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1st.. Jan. 2021

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Violin whole-body body resonances and modes

     This is for the brave!  Do not attempt to work on finding these ‘main body resonances’ until you are very familiar with using Audacity sound and FFT software and finding tap tones on the belly and back plates. It can drive you mad, .... but a good violin needs to have these key 7 resonances below 700 Hz put where they should be.

 It only takes about 5 minutes to find all the key body modes. These modes can also be seen at the Strad3D modal view site here.

  There is a website - John Schmidt Violins, Laurinburg, North Carolina, USA - that has two .pdf files (“Violin Mode Measurements 1 and 2” , half way down on the left and written by Don Noon). In them you can see how to measure A0, A1, B1- and B1+ body modes on completed, strung up violins: how to do it is also summarised below. And you can also see the  Maestronet chat pages about B1+ and B1 - for Don and Anders Buen’s discussions that lay out the basics. John McLennan has a useful web page describing and documenting the violin body modes here too.

How to do it ...

                             damp the strings and hold the violin at the top block with the left hand. Don Noon suggests you can see the individual body resonances by tapping and putting the microphone close to different places on the violin body, with the frequency peak of interest (usually) the highest of several in the recorded FFT for that microphone position and tapping point,

The microphone position and the tapping points are as follows:

For ........

• A0      - close mic. at the upper part of an f-hole while tapping anywhere on the body,
• a video of how to measure A0 can be found below, as it’s easily done when B1+ is measured
• B1-    -  close mic near the center of the back, and tap at the centre of the back,
• I have posted a video of how to measure the  ‘B1-’ body resonance here on YouTube .
• B1+    - close mic the violin top, just above the f-holes, and tap the bridge with a light pencil,
• I have posted a video of how to measure the  ‘B1+’ body resonance and A0  here on YouTube .
• A1      - close mic at the lower eye or the lower ‘O’ of an f-hole, and tap a bout or tap the belly next to the tail-piece
• B0     - hold the violin at the lower widest point, tap the scroll and place the microphone at the centre of the back.
• CBR or C2¹  - on the violin’s back close mic at the edge of a C-bout, and tap the opposite C-bout.

You will then see that

• A0   (the Helmholtz) peak about 270 - 280 Hz,
• B1-   is at about 410 - 460 Hz, and
• B1+  is at 510 - 550 Hz, and also
• A1    is usually between B1- and B1+ at 450 - 485 Hz,
• B0    is at about 270 Hz if there is a good ebony fingerboard.

      The example right is an Audacity FFT plot for my red  ‘Juzek’  Czech (Shonbach) violin, tapped on the side of the bridge with a pencil.

   There is 50 Hz hum (as always in the UK),

• A0 is at 265 Hz (a very high peak),
• ‘B1-’ is at 449 Hz,
• there is a little of A1 visible at 465 Hz, and then there’s
• ‘B1+’ at 540 Hz.
• ‘CBR’ (C2) should be at 400 Hz.

The extract of this plot with these peaks is here.

You can see the exact same Audacity FFT curves/plots in the 2 papers by ‘Don Noon’ on the Schmidt website mentioned above.

  First, the A1 resonance, and this is a resonance mostly of the air column along the violin that is also linked to the air volume within the body and the f-holes, that is  to A0. This is found like this:-

    With the strings damped, hold the violin at the upper block and tap the belly next to the tailpiece with your finger or knuckle. Position the mic. so it is right at the lower ‘O’ of the right hand f hole - or right in it if possible! Then you will see clear resonances at A0 (~270 Hz) and also A1 (~450 - 485 Hz) as distinct peaks.

     With this method you can see the very strong A0 at 263 Hz for the ‘Juzek’ . If you click on the picture right the A1 mode frequency also shows up as a strong peak at 462 Hz. The extract of this plot can be seen here. The B1+ and B1- mode peaks are at a very much lower amplitude.

   If you look at Patrick Kreit’s site (or better, get his book!) you will see he strongly recommends that the relationships between these key body resonances should be as follows for a concert quality violin:

- a delta of 75 to 95 Hz between modes B1+ and B1-

- a delta of 60 to 90 Hz between modes B1+ and A1

- a delta of 0 to 16 Hz between modes A1 and B1-.

   But be aware too that when the tailpiece and chinrest are added to a violin when it is strung with the stings then B1- and B1+ both drop by 5, 10 or even 15 Hz! Their weights affect the body resonances.  A1 is unaffected.

 Using the instructions given in Don Noon’s paper on the Schmidt website you can also easily find the ‘CBR’ or C2 mode* which lies between 350 and 420 Hz, but sometimes you may get 2 of them very close! The ‘Juzek’ has the CBR at 370.5 Hz.

