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yapkv

recreating Stradivarius form

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I have been reading works by Francois Denis, Geoffroy Mercier, and Sergei Muratov from their website and tried to understand their methods in generating the violin form. I wish to share some of my findings here with all the maestronetors.

Before I start my grumbling I wish u all to excuse my lousy English. I haven't been writing English for quite some time :)

After trying to understand how Francios Denis, Geoffroy Mercier and Sergei Muratov come out with their methods of generating their violin forms, I realised there are quite a bit of similarity, that is the use of golden division. Golden Division can easily be achieved by the use of a compass and a ruler. I tried to study Geoffroy's methods and I realised that his methods may be the closest way how Stradivari may have come out with the violin shape. I haven't got a chance to read Francios Denis book but from the flash demo from his website I found that Denis uses a lot of division of 4,5, 7 or 9 and i found that may be too tedious for Stradivari without precision measurement tools and a bit of calculation. Sergei Muratov works are fun to read, and does provide a lot of information about different moulds, but his method of using spirals to generate the mould doesn't seems too convincing neither. There are some similarity between Francios Denis and Geoffroy Mercier works especially using circles and arcs to generate the upper and the lower bouts.

Combining works done by these three masters, I came out with a method that hopefully resemble one of the strad mould. I would like to share this with everyone and hope that someone can verify that too.

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Golden division

Golden division is widely used in creating the violin form.

There are two ways to generate golden division: externally divided and internally divided.

Here is an example of a external golden division:-

external-golden-division.png

Let's say we want to find out the external golden division of line AB,

Step 1. Create a square from line AB -> ABCD

Step 2. Find the mid point of AB -> point E

Step 3. Using a compass, with point E as base point, draw arc from C.

Step 4. Extend line AB, the intersection of arc from step 3 -> F.

FA : AB = Golden division.

Here is an example of a internal golden division:-

internal-golden-division.png

Let's assume PQ is the line that we want to divide using golden division

Step 1. Find out half of length of PQ and draw a perpendicular line PR,

where PR = 1/2 PQ

step 2. Find draw line QR and form a triangle

step 3. Using a compass, with base at R and radius = PR, draw an arc cutting line QR, the intersection = point S

step 4. using the compass, with base at Q and radius = QS, draw an arc cutting line PQ, hence the intersection point T

PT:TQ = Golden division

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I shall put in all the post with pictures first and explain them later...

Deciding how wide the lower boat is

Most of the strad has lower bout of 206mm, minus off the rib thickness and the overhang, we can roughly determine that the lower bout of the mould is 200mm. Using a compass, draw a circle of 200mm with the center at the x-axis.

p01.png

On the same x-axis, draw another circle that cut through the center of the first circle.

I am not sure if this is conincident: by measuring between the intersection of the two circles, it comes out to be about 173.25 + 173.25 = 346.5mm

p02.png

Draw a circle with base at M and radius CM. Now we have point A,B,C,D and X,Y, with M as the center.

p03.png

Determine where the lower bout is

Draw a arc with base at M, and radius = AM or MB, cutting the y-axis or line CD.

We name this point G.

p04.png

Draw another two circle, with base at M, and radius = 1/2 CM and 1/4CM

p05.png

Locating the upper bout

The upper bout, Point F can be located by external golden divison of MD.

P06.png

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BTW, all these images were generated by using CARMETAL.

p07.png

Finding point J and K

Point J can be obtained by using internal golden division of line of 1/2CM.

Point K is basically 1/2 of FD, or by external golden division of GD (not shown here).

P08.png

The following is from Geoffroy work:-

Draw a line from Point C to Point X and Y.

p09.png

Locating point N

With base at point D, draw an arc from 1/2 XM or 1/2 MY. The intersection of the arc = N

p10.png

It is commonly known that the upperbout is 4/5 of the lowerbout. However I couldn't find any way to divide a line into 5 parts by using compass only. It may be coincidence that by measuring length NM x2, and use it to minus off the width of the lower bout, it comes pretty close to the width of the upper bout.

A horizontal line is drawn at point N, and point N1 and N2 is obtained either by the intersection of this line and the line CX and CY, or just by drawing an arc with base at N and radius = CN and get its intersection with the horizontal line.

P11.png

Center bout

The center bout is obtained by drawing an arc with base at N1 or N2.

The question is, how long should the radius be?

After a few trial and error, I came to the conclusion to use the point which is the intersection of the arc we drawn to get the point F and the two big circle we drew at the beginning. Using a compass with base at N1/N2 and measure the pencil to this point and draw the arc that form the center bout.

P12.png

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The following is similar to how Denis and Geoffroy draw the upper bout and lower bout outline.

Lower bout

With base at point F, draw an arc at point D using a compass.

p13.png

Setting the compass with radius = GD, put the pencil at the widest part of the lower bout and draw two circles that form the lower bout outline.

p14.png

Upper bout

Similarly, with base at point M, draw and arc at point C using a compass.

p15.png

Setting the compass with radius = CF, put the pencil at the widest part of the upper bout and draw two circles that form the upper bout outline.

p16.png

p17.png

Here we have the rough shape of the violin without the corner. Not that difficult isn't it?

p18.png

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Just to recap how the outlines are formed...

