Arching of the front and back, plus f-holes & bassbar

   For arching the plates, the best guidance I’ve found is in Sacconi’s book on Stradivarius’ violins called “The Secrets of Stradivari”, where he gives the ideal ‘contours’ of front and back plates, and tells us just where to put the highest point of the plate.

I like the method that Juliet Barker teaches at CVM in Cambridge that can also be found in her book. Instead of using the long and cross  ‘arching templates’ that so many books get you to cut out and use as a guide, while the inside of each plate is (perfectly) flat use a pencil gauge to create the arching contours of your choice. This ties up well with Sacconi’s ‘contours’ in his book mentioned above.

I cut elaborate cardboard contour guides (like David Langsather’s  and Sacconi’s) for use with the pencil gauge but in reality? It’s really about a feel and look for arching, especially when you’ve made and handled a lot of violins. The contour guides are just guides.

There’s also guidance in any of the various books on violin making in the ‘Really Useful Links’ page, but I have just discovered that Sergei Murgatov has written a book called “The Art Of The Violin Design” available on the web in English here, and it includes detailed arching (and sixths gauges) on pages 50 to 61. It includes arching for violas and ‘cellos too. He uses the the ‘Cornu spiral’ or ‘clothoid’ rather than the cycloid as the basis for traditional Stradivarius arching.

For belly plate Strad. arching: click on the picture right, and right click to save it in the new window

Other belly arching figures are here, and the belly sixths are here.

For back plate Strad. arching: click on the picture below:

Other back arching figures are here, and the back sixths are here.

The front and back should really have different arches: the front (the belly) has a flatter long arch and cross arching than the back. Some outline and arching templates for a ‘Strad.’ can be found here as upper part and lower part.

These can be printed out full size (use the scaling print option for your printer) and then cut and glued together to match ‘X-X’ or the bridge line.                                                                                             The scaling is:-           overall length = 356 mm.                                  Max. width for the upper bouts at template #1 = 2 x  82 = 164 mm. Max. for lower bouts at template #5                 =  2 x 103 = 206 mm.  The same arching templates can be used for back and belly without much error for your first violin.

Bruce Ossman in his book on your first violin (see here) has exactly the same the arching, back and front for simplicity, but there is no need to do so as you can alter it as you make it.

Here’s how Onnes Violins sets the arching on the back of a ’cello he’s making, using various workshop tools, including power tools!.  The same technique could be applied to a violin or viola. He also has an interesting page on thicknessing and tuning the plates of a ‘cello here using a laptop and Apple’s ‘Perfect Pitch’ program.

Darren Molnar has some interesting things to say about arching on his site, particularly about using Curtate Cycloids .

The Strad Magazine has a scanned copy of Quentin Playfair’s article on cycloids from The Strad, 1999: you can download: Part 1, and Part 2. I met Quentin again when he taught at Cambridge (CVM, UK), and here’s a picture of him (centre) in the workshop. A skilled craftsman who knows a lot, and can tell it with tact. These cycloid shapes are much easier to create (draw) than to describe, especially in maths, as they use parametric equations. But it’s quite easy to create an arching profile using a spreadsheet, and then use the pencil gauge shown on the Tools page. They are (much) easier to create than Murgatov’s clothoids!

 Roger Hargrave’s site library has an article on Guarneri’s arching and f-holes here.

Thicknesses of the front and back

    The New York Times printed an article in 1994 called “Perfect Violin - Does Artistry Or Physics Hold Secret?” which is available on Peter Zaret’s website here as a .pdf file. He has an interesting modification to the standard bassbar and other good stuff on violins. Anyway, the original article is difficult to read as the text is small, so I have reproduced Carleen M Hutchins’ thickness plans from it (see and click left) for a Mezzo violin (an oversize standard violin!), but the thicknesses are all but identical to Sacconi’s plate thicknesses for a normal violin. The text of the article is here. Right click it and use “Save target as ...” to save as a .jpg file. These plate thicknesses are a very, very good starting point.