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

  Footnote 1:  This “CBR” mode (called  "C Bouts Rhomboidal" by Bissinger:) was also labelled "C2" by Jansson, and "Vertical translation of C bouts" by Marshall .

Body resonance targets

     There is a useful article available on the web on ‘ideal target body resonances’ titled  “Measurements of 10 Preference-Rated violins”  paper given at  ACOUSTICS 2012 on (page 3608), written by C. Saitis, C. Fritz, B.L. Giordano, & G.P. Scavone.

    If you click on the picture right it will bring up the data from that article for the key body resonances of the best 3 of the 10 good violins they tested for sound quality, as perceived by a group of expert listeners.

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

     The Strad 3D Project gives us good information about the body resonances of 3 good Italian violins: one diagram from the site is extracted below, so click on it.

    It shows the peaks of the body modes that are best radiated from these violins.

  There is also helpful information in a “Probing the Secrets Of The Finest Fiddles” article from the Science Magazine, June 2010.

     Carleen Hutchins recommended matching the B0 body resonance to the A0 (Helmholtz) resonance you have measured above. If it is at too high a frequency, reduce B0 by adding weight at the end of the fingerboard. For example, use blue-tack stuck under the end.

    You can look at Jo Curtin’s “Good Vibrations” papers in the Strad or on his website to see where these key resonances are for some of the world's great violins! So if you want to copy one - you can try to copy the main body resonances too!

 Ideally the tailpiece resonance, usually at about 125 to 135 Hz should be at half of A0 and B0.

Oberlin Acoustics has a glossary online of these key terms and abbreviations here

The article Mode tuning for the violin maker  by by Carleen M. Hutchins and Duane Voskuil is rather an advanced paper, but if you can understand it, it covers all the basics on violin body resonances.

  Now what do we do with this information on body resonances ? 

          Carleen M. Hutchins’ work showed that the difference or ‘delta’ between the frequencies ‘B1+’ and A1 dictate how a violin projects, and quoting from her CAS paper:

A1 AND B1 FREQUENCY RELATIONSHIPS:  It has been found that the frequency spacing (delta) between the A1 cavity mode and the B1[+] body mode is critical to the overall tone and playing qualities, indicating whether a violin is suitable for soloists (delta 60-80 Hz), orchestra players (delta 40-60 Hz), chamber music players (delta 20-40 Hz), and below 20 Hz is easy to play but lacks power”    (Hutchins 1989).

Amongst my many violins I’d say that it is so!

   There are discussions among the experts on maestronet on just what the relationships are between the plate tap tones, weights and thicknesses. It is complex . Anders Buen has come up with a useful relationship I have reproduced here, where he says:

   I have developed a model (shown on the ‘Plate Tuning 4 Dummies’ page) that is based on the data from 25 violin samples. It follows each of the belly and back plates and their tap-tones right from the start of violin construction through to finished violins and the completed violin body resonances; all of these ~25 violins sound either good or very good.

Estimating B1+.                                                          Accuracy: sigma ~10 Hz.

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

   A very important element in what a violin sounds like is just how far B1+ is above the A1 body (or rather internal air) resonance is, the true ‘Delta’ given above.

  1) The data shows the most important factor for the ‘B1+’ frequency is

        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) the back plate Mode 5,

        b) the belly plate Mode 5 frequency, and

        c) the back plate weight.   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 affects the belly Mode 5.

  This is explained in much more detail on the ‘Plate Tuning 4 Dummies’ page. If you click on the frame right a small [Excel, OpenOffice or LibreOffice] spreadsheet will be downloaded allowing the estimation of the two violin body Mode B1 frequencies to be automated for you. You just input the plate tap tones and weights and the B1 frequencies are estimated for you.

    This can be opened on your mobile too using the Microsoft Office Excel program/app. Just the input cells are unlocked, allowing data input. OpenOffice and LibreOffice are free to download on Windows PC, and there are several Android mobile apps available too.

    The back is often seen as the sound ’reflector’ to the belly’s ‘projector’, so do not take too much wood off this critical area between the C-bouts of the back plate, including the area of the channel next to the linings.

    So by making or adapting the belly and back plates, with  .....

• good arching,
• careful edge-work and edge thicknesses and
• well chosen tap tones (Modes 2 and 5) based on
• low plate weights - heavy plates need higher tap tones -

you can predict to an accuracy of ~10 Hz the key violin body resonances and therefore be confident that your violin will sound excellent!