A website for the serious amateur violin maker, restorer and tinkerer. A violin front and back (the plates) can be tuned using tap-tones. Use tap tones to adjust the 2 plates of a violin to get the best sound, the kind of sound you want, or make an instrument that is easy to bow.

This site can help if you are making a violin or you want to improve  a low cost violin or viola.

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

post-25136-1224022475 Strad back graduation V1.1 smll1
tapping belly 2 sml

All you can ATE!

 A is for Arching,

   T  is for Tap-tones, &

      E  is for Edge-work.

harrison_strad_belly
harrison_strad_back

‘Harrison’ Stradivarius violin plate thicknesses

email: webmaster @platetuning.org

 Last updated:                                 20 th. May. 2017                    Copyright  (C)                www.platetuning.org

BuiltWithNOF

   I hope this page will help those making their first 10 violins: to you everything is new and so who can tell good from bad?

      If I had to name priorities on how to make a violin I would  say “A. T. E.” :-

  • ‘A’ stands for arching:    it has to be right!
  • ‘T’ stands for Taptones, so the violin will sound good, and
  • ‘E’ stands for Edgework. Tap-tones do not show up the way the edges are cut, so the channeling and edge thickness (how it becomes the rising arch of the plate) have to be right. So tap-tones do not measure plate edge properties well.
  •      There are people, perhaps even many people who regard tap-tones as astrology for violin makers, just so much mumbo-jumbo. Once you have enough experience, and I mean many years handling the best violins along with training by professionals, you probably wont need tap tuning: flexing a plate and feeling the thickness profiles will do on its own. But, and it is a big but, those of us who do not have this experience and can never hope to get it need all the help we can get.

      Measuring tap tones and plate weights keep me, and can keep us on the right track as they can help you create a violin with those 5 key body resonances in the right places!

     I have built a database of 25 sample (and very different) violins and measured 7 key variables of the 2 plates that go into building fully finished and playable violins. So that's from weights and tap tones of the plates to measuring the A0, A1 B1- and B1+ of the completed violins built from them. The results given below use this data.

  The basics of good violin plate tuning or the tap-tones come down to this.

There are several key areas that need to be understood:-

(1)Edges 1 The plate edges    

     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. 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.

(2) Moisture content (MC).

     The violin plates measured here have low moisture content (MC) at about  6%, which is normal for wood in a heated workshop in winter. All Mode 2 and 5 frequencies should be set up to 15 Hz lower with 12% moisture content (MC) when plates are tuned in summer.

   The dynamics of the violin are from the belly of the violin, and power comes from the back1It is important how much each plate ‘rings’ and what frequency that ring tone it is at. This is what Carleen M. Hutchins recommended 30+ years ago, and more modern measurements and work have shown her conclusions were broadly sound.

(3)  The Mode 2 (and Mode 5) Tap Tones 1ring tones of both front and back plates. 

  These are important characteristics of the violin plates as far as defining what the violin will sound like and how playable it is. They reflect your choice of central plate height, the arching and the edge work.

(3a) The Mode 2 ring tone of the back plate needs to be round about 160 Hz.     Data shows that the most important thing that determines a violins tone is the back plate's Mode 2 frequency. If it is well below this figure then start again.

(3b) The ring tones, both Modes 2 and 5, can be chosen, depending on the plate weights, to give you the tone you wanViable violin plates locus, Varnished, A1 = 467 Hz V3 smllt. 

  The ’Viable Plate locus’ chart left indicates the choice of Mode 5 tap-tone combinations that will work.

    The chart shows the back's Mode 5 tap tone along the bottom (x) scale, and the belly's tap tone (Mode 5) on the vertical scale (y), for varnished, finished plates. It is based on a model (revised May 2017, see the right column) derived to predict the key resonances (B1- and B1+) when the Mode 2 and 5 frequencies (tap tones) of back and belly plates are known. The equations are given, but note that Mode 2’s are assumed exactly half Mode 5, and Mode 2 is more important in both plates than Mode 5!

   It turns out from the data that it is the back plate's Mode 2 frequency that is the most important thing to get right! Do not thin the wood between the C-bouts of the back plate too much: in this area generosity is good.

   The Mode 2 frequencies of both plates can be chosen independently of the its Mode 5, but are usually just under half of the plate's Mode 5 frequency.

 After that the other thing you will need is a belly or front plate that is ideally of low weight: 55 to 65 grams is ideal but very hard to achieve. 75 to 80 grams is common and will still result in a good violin! 

