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:                                        21st. April 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. Taptones 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) has to be right. Tap-tones do not measure plate edges properties at all 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.

      Tap tones 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!

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

ThEdges 1ere are 5 key areas that need to be understood:-

(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 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 5 frequencies should be set up to 15 Hz lower with 12% moisture content (MC) when plates are tuned in summer.Tap Tones 1

(3)  The Mode 5 ring 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 plate height at the centre, the arching and edge work.

(3a) The Mode 5 ring tones of completed back and front plates both need to be between 310 and 380 Hz. If they are not in this range then start again. The dynamics of the violin are from the belly of the violin, and power comes from the back1.

 It 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 sound.

(3b) The ring tones (Mode 5) can be chosen to give you the tone you want.Viable violin plates locus, Varnished, A1 = 467 Hz V3 smll

   To get a violin that will sound and play superbly then use the chart on the right1: click on it to open up the ’Viable Plate locus’ chart left.

 This 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).

   It is based on a model (revised April 2017) I have derived to predict the key resonances (B1- and B1+) when the Mode 5 frequencies (tap tones) of back and belly plates are known. The equation is given on the chart.

  To make a violin for instance with ‘Orchestral’ tone (highly recommended, especially for a first violin) make belly and back plates with Mode 5 frequencies that fall somewhere in the dark green area. An example would be both back and belly plates with Mode 5’s at 345 Hz. There are a lot of choices of pairs of frequencies, but it is established practice to make the front plate or belly with a ring tone equal to or rather lower than the back.

  This chart is for varnished plates. Varnish will have added about 6 Hz to the belly’s Mode 5, but hardly anything to the back’s Mode 5 frequency.

    This is not law brought down by Moses from the mountain: but you will not go far wrong if you follow this!

 (3c) Choice of violin tone.

       Outstanding ‘Solo’ instruments’ have plates with Mode 5’s falling in the red area.  So what this shows is that if you want to make a ‘Solo’ toned violin you will need to make the 2 plates with ring tones up to 370 or 380 Hz if the wood you are using is both light and stiff.

For an ‘Orchestral’ toned violin I suggest you make 2 plates whose Mode 5’s are between 340 Hz and 350 Hz and the point where the Mode 5 tap tones falls in the dark green area..

   A very good choice is an amateur violinist or ‘student’ tone: for a violin that is easier to bow, sounds ‘warm’ and is well suited to smaller rooms and chamber music. You will need to have a back and a belly plate at about  330 Hz (unvarnished, 6% MC). The intersection of the Mode 5 tap tones just needs to fall in the light green area. It will be easy to bow and a delight for chamber and pub music.

Table 1 below will allow you to derive the expected B1- to B1+ ‘Delta’ (in Hz) for a pair of belly and back plates.
Plate samples spreadsheet Table of Deltas No 1, V1.91 smll

       I have assumed a typical A1 violin body resonance around 460 to 467 Hz 1. If your violin's internal air volume (cm3), body length and the f-hole size are non-standard it will have a different A1 body mode frequency.  This chart or table assumes that  Mode 2 is set at half of Mode5, that is they are octave plates.

(3d) 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 weight 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!)

(3e) 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.

 (4)  The final Mode 2 frequency of each violin plate.     

      The Mode 2 frequencies should also be at or just below half the Mode 5 or ‘Ring tone’ frequency.

 I have assumed for instance that Mode 2 is 0.5 x Mode 5 frequency in all the charts above: i.e. they are octave plates. Having Mode 2 any higher than this serves no purpose and increases its weight. Many or even most good violins have Mode 2  at about 0.43 x  Mode 5.  The Mode 2 of a belly plate is less important to a violin’s tone than Mode 5, so just set it at just under half of Mode 5 frequency using the techniques I show on the arching and thicknesses page, but do not thin the wood between the C-bouts of the back plate too much! In this area generosity is good.

 

 (5)  A low plate weight is an extremely and VERY GOOD THING.

       That is providing the tap tones are not too low. There is less material to soak up the sound energy.

    This needs very good, carefully chosen wood. With the very best low-density wood a soloist-quality 4/4 violin finished belly will be less than 70 grams, and a back, believe it or not, will be less than 96 grams.

     More often a finished belly plate on a factory violin or ‘unselected wood’ will be about 75 to 85 grams, and a back plate about 115 grams and sometimes more.

    A low plate weight with high tap tones is a measure of the quality of the plate, but makes no difference to the choice of tap tone (Modes 2 and 5) you need to make an excellent violin!

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

 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

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.  This Table 2 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,  and ...       plate weight = (plate length/reference plate length)^2.31 for each back plate with suitable constants.    The plate shapes for all the instruments are assumed to be all very similar.

4. Figures from Patrick Kreit thickness data.

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.
    • I did advocate using his ‘stiffness figure’ method for years on this site. I apologise profusely to anyone who used it, it is simply wrong and unnecessary.  Taking care of  late edges and using plate tap tones is enough.
  • An excellent book by Patrick Kreit “The Sound of Stradivari” came to my notice in 2011. 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.
    •     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 ignoring plate weights.

  •   My data so far shows a slight effect of plate weight. For both belly and back plates the important ‘delta’ (B1+ to B1-) of the final violin body is decreased by about 0.5 Hz per extra gram of plate weight of either plate.

 A ‘model    Moeckel's data, belly & back Mode 5's V2.1 smllthat uses tap tones to predict key body resonances 1.

        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+ violin body resonances and hence help you make what is likely to be a fine-sounding violin.

    With regard to accuracy of the model, the prediction of the ‘Delta’ between B1- and B1+ has a Standard Deviation (sigma) of 11 Hz.Mockel's data superimposed on Mode 5 locus diagram V2 smll

  Otto Moeckel’s data on old Italian violins can be fitted to the model with reasonable assumptions that are shown on the diagram.

 

    It is particularly noticeable that there are 5 points on the right that are well outside the model's coloured ‘viable’ zone. These have particularly high back Mode 5 frequencies of over 400 Hz.

    My data on 20 violins so far shows that if Mode 2 of the back plate is particularly high then you will need to leave Mode 5 high too to compensate: for each 10 Hz Mode 2 is higher than normal (say 165 Hz) you will need to leave Mode 5 in the back plate high by 14 Hz. The back plate’s Mode 2 is kept high by leaving the area between the C-bouts particularly thick.

 

     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 20 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 for B1- and B1+ by successive iteration, which is actually ‘goal seeking’ in a spreadsheet.

   B1- needs to be matched to the A1 (lengthwis einternal air)  resonance.

 

  It looks to me 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!

 

   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.

 

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.

 

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.

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  • Footnotes:   Dr. Harris’s paper can be found here.
  • 1  This model is derived as a new model derived from Alonso Moral’s paper of 1984, and uses data from some 20 violins where both plate Mode 5 frequencies are known along with their B1- and B1+ frequencies. 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 resonance’s we should look for in a first rate violin. The 3 coloured areas correspond to 3 different ‘Deltas’ (B1- to B1+ frequencies) in the final violin body that are 10 Hz apart. You will need to get Patrick Kreit’s book to get more 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.... 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. 
[PlateTuning.org]