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.

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 match.

Dr. Nigel Harris' ‘siffness figures'.

• Or you can use Dr. Harris's 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. It works well with good low density spruce or maple. Unfortunately Dr. Harris' method or theory it does not take into account enough of the effects of the plates' edges being attached to the stiff and relatively massive bouts.

 Or you can .......

•    use a modified version of  Dr. Harris's method. Here you Tune Modes 5 and Mode 2 and drop the tap tone frequencies if any plate has turned out rather heavy. I, and number of others who have contacted me via this web site have found that Dr. Harris' method gives plates that can turn out too thin.
•    In his paper Dr. Harris gives Stiffness Figures ¹ of
• 7,255,000 for backs, and  4,247,000 for fronts, with the back unvarnished and the front ‘raw', i.e. with no f-holes, bassbar or varnish. I personally have found this belly figure to be rather high, and a stiffness of 4,000,000 is fine if you don't do any ‘final' thinning later. Dr. Harris' violins are presumably intended for ‘solo' use, so I would expect them to be rather thick.
•   This number, Dr. Harris' “Stiffness Figure” is a simple product. It is the average of the Mode 2 and 5 frequencies (in Hz) squared, and then multiplied by the plate's weight in grams, and something similar explained too in Joseph Curtin's Strad article.
•   To take account of an inaccuracy in Dr. Harris' Stiffness Figure (an error due to the effects of the stiffness and weight of the edges of the plates), I define the plate's ‘stiffness' as  f² x corrected plate weight, that is for the weight take the average of the ideal plate weight and its actual weight.

Patrick Kreit.

          After reading Patrick Kreit's book “The Sound of Stradivari” in 2011 I realised  that Dr.Harris' work on plate Stiffnesses needs to be amalgamated with Patrick Kreit's work because most of the wood we find is not the very best, especially the spruce. The violin plates that are made from it are just too heavy.  

      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.

    If the plates are of good, light, stiff wood then the belly Mode 5 should be either equal to, or up to a semitone below the back plate's Mode 5 in the range 315 Hz to 370 Hz, just as is traditional!

     But if either plate turns out heavy, and most do, it will need a rather lower Mode 5 frequency than that shown. See the charts on the page ‘Platetuning 4 dummies'.

The stiffness figures for back and front need to match.

            The diagram here (right)  shows how to choose a pair of tap tone (Mode 5) frequencies for the belly and back plates that will work very well together.

   You can also choose the kind of tone you want your instrument to have, from ‘chamber' tone with easy bowing to ‘solo' if you want to be heard at the far end of a concert hall. The diffrence is only a few percent more or less in the tap-tone frequencies!

Formula for plate stiffness figures

   Since coming across Evan B. Davis paper at the Stockholm Conference in 2013  I found it necessary to update the formula or relationship between a plate's Stiffness and Modes 2, 5 and the plate's weight, so now the plate stiffness figures used are 2.15 times larger than those based on Dr. Harris' work.

  Evan Davis suggests a relationship to derive the stiffness figure for a plate that sums the squares of Modes 2 and Mode 5, and them multiplies that by the plate weight. These higher (and more accurate) stiffness figures are now used in this formula below and in all the data presented on the ‘Plate tuning 4 dummies' page, but to take account of the edge effect (gluing the belly at all edges to the bouts and blocks) I take the plate's weight  to be the average of the actual weight and a reference weight. The table of reference weights is at the bottom the page ‘Plate tuning 4 dummies'.

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• Footnote 1: This formula or relationship can be found in Dr. Harris's paper 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. 

      The formula of the chart that follows is based on Evan Davis' work shows the relationships that needs to be in place between the 2 tap tones and the plate weights for a good violin, once the kind of tone you want has been chosen :-

    It is interesting to note that for a ‘good' sounding violin the plates' stiffness figures need to be  within ~ 2 or 3% of the figures given in the formula above. This explains why factory fiddles have plates that are so wrong most of the time because they are too heavy: it just does not happen by accident!

