height.

    My results show figures similar to those of Moral, but importantly I have found that the two plate's Mode 2 frequencies and their weights have a much more important effect than Mode 5!

Second Version (Version 2.0) of the model.

     I first published this model in the summer of this year (2017), but when tested by well known violin makers (see Maestronet) it was found to be ‘no better than random'.  Since then I have gone back to the data set, removed samples where data is questionable, and also used a method of ‘pivoting' the results around the 2 violins (by Peter Grankulla) that I know to have excellent, indeed the best data. This has dramatically reduced the sensitivity to both the plate weights and Mode frequencies in the model which seemed to have been problematic.

   The belly plate weight and the back's Mode 2 frequency dominate the resulting key body resonances.

This page has been updated with revised data 30th November 2017.

Table 1

    By taking 25 violin examples where the plate Mode 2's and Mode 5's and the final violin B1- and B1+ mode frequencies are known I used a method of seeking multiplier values that give the lowest standard deviations for B1- and B1+ by successive iteration. This is a technique used elsewhere in Finance to minimise risk in investment portfolios.

   There is a spreadsheet included below that allows you to estimate the two B1 frequencies easily.

    The details of just how each factor changes the B1-, B1+ frequencies is given in this table above.

  In summary:-

Estimating B1-.                                       Accuracy: sigma ~12 Hz.

   1) The data shows the back plate's Mode 2 frequency effects ‘B1-'.

         A  high back plate Mode 2 increases B1-, but decreases ‘B1+': see below. The belly Mode 2 frequency affects ‘B1-' too.

  2)  Other things that slightly affect the ‘B1-' body mode frequency are :-

         a) If the two plate weights are high, that is they are heavy plates, they both seem to decrease the ‘B1-' body Mode frequency..

         b) the back plate Mode 5 if it is high also increases the ‘B1-' body Mode frequency.

       >> Ideally ‘B1-' needs to be matched or close to the A1, the lengthwise internal air resonance. It should ideally be within 0 to 16 Hz of ‘B1-'.   A1 is typically 462 Hz, in the range 450 to 485 Hz.

Estimating B1+.                                         Accuracy: sigma ~10 Hz.

      >>  Ideally ‘B1+' is 60 - 90 Hz above A1.

  1) The data shows the most important factors for the ‘B1+' frequency are

        a) the back plate's Mode 2 frequency, and

        b) the belly plate weight. A heavy belly plate reduces ‘B1+'.

  2) The next most important things are:-

        a) belly plate Mode 2, and

        b) the back plate Mode 5,  and

        c) the back plate weight.

 The table, Table 2 below shows what effect increasing each item by 10 Hz or 10 grams is likely to have on the ‘B1+' body mode frequency:-

Table 2

     I hope it is clear from the table above that the Mode 2 of the back plate  can be used to offset excess weight in the belly plate.

   The challenge is to find plate weights and tap tones that not only give a ‘B1+' body resonance around 540 Hz but to keep the ‘B1-' frequency high enough to be near the A1 frequency. There are many combinations that can achieve this, but you might like to try  the following ...

  - first making the belly light, say Mode 2 - 155 Hz, Mode 5 - 330 Hz, weight 67 gms. and

 - then the back plate with Mode 2 - 168 Hz, Mode 5 - 370 Hz, weight 90 gms., but such a low weight in the back does require very good maple.

   A way to do this is to measure the weight of the finished belly or front plate and then make or modify the Mode 2 of the back plate to give the ‘B1+' body resonance you want: typically a ‘B1+' of 550 Hz. A high back Mode 2 means a thicker area between the C-bouts of the back.

  If you click on the frame right a small spreadsheet will be downloaded allowing the estimation of the two violin body Mode B1 frequencies to be automated for you. It can be opened in MS Excel,or the free  OpenOffice or LibreOffice.  Google Sheets will open it too, but cell locking does not work.

  You just input the plate tap tones and weights and the two B1 frequencies are estimated for you.

    This can be opened on your mobile too using Microsoft Office Excel. The input cells are unlocked, allowing data input. There are several Android mobile apps available too.

       I will update the small spreadsheet in a few days. 

  The table below shows how you can trade any excess weight in the belly plate for extra back thickness between the bouts, i.e. a higher back plate Mode 2.

  Select the column for the belly plate weight you have and then read off the back Mode 2 required to give the ‘B1+' you want.

  Corrections for the Belly plate Mode 2 (how far it is from the average I have given above), and Bock plate Mode 5 (again how far it is from the average I have given above) can be applied using the grid printed borttom left. The instructions are given bottom right on the

   The Mode 2 frequencies of any plate can be set independently of the its Mode 5 by thinning a plate in carefully chosen areas.

This page has been updated with revised data 30th November 2017.

Table 3 (Version2.0)

   Data shows surprisingly that the Mode 5 of the belly or front plate is not particularly critical: keeping plate weight to a minimum is what really matters.

   It looks as if Sr. Stradivarius set the key body resonances after completing the violin, as he only finished the edge-work and inserted purfling after gluing on the belly!

  The key violin body resonances are very sensitive to re-thicknessing the plates on the outside  of the plates rather than the inside: so beware!

   A few scrapes on the outside of one or both plates can drop the body resonances quickly, and they can't be raised again!

The ‘ideal' body resonances.

        There is data available on the key body resonances of important Italian and other violins in The Strad and other magazines. The data I found is that is most accessible is an article called “Measurements of 10 Preference-Rated violins”,  a paper presented at ACOUSTICS 2012 written by by C. Saitis, C. Fritz, B.L. Giordano, & G.P. Scavone: it can be found here.

  I've also extracted the data from Jo. Curtin's ‘Strad' article of July 2009 into a chart (click on the chart right) and the [LibreOffice] spreadsheet made from it is here.

   If you look at the page Resonances of the Violin Body I have extracted and enlarged the data on the best 3 violins of the 10 tested for sound quality to show the kind of body resonances you would be looking for.

   A Charles Davis was in touch to tell me about another of  Joseph Curtin's Strad magazine articles on Stradivarius' front plates, published October 2006, found at the Strad magazine website. Jo Curtin gives useful tap tone frequencies there.

                             ------------------------------

 Footnotes:  

• Dr. Harris's paper can be found here.
•   ** Interestingly, F.J.Fetis' book “A Notice of Anthony Stradivari”, on page 81, is the only one to say that the back, (actually Villaume's real Strads and Guarnarii violins of 1850, obviously with ff's bassbar & varnish)  should be tuned a tone lower than the belly.  Heron-Allen in his “Violin Making, as it was and is”, on  page 132 says the back should be a tone higher than the belly. Other sources say they should match .
• *** CAS = Catgut Acoustical Society, now part of the Violin Society of America, the VSA.
• ****   I had a good violin with a finished front of 101 grams! This was the third fiddle I ever worked on and though heavy, it produced an excellent tone. It was an oddity that set me on the road to tap tones .... a belly with a Mode 5  at only 316 Hz (final, with ff's, varnish) make such a good sounding fiddle ? Odd.