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 Last updated  7th.   May 2012  (C)   Copyright          platetuning.org

What are the plate Modes?

   Other sites give lots of information on how to see the patterns that arise when a plate of any shape is vibrated at one frequency. Have a look at the Really Useful Links page.

  The mode lines were originally discovered by a Mr. Chladni. His patterns of vibrating plates are well documented: have a look for instance at this UNSW site, and look at Chladni patterns for Violin plates  ..... or look on on YouTube.  This Ernst Chladni(1756-1827) was a German physicist, and is known as the ‘father of acoustics'.

What they tell us

The Modes, particularly Modes 1, 2 and 5, tell us about important characteristics of the wood :

• its bendability (speed of sound) across the grain is mostly ‘measured' by Mode 2, and
• the speed of sound or ‘bendability' is along the grain is mostly ‘measured' by Mode 5.

If we get these under control (i.e. known), then we are ‘copying' what Sr. Stradivari did hundreds of years ago, and he knew that if he made a plate a particular way then an excellent violin would result.

By setting the Modes 2 and 5 to ‘standard' frequencies, just as we make all the other dimensions of a violin completely standard with a Strad or Amati model, we control at least 2 of the 4 key body resonances of a violin. These 4 key resonances have a profound effect on the tone of a violin and are as follows: -

• The B1- and B1+ body modes are directly affected by setting the tap tones to ‘standard' values.
• The A1 mode is determined by the internal length of the violin, which is partly why violin length is standard to within 5 mm. A1  is unaffected by tap tones.
• The A0 mode is the Helmholtz or ‘cavity' air resonance mode, and is affected by the internal air volume, the size or area of the f-holes and also slightly by the stiffness and mass of the plates and bouts. Installing the soundpost stiffens the plates and A0 rises by about 30 Hz.

So the tap tones put the B1- and B1+ body resonances in the right places, and by using standard dimensions for the body we get the other 2 in the right place. And what about all the many higher body resonance modes? We rely on good craftsmanship, choosing good wood, and a dollop of good luck.

We may find that a tap tone of say 350 Hz on the free plate produces a resonance of say 440 Hz in the final violin and  not 430 or 450 Hz. It reminds me of aiming an arrow when shooting a bow. We calibrate the sights on the bow because gravity, the arrow and how it flies are almost the same every time. We set the tap tones as suggested because a violin is, as far as we can make it, a standard shape, and the ~1.5 times increase  (a fifth) in the tap tone to become the main body resonance is what it does when we glue the body together. Patrick Kreit's book The Secrets of Stradivari takes this a whole lot further. The new site about this book can also be found here.

Have look at Carleen's paper for more on these key body resonances, and there's much more on my ‘Resonances of violin body' page too.

What we are missing however is the Italian Special Magic of scraping here, scraping there that allowed Sr. Stradivari to tune the plates after the violin was assembled (‘in the white') to turn a good instrument into one of the best violins ever made. I do think Herr Schleske has come closer to reproducing this magic consistently without having to resort to sacrificing frogs legs and/or nubile virgins.

Again, good violinmaking practice is the foundation. I have found that I need to convert the violin I'm working on to be as near a ‘standard' good-practice violin as possible. It needs good blocks: you may need to add corner blocks if they are missing, as so often the case with old, cheap factory fiddles, and you may need to reduce the bouts (sides) to 1.0 to 1.4 mm thick by carefully grinding then down with a Dremel hand-router fitted with a sanding cylinder. Some fiddles have bouts over 2 mm thick.  By adding good, standard blocks and thinning the bouts I remove most of the variations in sides (bouts) and the structure so that a tap tone of say 350 Hz on top or back plate really does become 440 Hz in the complete violin.

Historically speaking

     The first reference I can find to these ‘Modes' and ‘nodal lines' on violin fronts and backs is in a Victorian book on violin making of 123 years ago!  “Violin - Making: as it was and is” by Ed. Heron-Allen, published 1885-6. The author studied under (one of the) Georges Chanots, probably in London or Manchester.

There are some contradictions and “mistakes” especially on belly tap tone frequencies, but amazingly, re-reading it the other day, I found a reference to Modes 2 and 5 tap tones visualised using sand, using a rosined bow drawn across the edge of the plate to excite the modes.        Chladni's book on plate acoustics was in circulation a full 70 years (1787) before Mr. Heron-Allen was writing.