Time for Examples : Belly plate

     The easiest way by far to proceed now is to use the graphic charts on the ‘Plate tuning 4 dummies' page,and there is a worked example given on the ‘Examples' page.

 If you want to see how the ‘exact' method works, the following may be helpful:-

      Using the method based on Evan Davis' relationships, a good belly or front plate of spruce might have a Mode 2 of 172 Hz, a Mode 5 ring tone of 328 Hz, and a weight of 72 grams in the raw with no f-holes, bassbar or varnish. 

    Now adding the two Modes 2 and 5 squared together gives 172² +  328² = 137,168 ,  and then multiplying this by the corrected plate weight, i.e. (72 gm. actual wt. + 64.7 gm. ref. weight ) / 2, = 68.35  grams, giving a [modified] Davis' Stiffness Figure of 9,375,433.

   Since this plate is without f-holes and bassbar it should be around 11% less than the 10,000,000 given in the formula above.

       It is worth noting that roughly speaking, a belly plate ring tone or Mode 5 will be increased by about 0.7 of a semitone, or be raised by 14 to 15 Hz when the f-holes are cut and the bassbar added (which itself increases Mode 5 by 2 to 3 semitones), and the plate varnished. This is equivalent to a Stiffness Figure increase of up to ~12.5%.

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

Back Plate

          Similarly, an example of an unvarnished back plate with Mode 2 of 171 Hz, a Mode 5 of 345 Hz and weighing 125 grams would have Davis' stiffness figure of:  171² +  345² = 148,266. The weight figure to use is  (125 gm. + 109.3 gm.)/2  = 117.15 gm., therefore  148,266 x 117.15 = 17,369,362.  So sitting between 16x10e6 and 18.8x10e6 this back will have an ‘orchestral' to ‘solo' tone if paired with a suitable belly plate.

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 (Jun08) 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!

Different ‘Stiffness Figures” for different tones.

   Among Carleen Hutchins' figures for higher or lower tap tones for a range of violin tones, she found that both front and back plates with Modes 2 & 5 of 170 & 340 Hz gave a ‘Student  or Chamber instrument 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 in both plates: but be warned you will need the very very best low density spruce and maple to do it. Other tap tone frequencies in between gave ‘amateur, ‘Orchestral' or ‘teacher' violin tone.

  So far I have found that working on 2 dozen violins the ‘plate stiffness' method works very well indeed.

Working in a workshop.

   To avoid the maths and even using a calculator, I now use the charts on the page ‘Platetuning 4 dummies' as they are quick and easy to apply in a workshop.

  You only need to

  (1) measure a plate's weight with kitchen scales and

  (2) measure the plate's Mode 5 (and 2) with a computer: just a few moments work nowadays.

  (3) Look up the plate stiffness figure on the two charts, the chart for a belly and the chart for a back.

  That's it! Easy and accurate!

Plotting the Stiffness Factor for a plate as you go along.

  The method I used to use was as follows: I kept a constant watch on the calculated 'Stiffness Figures' of front and back as I evenly thinned the plates from the inside. Back & front have to match subject to the rules above, and don't make the back too thin!

  The wood you have may limit your choice of ‘tone' perhaps, but you can put in a rather higher new bassbar  to raise the stiffness factor of the front, and graft (i.e. glue) in a round or oval maple patch (~45 x ~50 mm across) into the middle of the back to raise its stiffness figure if needs be.

  It took me a week or two to get used to the method. I did calculations at every step (!), but they were simple: sum the squares of the plate's Mode 2 and 5 frequencies, and measure each plate's weight as wood was removed from the inside of each plate as I went along, and find the average of it and the plate's reference weight. Multiply them.

Spreadsheets.

   If you prefer not to use the graphic charts on the ‘Plate tuning 4 dummies' page than you can proceed as follows:-

  I recorded the details (Mode 5, 2 and weight) at each step for each plate as I went along, I mostly used a simple spreadsheet to do all the calculation for stiffness figures on the same PC I'm was measuring the Mode frequencies on.

  Creating the spreadsheet means you will best understand the relationships between the quantities you will be measuring.