  The data also shows surprisingly that the Modes 2 and 5 of the belly or front plate are not critical, so normally makers will set the Modes 2 and 5 frequencies a tone (~12%) lower than those of the back plate to keep its weight down.

(4) Choice of violin tone.

   By setting yourself targets for B1-, B1+ body frequencies and the ‘Delta’ or difference between them then you can select the kind of tone you want from the violin. Higher frequencies shown as ‘ideal’ on the page ‘Resonances of the Violin body’ give solo grade instruments.  But selecting lower target frequencies will give a violin that is much easier to play and suitable for orchestral or chamber music. Choosing lower tap tones for the belly plate especially helps in making a chamber instrument.

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

(5) Real wood is never ideal.

   If the wood you use (spruce for bellies, maple for backs) is not the best then that plate will usually turn out heavier than the reference weights given below.

     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 exactly 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!)

 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 bassbar.

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

     The ‘reference’ weight of each plate is as follows in Table 3 below 3 :   This includes the standard or reference weight of violin, viola, ‘cello plates, and includes the ‘Tenor Violin’, which has plates (but not bout heights) very similar to the 1/2 size ‘cello. This table may help you understand how good your plates are! For given tap tones low weight is good!

TABLE 3:

 [see Ref. 3 below]

Instrument

Back length

in  mm.

Back length

in  inches (“)

Reference Belly weight.

in grams

Reference Back weight.

in grams

1/2 size violin

300

11.8”

41.7

73.1

3/4 violin

330

13.0

53.1

91.1

4/4 violin   

357

14.1”

64.7

109.3

15 1/4" viola

387

15.2

79

132

15 1/2" viola

394

15.5

83

137

16" viola

406

16.0”

90

147

16 1/2" viola

419

16.5

97

158

 

 

 

 

 

'Cello, 1/4 size

580

22.8

221

336

'Cello,1/2 (half) size

650

25.6

295

437

Tenor Violin

654

25.7”

300

443

'Cello, 3/4 size

690

27.2

343

502

'Cello, 7/8 size

720

28.3

382

554

'Cello 4/4 

760

29.9”

438.2

627.8

     David Langsather gives very 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.

 

Footnotes:

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!

3.  The Table 3 (see above) is derived simply from taking the 2 known plate reference weights: violin and ‘cello, and assuming a straight power relationship between them.

      So plate weight = (plate length/reference plate length)^2.53 for each belly plate,  plate weight = (plate length/reference plate length)^2.31for each back plate with suitable constants.

 The plate shapes for all the instruments are assumed to be all very similar.

 

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.

First a warning: a note on humidity

     It is worth noting that tap tones change all the time (!) with the moisture content (MC) of the  wood. So 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.

 In making or modifying a violin or viola for good or better tone you can choose one of a number of methods. These are, in historical sequence:-

  •   Use craftsmanship! Get help, get trained, get experience, and make your first dozen violins. There is no substitute for knowledge, craftsmanship and for experience, not least in choosing your wood.
  •   There are many plate thickness maps available, and there are some available free on the web. They kind of work, but most plates need to be thicker or thinner than the map, as every bit of wood has different elasticity so I recommend ‘tuning the plates’ too! Dominic Excell’s articles on a First Violin does not use plate tuning (but I’m talking to him!).
  •   If you do choose to use wood tap-tone tuning methods, then adjust the traditional Tune Mode 5 (Ring tone) with the back Mode 5 sounding F#, and the front at F as a ‘raw’ plate before f-holes are cut. This ‘F’ later becomes  F# and even G with f-holes, bassbar fitted and varnished . The tap tone must be a full, true ring, the best you can get. Mode 2 frequency ‘floats’, and the plate’s weight is ignored. Typically, allied with good practice, very good wood and experience it works well**.
  •    use the ‘CAS’ method: Tune Mode 5 and Mode 2 to be an octave apart (Mode 5 = 2 x Mode 2). This is Carleen Maley Hutchins’ (or the CAS***) method. It works well if you are choosing the best wood.  Modes 2 & 5 frequencies of front and back should be equal.
  • Dr. Nigel Harris’s came up with a method Tune Modes 5 and Mode 2 and take the violin plate’s weight into account by making the ‘plate stiffness’ proportional to the plate’s weight. Dr. Harris may achieve tonal repeatability using his ‘stiffness’ method but my data shows that heavy plates need to be made with significantly higher not lower tap tones!
    • I did suggest using his ‘stiffness figure’ method for years on this site. I apologise profusely to anyone who used it, it is simply wrong and unnecessary.
  • An excellent book by Patrick Kreit “The Sound of Stradivari” came to my notice in 2011.  Dr.Harris’ work on plate Stiffnesses is not compatible with Patrick Kreit’s work. I have found that light plates are much better, and so far as I know Patrick’s book explains the only method to produce the lightest plate from any given piece of wood.