 

 It's fascinating to think that he may himself have seen patterns in sand, as shown right, as he drew a bow across the edge of a plate he was holding. This is on pages 132-133 of his book.  He refers to Mode 2 as the “normal tone”, and believe it or not, refers to “nodal lines” in the tech. footnote on page 133.  As a reality check, this is from 125 years ago. What's new under the sun?

Here is a webpage at UNSW that shows these modes of vibration.

What are Modes?

    What is Mode 2 or the X-Mode?  and what is Mode 5 or the Ring-Mode?  Here are the ‘tea leaf' patterns that show up when the plates are vibrated using a loudspeaker underneath at a particular frequency - the ‘tap tone'. It is a resonant frequency of the plate as a whole.

 On the left here is one of the excellent photos on Joseph Curtin's website and shows the most important Mode in a belly plate, Mode 5, the ring tone. The black lines are the nodal lines on a violin belly vibrating in Mode 5 at about 350 Hz. The pictures below show Mode 2 in a front plate at about 170 Hz. Have a look too at a BBC web page here that uses “holographic interferometry” (!) to do the same thing - only even better!

These pictures show that when a plate, either the front or back of an instrument is vibrated at one constant frequency then fine sand, tea leaves, sawdust or glitter placed on it will move to areas of the plate that are not moving i.e. not vibrating. This only happens at particular resonant frequencies, and finding those resonant frequencies is what this is all about. These lines of no motion are called the ‘nodes', or in this case the ‘nodal lines'. Anti-nodes are where the motion is at a maximum.

   In summary: The “nodal lines” are the black lines in the photos and videos where the plate does not  vibrate at that particular frequency. So the plate can and must be held somewhere on a nodal line without affecting the vibrating pattern of that Mode.

 There is a good YouTube video by Jonathan McKinley (click on the picture left) that clearly shows plate modes 1, 2 and 5 vibrating as the tea leaves migrate to the lines of zero-vibration - the nodal lines of the violin plate as the vibrating frequency is gradually increased. Jonathan McKinley  has photographed his violin parts here too: but his belly:  Mode 2 is high, and Mode 5 low!

            Understanding these Modes and their shapes is fundamental to understanding tap tones. You will need to know how to get these Modes vibrating. It was Carleen who first used a speaker placed under a plate at an anti-node, and fed the ‘speaker at various frequencies until a glitter pattern showed up.

          These patterns are well illustrated by other website pages to be found in the “Really Useful Links” page. If you click on either these two glitter patterns you can see the nodal lines on a back plate that Alan Jhones from Brazil sent me (thanks!). Mode 5 is the one above, and Mode 2 is on the right.

         We can also get the plates vibrating by holding at a point on a nodal line, and tapping at an ‘anti-node', or a point where the vibration is or will be a maximum: it works well, but there is information lost about the detailed shape of the nodal lines: Carleeen thought that is important.

Animations of plates vibrating 

 Borman Violins also shows some excellent and fascinating animations of violin and other plates here vibrating in situ on a violin and viola, made possible by the work of instrument maker George Stoppani.

 This helps us understand how the vibration of the belly and back plates vibration modes while free (as we measure them) are linked to how they behave actually in a completed instrument.

Vibration modes of the completed violin

 Getting the tap tones right for the plates will give you a good chance that the resonance modes of the completed violin body will be right - or at least similar to the world's greatest violins!  Have a look here for the resonances of the completed violin body ......

...but what tap tones don't tell us

     Well you wont make a violin that sounds like a  £15,000 violin using tap tones like this unless you are very, very, very, very lucky and at least prepared to let an expert choose the (costly) wood to start with.

There is another and much higher level of the art, experience (and science) that the master craftsman has that us mere mortals can only dream of.

     You can glimpse some of it in the work some are doing to actually listen openly to what violins sound like: there's a discussion here on maestronet for instance, which I've edited to a .pdf document here to make more of a narrative (and remove the occasional name calling these forums suffer from).

     Others for instance have tried area tuning ( see this fascinating site of Keith Hill's) and ‘Vigdorchik strip' tap tuning (see David Langsather's example here) which I think has great possibilities, but you will need a lot of faith, patience, and a very, very good ear to do it. And much of a lifetime.