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 and finding tap tones on the belly and back plates. It can drive you mad.

There is a website - John Schmidt Violins, Laurinburg, North Carolina, USA - that has two .pdf files (“Violin Mode Measurements 1 and 2” by Don Noon), and also see  Maestronet chat pages about B1+ and - for Don and Anders Buen’s discussions that lay out the basics and how to measure A0, A1, B1- and B1+ body modes on completed, strung up violins. It only takes a couple of minutes to find all the key body modes. These can be seen at the Strad3D modal view site here.

 I damp the strings with a rag stuffed under them, hold the violin at the top block with the left hand, and tap on the side of the bridge with a pencil or biro. With the mic must be over an f-hole all the main body resonances except CBR and A1 are visible as peaks.

 Don Noon measures body resonances more accurately :

• A0      - close mic at the upper part of the f-hole while tapping a  bout
• B1-    - close mic near the center of the back, and tap nearby
• CBR  - close mic at the edge of a C-bout, and tap the opposite C-bout [on the back]
• B1+    - close mic the violin top, just above the f-holes, and tap the bridge with say a pencil,
• A1      - close mic at the lower eye of an f-hole, and tap a bout [or the belly next to the tailpiece]

You’ll then see

• A0    (Helmholtz) peak at about 270 Hz, and
• B1-   at about 410 - 460 Hz, and
• B1+  at 510 - 550 Hz, and also
• A1    between B1- and B1+ at 450 - 485 Hz.

      The example right is an Audacity FFT plot for my red  ‘Juzek’ 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. 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.

To find the important A1 resonance properly (and this is a resonance mostly of the air column along the violin): 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 - right in it if possible! Then you’ll see clear resonances at A0 (~270 Hz) and also A1 (~450 - 485 Hz).

     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 - mode peaks are very much lower.

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-.

Using the instructions given in D. 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.

   * This “CBR” mode was labelled "C2" by Jansson , and "Vertical translation of C bouts" by Marshall .

 Carleen recommended, as do I, matching the B0 body resonance to the A0 (Helmholtz) resonance you have measured above. Adding weight to the end of the fingerboard is easily done, temporarily if need be with blue-tack.

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 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 very complex indeed. Anders Buen has come up with a useful relationship I have reproduced here where he says:

     “ The B1+ is slightly more determined by the back plate, while the B1- is more determined by the top. The [critical] distance between the B1- and B1+ is much determined by the back plate central thickness”.

    So, for the back plate the thickness of the area between the C-bouts, which is most closely tied to and measured by the back’s Mode 2, is very important.

   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!

    As mentioned above, Patrick Kreit gives a lot more detail (and I mean a lot) in his book “The Sound of Stradivari”.  He tells us that the sound, dynamics and clarity of a solo-grade violin, Strad or Guarnerius model, is based on the exact frequencies and ‘deltas’ of the B1+, B1-  and A1 body modes, and also on the frequencies of the A0, and the B0 and CBR (C2) modes.

While reading Patrick Kreit’s book I modified a 40-year old, very cheap Chinese ‘Skylark’ violin to put the Mode 5 frequencies of the belly and back plates where Patrick said they should be, and with their Mode 2’s an octave below. The key body resonances ended up where he said they would be (A0, A1, B1-, B1+). This ‘Skylark’ is now the best sounding and easiest to play violin I have among my 12+ violins, which go up to ~$2.5k each. Apart from putting the Mode 2 an octave below Mode 5, his plate-tuning methods are based mainly on tuning Mode 5 of the plates, and knowing what the wood’s moisture content is at all times.

Testing my violins I can find all of these body resonances / modes as good, clear peaks in their FFT (Audacity) plots, and they are of similar amplitudes.

You can look at Jo Curtin’s 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!

Getting the tap tones of the plates right goes a long way to getting these key body resonances just where they should be for a good violin. We do know that the plates’ tap tones need to be within a particular range for a decent violin: what I’ve found is that matching them, as Carleen Hutchins did, gives a better violin, and taking the plates’ weight into account too is also a step forward!