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.
The Strad 3D Project gives us good information about the body resonances of 3 good Italian violins: one diagram from the site is extracted right, 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.
The data shows the most important factor for the important B1+ frequency is
1) a) the back plate's Mode 2 frequency. A high Mode 2 frequency is likely to affect B1+ by up to 40 Hz, and
b) the belly plate weight. A heavy plate reduces B1+ by as much as 13 Hz.
2) The next most important things are:-
a) the back plate Mode 5 frequency,
b) the belly plate Mode 5 frequency, and
c) the back plate weight.
These 2(a), 2(b) and 2(c) may affect the B1+ frequency by about 5 Hz each. A heavy back plate reduces B1+.
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.
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 10-15 Hz the key violin body resonances and therefore be confident that your violin will sound excellent!
How the main body resonances depend on the plate tap tones
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.
The diagram right (click on it) shows how important it is to get the plate tap tones right because they determine the main body resonances. The Mode 5 of the belly plate mostly sets the B1- frequency, and the back plate’s Mode 5 mostly determines the body B1+ resonance.
For example, 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 among 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 also knowing what the wood’s moisture content is at all times. I have found with my data that Mode 2 measurements are actually more useful than Mode 5, but you do need to know both.
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.
Getting the tap tones of the plates right, based on measuring the plate weights, goes a very long way to getting these key violin 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 selecting them to give particular B1- and B1+ frequencies close to the A1 (internal lengthwise) air resonance, gives a better sounding violin.