Violin outline design
Before looking at arching you may want to create your own (perfect) plate outline.
The ‘Four Circle’ method is described in detail by Kevin Kelly of Kelly Violins: there are 4 or more of his videos on YouTube. But the easiest way to understand the method is to start with Russell Hopper’s diagram (click on image right).
Robert Zuger also has some interesting things to say about the violin shape and arching.
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.
You can use the long and cross ‘arching templates’ that so many books get you to cut out and use as guides, but I prefer the method that Juliet Barker teaches at CVM in Cambridge that can be found in her book. When the underside (inside) of each plate is (perfectly) flat you can 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 did cut out a cardboard contour guide (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 guides.
There’s also guidance in any of the various books on violin making in the ‘Really Useful Links’ page, but I discovered that Sergei Murgatov has written a book called “The Art Of The Violin Design” available on the web in English here that includes detailed arching (and sixths gauges) on pages 50 to 61. It includes arching for violas and ‘cellos too. He uses the fascinating Euler or ‘Cornu spiral’, ‘clothoid’ or ‘Transional Spiral’ rather than the cycloid as the basis for traditional Stradivarius arching.
A fun curve: easy to draw or construct because it's degree-of-curve increases directly as the distance along the curve from the start point of spiral, but hard to describe in school maths.
There is an article about using Curtate Cycloids here, and many makers use the cycloid as the basis for arching templates: for instance there is an online calculator here, but this one does not give control of parameter ‘b’ for arching fullness.
Recently I found that my best sounding violin has much fuller arching than any ‘normal Strad’ copy, particularly on the back. So I needed to work out theoretical arching templates for this fuller, fatter arching so I can copy it properly. Using the (curtate) cycloid curves in this spreadsheet I have calculated the arching for various cycloids from ‘flat’ to positively obese.
Violin back (long) arches most seem to have a parameter ‘b’ of 5.5 (+-1, for a = 10), and I’ve checked that against the Strad. ‘Messiah’, Guarnerius (b = 5.3) and also Harry Wake’s (b = 5.9) and Henry Strobel’s (b = 5.5) contour guides. The .pdf document can be found above: click on it and save it. Note that the arch height is wildly exaggerated in these plots! Some violins have arching so full the cardioid shape cannot plot it at all.
Don Morris has published some free plans for a “ 1720 Strad” violin. If printed on A4 they need enlarging by 65% to get full scale for a 356 mm body length. You can also buy plans of violins and other instruments off his site. Dimensions are in US inches. A copy of his plans are here as a .pdf too. Standard measurements for 4/4 and fractional sized violins can be found here too.
For belly plate Strad. arching: click on the picture right, and then 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 there’s a picture here, or click on the picture right:
Other back arching figures are here, and back sixths are here.
Vojtech Blahout’s website on violin making has excellent resources and there are arching templates avalable to print here for the belly and here for the back plates.
The front and back should really have different arches: the front (the belly) has a ‘flatter top’ to the long arch (and cross arching) than the back: often called a ‘platform’. An outline and the 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 of upper bouts at template #1 = 2 x 82 = 164 mm.
Max. of the bouts at template #5 = 2 x103 = 206 mm.
The same arching templates can be used for back and belly without much error for your first violin.
There is a chapter 5 of Roger Hargrave’s book available here on arching a thicknessing, and a CT scan (!) of violin back and front plates here, which is an extract of a VSA paper by Borman and Stoel.
Bruce Ossman in his book on your first violin (see here) has 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 but is very risky. 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.
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. 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 and are (much) easier to create than Murgatov’s clothoids!
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 (click left) for a Mezzo violin (which is 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.
These plate thicknesses are final thicknesses, so initially your plates should be thicker than these.
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 (the Ole Bull Guarnerius of 1744) than can be found on the Christophe Landon’s Violins web site. 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 and then final thicknessing: the back
I have derived the figure right to show where to thin a back plate to reduce either Mode 2, Mode 5 or both frequencies from Carleen Hutchins’ data.
First on the left are the ‘starting’ thicknesses: remember you cannot ‘add’ wood, so tuning plates is always by removing or thinning wood.
Always start too thick!
Click on it to see the diagram in detail. Right click it and use “Save target as ...” to save as a .jpg file.
As an example using this data, I needed to reduce Mode 5 of a viola belly without reducing Mode 2, so I took the outermost areas top and bottom that are shown in the figure above from 3.0 mm to 2.4 & 2.5 mm. This took the plate’s Mode 5 from 278 Hz to 263 Hz, but left Mode 2 unchanged at 113 Hz.
At the top of this (and all pages) are the thicknesses (graduations) for the average of 48 Stradivarius violin backs (with thanks to Anders Buen) and you will also find there the Harrison Stradivarius back and the belly plates thicknesses.
Included here also are the Josť Contreras Violin 1767 plate thicknesses as published in the ‘Strad’ magazine Dec.2014. Photos can be found here .
