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 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.

 A is for Arching,

   T  is for Tap-tones, &

      E  is for Edge-work.

Making or modifying a violin for good tone

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 will need to be  reduced by about 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 very 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 very 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 in general it is easy to show that you do not need to take a plate's weight into account when tap tuning plates.

You only have to make a violin with heavy belly (say 90 gm.) and light back (say 90 gm.). The key body resonances fall where they are predicted without taking any account of plate weights. I should know: I have many, many cheap violins with heavy belly plates: they can all be made to sound good and have those key violin body resonances in the right place by completely ignoring plate weights.

  I did advocate using his 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” in 2011 came to my notice. I realised  that Dr.Harris' work on plate Stiffnesses is not compatible with Patrick Kreit's work. Light plates are better, but can be treated just the same as heavy ones.

 A ‘model' that uses tap tones to predict key body resonances.

       Otto Moeckel published a book “Die Kunst 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 here: click on it.

    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 fairly accurate model to predict the B1- and B1+ resonances and hence what is likely to be a fine-sounding violin..

    With regard to accuracy, the prediction of the ‘Delta' between B1- and B1+ has a Standard Deviation (sigma) of 18 Hz.

    The predicted ‘Delta' (B1- to B1= frequency gap) against the back and belly plate Mode 5 tap tones is shown here on the right (click on it). It shows that the model predicts a wide range of viable combinations of back and belly tap tones that can be put together to make a viable violin. Otto Moeckel's data on old Italian violins can be fitted to the model with reasonable assumptions that are shown on the diagram.

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• Footnote 1:   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.... why should such a belly with a Mode 5  at only 316 Hz (final, with ff's, varnish) make such a good sounding fiddle ? A standard front is nearer to 65 - 70 grams with ff's, bassbar and varnished, and even as low as 57 grams. 

     So to predict the ‘Delta', the frequency gap between B1- and B1+ use the chart given on the right here: click on it.

   The different ‘tones' of the violin can be chosen as shown: ranging from ‘easy bowing' for students, to ‘chamber instrument' (very responsive!), to ‘Orchestral tone', which carries well, to ‘Solo' which carries very well  ..... but does require great expertise in bowing.

  The Tables

        Table 1 (right) allows you to choose the ‘Delta' for any given violin tone as described above. It ranges from

• ‘Easy bowing' tone (‘Delta' around 60 to 75 Hz)
• ‘Orchestra tone', (Delta' around 80 Hz, and
• ‘Solo' tone, (‘Delta' 85 to 95 Hz.

   I do not recommend going above a ‘Delta' of 95 Hz

Table 2 (right).

     If you know either the Mode 5 of a back or belly plate then Table 2 right will give you the range of viable plate Mode 5 frequencies to go with it to give you a ‘Delta' of your choice, ranging again from ‘Easy bowing' to ‘Solo' tone.

Sensitivity

       You may be able to see from the charts above that ‘Delta' (the B1- to B1+ body resonance gap) is ~3 times more sensitive to Mode 5 of the back plate as Mode 5 of the belly plate.

   For this reason it is recommend that you start with a back plate and them match the belly to it!

The ‘model'.

     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. It is not sophisticated.

    By taking 18 violin examples where the plate Mode 5's and the final violin B1- and B1+ mode frequencies are known I simply used a method of seeking equation values that give the lowest standard deviations by successive iteration. They need to be matched to the A1 (lengthwise air)  resonance.

  The relationships (Mode 5's to B1+ and B1-) are shown in each of the 3 tables above: they work well, but please take note of the Standard Deviations (likely errors), as you may well have to make adjustments after assembling the violin for he first time (!), or remove the belly plate to re-adjust the thicknesses.

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

  The key violin body resonances are very sensitive to re-thicknessing the plates on the outsides: much more so than thinning 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!

Time for Examples :

   Belly plate

    TBA.

 There is a Wiki page giving the relationship between frequency (Hz) and modern pitch here.

   Back Plate

     TBA.

   What to set the Mode 5 tap tones of the plates for the various choices of tone is explained on the page ‘Platetuning 4 dummies' and the outline of how to do it is explained.

Plate weights

    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.

   A Charles Davis has been in touch to tell me (Jun ‘08) about Joseph Curtin's Strad magazine article on Stradivarius front plates: found at the Strad magazine website. Jo Curtin uses a ‘stiffness number' based on f² x weight /100,000 for each Mode separately, but there is some useful tap tone frequencies here.