  The thickness of front and back plates for great Guarneri ‘del Gesu’ violins can be found here, reprinted from ‘The Strad’ Sept. 2005. Borman Violins also shows some fascinating animations of violin and other plates here.

 There are also plans (A3 size) available for the Ole Bull Violin Project than can be found on the Landon Violins web site, plans for the Ole Bull Guarnerius of 1744. These include the shape, the arching and the plate thicknesses.

Erik Jansson also gives guidance on thicknesses in his articles “Acoustics for Violin Makers”, Chapter 5, Fig. 5.21, page 24.

Rough thicknessing: back

      I have derived Fig. 2 below to shows where to thin a back plate to reduce either Mode 2, Mode 5 or both frequencies. Again, click on it to see the diagrams in detail. Right click it and use “Save target as ...” to save as a .jpg file.

  There is some agreement between the various reference books, and the other sources for back thicknesses  as to where the thickest point on a violin back should be.

Summarising these sources, and ignoring differences in plate shape :-

•   Stradivarius put the thickest point ~ 46% down from the top of the back plate [source: Sacconi and Courtnall and Johnson.],
• Other sources (e.g. CVM, Juliet Barker and her team] and others) put the thickest point about halfway (50%) of the way down the back, and
• Guarneri del Gesu usually put it ~ 55% of the way down,

with all distances measured from the bottom of the top block to the top of the bottom block. This ‘thickest point’ then acts as the centre point of the ovals or circles that guide the thicknessing of the central area. It is sometimes slightly offset by ~10 mm. towards the sound post: see the work of ‘Jack’ Fry below.

 To get the back to the right kind of thicknesses to start with I use a cardboard ‘pattern’ with cutouts as shown right. It is a remarkably effective technique I copied off others like David Langsather.   So choose your model, make your choice.

There’s an interesting YouTube video here showing how to use a ‘graduation punch’ in thicknessing a plate.

If you didn’t over-thin the back it is then ready for plate tuning! See above for where the thickest point is.

Rough thicknessing: belly

    I have derived a Fig. 1 left to show  where to thin a front plate (the belly) to reduce either Mode 2, Mode 5 or both frequencies. Click on it to see the Figure in more detail.  Right click it and use “Save target as ...” to save as a .jpg file.

  This is a revamp of Erik Jannsson’s work referenced earlier, which itself seems to be based on Carleen Hutchin’s work of 1982, published in the CAS (VSA) Journal.

As an example using this data, I recently needed to reduce Mode 5 of a viola belly without reducing Mode 2, so I took areas marked the colour orange in Fig. 1 above from 3.0 mm to 2.4 & 2.5 mm. This took Mode 5 from 278 Hz to 263 Hz, but left Mode 2 unchanged at 112.8 Hz.

The f-holes

 The Strad  f-hole shape can be taken for example from Stroebel’s book on violin making, or from an article in  Roger Hargrave’s site library where the article on the Mackenzie Stradivarius violin has dimensioned drawings with f-holes shown. The Strad ran an article on the detailed positioning of f-holes too, which is here. A 1733 Guarnerius is also described and drawn here, with f-holes and plate thicknesses.

The bassbar

The bass bar should be 5.5 mm thick, or 6 mm if the belly has low arching or has wide-grain. Its final cross-section shape will be a ‘parabola’ (inverted U shape).

The ends of the bassbar should be either 40 mm from the top and bottom edges, or other makers end the bar when it is at the 3/4 way point from bridge line to top and bottom edge.

 The outside of the bassbar must sit 1.0 to 1.5 mm inside the left foot of the bridge, i.e. the bassbar must be under the left foot to take the pressure of the strings and pass the forces and vibrations to the belly. The top end of the bassbar (nearer the top block) needs to be ~2 mm closer to the belly centre-line than at the bridge position, or you can use the ‘sevenths’ method text books describe for more accuracy.   There was an article by Dominic Excell in The Woodworker, Jul ’96 (which alas is long since out of print) available here as a .pdf file. It shows how to cut f-holes and how to position the bassbar using the ‘sevenths’ rule.