The belly or front plate (click on the left picture) has ‘standard’ thicknesses at more or less 2.7 mm all over, but note it is thicker around the sound post.
The back (click on the right picture) is interesting in that it shows clearly the ‘pear shaped’ area in the centre of the back plate, and in this example just how far it extends into the upper and lower ‘lungs’.
This will keep Mode 2 of the back up and give power to the violin's sound projection. The back's thicknessing pattern is centred around the bridge line of the plate.
To the left here (click on it) are the belly and back plate thickness plans for the Guarnerius ‘Del Gesu’ ‘Lord Wilton’ violin of 1742, again from the ‘Strad’ magazine: I have added the thickness contours on the back.
This violin shows even more clearly the ‘pear shaped’ central area of thicknesses up to the highest point of 4.8 mm. This thickest point is well above the bridge line. This may even be the most straight forward way to set the thicknesses of a violin back plate: notably different to the Stradivarius thicknesses!
The edges of the back are all about 2.6 mm except 3.0 mm around the C-bouts.
The belly's edges are thicker at about 3.0 mm all around the edges.
The back plate’s thickest point
There is some agreement between the various reference book and other sources of back thickness data 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 (10/21ths) from the top of the back plate [source: Sacconi and Courtnall and Johnson.], and that position is the one I have shown on the two figures on this page for front and back plate thinning.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’s a quick and 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.
Have a look at the page here to see what tap tones you need to get the back and then the front plates to.
Rough thicknessing: belly
I have derived this diagram right to show where to thin a front plate (the belly) to reduce either Mode 2, Mode 5 or both frequencies.
This is a revamp and 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.
This diagram is showing how to get a plate to certain tap tones (Modes 2 & 5) in a belly or front plate before the f-holes are cut and before the bassbar is added. You will need to know that cutting the f-holes reduces Mode 5 of the plate by 1 tone, that is its frequency by about 12 %. Then putting on a new shaped bassbar of about 12 mm high will raise Mode 5 by about a tone (+ 12% of its frequency), restoring it to where it was! It has a similar effect on Mode 2.
Warning: Tap tones are not good at showing how you have thinned the plate edges: they give you data mostly about the wood and its arching and thicknesses towards the centres of the plates. I recommend that you spend time getting all the plate edges and the 10 mm inside them to the correct thicknesses before starting plate tuning!
Note that when a belly or front plate is varnished later, both Modes 2 and 5 will be each be raised by about 6 Hz as the varnish stiffens the grain in both directions.
Final frequencies for Modes 2 and 5 can then be adjusted by thinning the nearly final plate very carefully in places and by selecting an appropriate height of the bassbar. In both cases you can reduce the tap tones frequencies, but never increase them!
Does thinning in one area affect the Modes 2 & 5 plate frequencies?
In a forum discussion between Don Noon and Anders Buen on maestronet here Marty Kasprzyk produced an illustration which alas is nonsense.
I’ve gone back to Oliver E. Rogers paper of ~1990 in the CAS Journal (Vol. III) to produce a simplified diagram (see right and click on it). This shows where to thin different and specific areas of the 2 plates to change Modes 2 and 5. This is much more complex than you would expect!
Alan Carruth’s plate tuning article has good data too on where to thin on page 6 (his p. 47): have a look.
The belly’s 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 belly’s 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): it is better high than wide.
The ends of the bassbar should be 40 mm from the top and bottom edges, but 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 downward forces of the strings and pass those 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, or rather is an article by Dominic Excell in The Woodworker, Jul ’96 available here, article number 12. It is password protected: the whole set is available for 15$ US. 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 has a ‘hump’, but Stradivari’s originals were just a very low, short flat bar. A Strad magazine has promoted a triangular shape (Jo Curtin, ‘Trade Secrets’, Nov ‘05, available here) with the highest point under the bridge. I have had some success with a ‘flat topped bar’ (left 1) tapering down from a point 60+ mm. from each, as described by Patrick Kreit, and the shaping is easier. Some makers 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 11 to 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.
The plate thickness data given here and in Hutchin’s papers 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 (length wise) 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-based 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.
Assembling a violin.
Stewart MacDonald (StewMac) sell various violin items, and that includes a 4/4 violin ‘kit’. The assembly instructions are rather useful too: they can be found here, and show how to insert purfling, the shape and position of a bassbar and how to attach the neck and fingerboard.
Physicist "Jack" Fry, with the help of violinist Rose Mary Harbison, has been working to rediscover the legendary sound of the Strad. 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. There is a video of Jack’s lecture (1 & 1/2 hrs.).
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.
Footnote 1: This is/was a problematic belly with very low Mode 5 ring tone without a bassbar. As you can see it is poor and rather damaged ‘spruce’ wood that looks chemically treated, and is prone to splitting. Odd how this is my best-sounding violin.