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’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 to show where to thin a front plate (the belly) to reduce either Mode 2, Mode 5 or both frequencies. 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.
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!
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.