The picture right (click on it) shows the wood for the bassbar being chalk-fitted onto the belly. I use 2 or more thin blocks temporarily glued on with white glue to hold and guide the bassbar wood during fitting and gluing, and I also use brightly coloured chalk on everything but a Strad.: it’s easier to see than white.

There are many shapes of bassbar: the fashionable one is ‘hump shaped’, but Stradivari’s originals were just a low flat bar, the Strad magazine has promoted a triangular shape (Jo Curtin, ‘Trade Secrets’, Nov ‘05, available here) with the highest point under the bridge. Patrick Kreit uses a flat bar tapering down a few cm. from each end, so the shaping is easier. Some keep the bar at full height just for the length of the f-holes. Take your pick.

You must now choose where the highest point of the bassbar is: at the bridge position or closer to the mid point of the bassbar, but best is to put it half way between the middle of the bar and the bridge line.

The figure right (click on it) shows the ideal (logarithmic) shape of the top of a ‘humped’ finished bassbar as it slopes from the highest point towards the ends. There are heights from 11 to 15 mm shown, but start shaping at no less than 15 mm.

This graph needs to be scaled of course, as the bridge position (the ff inside nicks) is closer to the bottom edge than the top! A typical finished bassbar is 12 mm high at its highest point (measured down the the belly on the inside, centre-line side) and is 6.8 mm high halfway (50% of the way) to the end in both directions, and the ‘half height’ point is 56% of the way to the end.

   The bassbar’s height needs to be reduced as you tune the belly plate for Mode 5 to get the Stiffness Factor you want. You will need to keep the bassbar’s top shape correct, so there’s quite a lot of measuring, checking, carving and planing (thumb plane work) to do. Note the bassbar needs to be rounded to a parabolic cross-section but is nearly semicircular at the ends. Reducing the bassbar height has little effect on Mode 2.

Raising Modes 2 & 5 in a thin back.

This thickness data is especially useful if you need to add a maple patch to the middle of the inside of a back that is too thin i.e. has too low a Mode 2 or 5. This is more like ‘doubling’ as it can cover quite and area. I’ve found that a wide patch of say 3 - 4 mm thick (which may be made up of layers of maple veneer) increases mostly Mode 2, and a long (lengthwise) patch of 3 - 4 mm thick increases mostly Mode 5. You will need to shape and then ‘chalk fit’ the maple patch before gluing or use layers of veneer, but I have sometimes used fluid Araldite (2-part resin glue) to stick a patch on a cheap factory fiddle, as the patch can be fitted less exactly - the resin glue acts as a filler, where animal hide glue does not.

There’s first-hand guidance on thicknessing in Sacconi’s book on Stradivarius called “The Secrets of Stradivari”, and in other books to be found on the ‘Really Useful Links’ page.

‘Fiddlehead’ has been working with the famous Jeff Loen on Strad plate thicknesses, and these can be found here for the Harrison Strad of 1693 for front and back.

Have a look too at David Langsather’s website page for a quick and practical approach. He has the thickest point about 55% of the way down the back.

Osnes Violins in Alaska (!) shows how thickness graduation is done here on a ‘cello, and shows plate tuning, cutting the ff holes, and fitting the bass-bar.  He uses a power router/cutter to remove the excess wood from inside the back of a cello.

Physicist "Jack" Fry, with the help of violinist Rose Mary Harbison, has been working to rediscover the legendary sound of the Stradivarius violins.  William (“Jack”) Fry has a lot of interesting things to say about the effects of tiny local thickness differences, especially at the end of the fibres that go over the sound-post (over an area shaped like a ‘tongue’ of thicker wood), and an area at the violin’s edge at and above the right-hand f hole. The video of Jack’s lecture (1 1/2 hrs.) can be found at the website above.  His books titled “A Physicist's Quest for the Secrets of Stradivari” (with DVDs) are available here, and an article on him and his quest is here.  Many thanks to Jeff Minniear of Schenectady NY for the links and articles.