How does a violin or a Hardanger fiddle work?

A lot of open information is now available on how good violins are built. Books containing high resolution pictures, thickness graduation maps, and geometrical measures of great old Italian violins can be bought. Some of this is now available on the web like e.g. the The Luthiers Library. Articles are publicated on e.g. CT scanning of fiddles (at hospitals), plate tones and -weights from known top instruments, along with e.g. information on the density in the wood, archings, and so on.

There are also good aids available for documentation of instruments acoustically or technically even in a normal workshop environment. Thickness graduation meters, weights, equipment for measurement of the soundspeed in the wood, equipment for measurements and documentation of arching shapes, f-holes, and so on. Software utilizing the soundcard in the PC can analyze the resonances in the fiddles. Most of us now have equipment for recordings.

Master of science thesis on vibrations in violins from the NTNU

During my project and master thesis I used a special optical laser based measurement system that directly showed the vibrations in a violin and how they looked. One of the instruments was a Gaetano II Guadagnini from about 1800 which is played by a known Norwegian violinist. I also measured some other violins and a Hardanger fiddle. A literature study was also done on the subject. This became my way into acoustics. We had a few acoustics related courses and physics which has quite a lot acoustics related theory involved. E.g. the quantum mechanics does have a technical nomenclature and concepts basically coming from the acoustics, mechanics and statistics theory. The atoms can be looked at as small "musical instruments" where the "music" is shared as electromagnetic waves, e.g. as light and heat.

I used TV-Holography showing the vibrations in the violins on a TV-screen and in digital images. Typical wave forms are shown at the resonances. Similar shapes are seen in the different fiddles, so it is possible to put names on them. In the images out to the right you can see examples of digital images of the vibration shapes. In the spectra below you can see examples of how they are distributed over the frequency and playing register as "mountain tops"

Examples of an acoustical tool for acoustical analyses of fiddles

I mainly use my ears and six tuneable tuning forks when I work on the fiddle plates. I do not hear all notes equally well, especially not if listening to the violin body. I then use the PC with a good soundcard, a good microphone and an analysis program called SpectraPlus. Resonances of the fiddles can be extracted as shown below.

The sound spectrum you see above are the resonances from a well known Stradivari violin from 1715 (orange curve) and from a Guarneri-model violin I have regraduated (blue curve). The curves do resemble each other to some extent. E.g. the main air resonance, A0, and the resonances, T1 and C3, about at the same place in frequency (tonal pitch). There are some similarities around 1kHz and between 2- and 3kHz. But there are also some differences: The fundamental note on the first finger on the A string is stronger on the Stradivari and there is less "noise" above about 4kHz. The details between 1- and 2 kHz also show some differences.

Such curves does, of course not, replace the necessity to play and listen to the fiddles, but it can be a tool in the process and the documentation. With numbers on the properties of the fiddles, it is possible to correlate these with how the fiddles are built and how they are to play.

The vibration shapes of the resonances can be shown using software developed by the english violin maker George Stoppani.

How does the spectrum from a Hardanger fiddle look in comparison to violins?

There are many similarities between the sound spectrum from the body of a Hardanger fiddle and a violin. Below you can see the spectrum from my Hardanger fiddle compared to the Stradivari. They are measured in different rooms and using two separate, but still, similar measurement systems. The level of the curves are thus set manually. The distribution of sound over the the spectrum can be compared, as the level is normalized to the input force in both cases.

The main air mode, A0, lie a bit higher in this Hardanger fiddle, the C3 resonance is weaker and lie a bit lower in frequency than in the violin. But the findamentals on the e-string is likely to be stronger in this Hardanger fiddle than in the Stradivari. The "cut off" in the higher frequencies lie a bit lower in the Hardanger fiddle than in the violin. At first sight this might sound a bit strange and counter intuitive, as normally the Hardanger fiddle sound brighter than most violins.

What we see is the sound from the bridge and the body of the fiddle. We may call it the "filter" the strings notes are heard through. The brighter and often more intense tone in Hardanger fiddles are likely to be related to the higher tuned pitch and the thinner strings used. In the eastern norway districts the a string is usually tuned to b, c or sometimes c#. Normally the thinner and lighter strings, and the shorter string length, make the sound level from a Hardanger fiddle somewhat weaker than from a violin, even if it might be perceived as being more intense.

Some of the fiddles on the west coust use lower pitched fiddles. Often the a string can be tuned to a#. A lower pitch and thicker strings make the sound darker and possibly somewhat more "woody".

How are the Hardagner fiddles built compared to violins?

This is a whole and not much researched science. In general the archings on a Hardagner fiddle are often flatter across the plates, especially in the central part between the f-holes. The f-holes are in general longer, the strings are shorter, the plates often thinner, especially in the back plate and the bouts. But is often thickner in the central part of the top. possibly to compensate for the flatter arch and longer f-holes making the central part less stiff. Different makers may have their own special traits in their making. Some of the Steinkjønndals fiddles do e.g. have thin backs.

More visible are the resonance strings, the special bridge and the strings. In some ways the Hardanger fiddle do have some similarities with the baroque violin which most of the fine old violins have been once. The decorations are also, of course, a difference. But there are also examples of violins with decorations, even back to the 1500'ds Andrea Amati, his sons and the grandson Niccolo. Later also Stradivari made a few such decorated examples.

Calculated vibrations

Here you may see a movie of the first main body resonance of a violin, B1-. Its made from calculations using a finite element program called Abaqus. The model is made by John Masters and I have modifies it slightly with somewhat thinner plates.

Click on the picture below and you will download a movie of the B1- seen from the top and the side. B1- is the same mode as the T1 you see at the grey scale figures at the upper right hand.