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

 

        Otto Moeckel published a book “Die KuMoeckel's data, belly & back Mode 5's V2.1 smllnst des Geigenbaus” in 1930 which had data on the tap tones of the plates of 30 good Italian violins including 7 Stradivarius violins .... [with thanks to Anders Buen and Maestronet]. It is shown on the right.

    The 30 violins have belly plates with a  Mode 5 averaging about 355 Hz +/- 45 Hz, and back plates with an average of about 366 +/- 59 Hz.

   You can see it is difficult to discern a pattern from this data, but it does set a target or test for any ‘model’ that attempts to predict the key body resonances of  violin starting from the belly and back plate tap tones.

   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 Mockel's data superimposed on Mode 5 locus diagram V2 smllwhat is likely to 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.

  Otto Moeckel’s data on ‘old Italian violins’ can be fitted to the model with reasonable assumptions that are shown on the diagram. On the diagram there are 13 violins outside outside the model's coloured ‘viable’ zone. These have very high back Mode 5 frequencies, but their Mode 2 frequencies are not recorded.

     It turns out from the data that it is the back plate's Mode 2 frequency that is most important. The back plate's Mode 2 is kept high by leaving the area between the C-bouts particularly thick. The table below shows what effects the back plate's Mode 2 and the belly's weight have on the B1- and B1+ body mode frequencies.

 

     The model to predict B1- and B1+ from the plate Mode 5 frequencies 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 weights and the bass-bar height.

    My results however show different figures from those of Moral, but then he did not measure Mode 2. I have found that the back's Mode 2 frequency dominates the resulting key body resonances.

Estimated B1-, B1+ from plates, V1.1 smll

    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.

 

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

 

  In summary:-

 

Estimating B1-.                                                      Accuracy: sigma ~12 Hz.

   1) The data shows that the most important factor in what frequency B1- will be  is the back plate's Mode 2 frequency.  In any violin this is likely to affect B1- by about 10 Hz.

  2)  The next most important things are:-

         a) The back plate Mode 5 frequency.

         b) the back plate weight and

         c) the belly plate weight.

  These (a), (b) and (c) may affect the B1- frequency by about 5 Hz each.  A heavy back and belly both reduce  B1-.

  3) The least important things are the belly plate's Mode 2 and Mode 5 (which is surprising!), and the bass-bar height, although that does affect the belly Mode 5.

 

       >> 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-, and A1 is typically 462 Hz and 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 factor for the B1+ frequency is

       a) again the back plate's Mode 2 frequency. A high Mode 2 frequency is likely to affect B1+ by up to 40 Hz, and

        b) the belly plate weight.  A heavy plate reduces B1+ by as much as 13 Hz.

 

  2) The next most important things are:-

        a) the back plate Mode 5 frequency,

        b) the belly plate Mode 5 frequency, and

        c) the back plate weight.

  These (a), (b) and (c) may affect the B1+ frequency by about 5 Hz each. A heavy back plate reduces  B1+.

  3) The least important things are the belly plate Mode 2 and Mode 5, and also the bass-bar height, although that does affect the belly Mode 5.

    Estimating the frequency difference between B1+ and B1-.                                                                                                        Accuracy: sigma ~13 Hz.

     The data shows that the most important factor in what the difference will be is

      1)    a) the back plate’s Mode 2 frequency. This may affect it by ~12 Hz.

             b) the belly plate weight.    A heavy plate reduces it by  ~10 Hz.

      2)  The next most important things are:-

               a) The back plate weight, and a heavy back plate reduces the difference.

               b) the belly plate Mode 2 frequency, and

               c) the belly Mode 5 frequency.

     These (a), (b) and (c) may affect this frequency difference by only about 2 Hz each.

 

   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.

   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 Joseph Curtin’s Strad magazine article on Stradivarius front plates: found at the Strad magazine website. Jo Curtin has some useful tap tone frequencies there.

 Footnotes:

  • Dr. Harris’s paper can be found here.
  • 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.
  •   ** 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.
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