P19.png

p20.png

Corners

I do not have much luck in finding how exactly the corners are formed. Most of the followings are just my guesswork.

Lower bout corner curve

1. with base at K, draw an arc from the widest part of lower bout

2. with base at G, draw another arc from 1/2 MX or 1/2 MY

3. From the intersection point of the above arcs, draw an arc that flows smoothly with the lower bout outline

p21.png

Center bout lower corner curve

Ok this is a bit of guesswork.

[method 1]

1. with base at G and radius of GN, draw arc near the lower corner.

2. with base at N and radius of FN, draw arc near the lower corner again.

3. with base at the intersection of the two above arc, draw arc that continue from the center bout outline until it meets the other arc.

p22.png

[method 2]

similar to method 1, but obmit step 2 of method 1, and take the intersection the arc and the straight line that defines the width of the upper bout as the center.

p23.png

Center bout upper corner

1. Draw two straight line 45 degrees from point F and point K.

2. Draw an arc continuing the outline of the center bout with the intersection point of the above as the center of the arc.

Upper bout corner

1. with base at point J, measure from this point to 1/2 MY, draw an arc

2. from point N, draw a line to the intersection of horizontal line at J and outline of the centerbout upper corner, and get the intersection point

3. with base at the intersection point, draw an arc that extend from the upper bout outline.

p24.png

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p25.png

p26.png

p27.png

p28.png

Does it look like a strad mould? may be not in this diagram, due to the fact that the outline generated here is too thick.

The above method may not fit all the strad outline. "Titan" may be one of them that fits.

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It seems you did a lot of work there and are really interested in geometry.

To be honest, I didn't read it all.

Some points:

You really should read Francois Denis' book. It has not only the construction for the Stradivari molds, but it also covers the Renaissance math/architecture background.

There is also a chapter about the golden number and why it may be overrated...

The relations he uses can all be created with a compass/ruler.

Unfortunately the form you have drawn doesn't look even close to any stradivari mold. At least to my eyes.

Matthias

Edit:

Reading through my post, I realised, it sounds a bit negative. Please take it as constructive criticism and don't be discouraged.

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A tracing or rubbing directly from a Strad would be nice. :) I do not doubt that the golden section can be used to describe anything if you use enough of them.

The end result doesn't seem quite right.

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My thanks as well for sharing.

And I am amazed that we have participation from Kota Kinabalu, Sabah, Malaysia.

That's almost as far away as Wyoming.

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FWIW F. Denis does not restrict himself to the golden section, and in fact considers it somewhat over-rated in terms of relevance to period practice.

Since long Strads were made before Stradivari's "golden" period, I would assume the "golden division" was not applicable to the design; and there was no "simple digital ratio" in proporation either. I would guess that Stradivari drew the long model shape by free hand, or simply modified the previous design by lengthening here and shortening there.

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Since long Strads were made before Stradivari's "golden" period, I would assume the "golden division" was not applicable to the design; and there was no "simple digital ratio" in proporation either. I would guess that Stradivari drew the long model shape by free hand, or simply modified the previous design by lengthening here and shortening there.

Hi David,

If I remember right, Denis makes a good case for a geometric/proportional construction for the long form. I assume you're joking about the golden division in Stradivari's golden period? :)

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Since long Strads were made before Stradivari's "golden" period, I would assume the "golden division" was not applicable to the design; and there was no "simple digital ratio" in proporation either. I would guess that Stradivari drew the long model shape by free hand, or simply modified the previous design by lengthening here and shortening there.

I think Mr. Denis makes the point in his book that by the time Strad came around, strict adherence to proportion and ratios was on the decline, and measurement by numbers and rule was beginning to usurp the old ways of design.

But, what is probable was that he began with the grand Amati, ( as did most all of them ) and modified that to fit his ideas, by adding or subtracting a 'point' or two here and there. So I think you are right in your last sentence David, he modified to what he will.

This may be why trying to recreate Strads form following strict Proportional rules ( golden or no ) usually ends up a bit short.

To find a patten that is re-producable using strict proportion and ratio, you really got to go back to the source of all our great inspirations, the house of Amati.

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I think Mr. Denis makes the point in his book that by the time Strad came around, strict adherence to proportion and ratios was on the decline, and measurement by numbers and rule was beginning to usurp the old ways of design.

Yes, when Patrick Robin was here he blamed Mr Strad for moving away from the "old" proportional methods and getting us more into a measurement-based system.

RE the OP, I haven't worked through it carefully but it seems similar to the Denis method which I have just started to play with recently. I have drawn out an Amati violin and a few violas, and I'm particularly excited by its applications to viola design. For example I was able to draw up the Andrea Guarneri viola, and then by tweaking one measurement I could make up a new model with a slightly shorter body length (16 inches). Once you get used to the technique it only takes 15 mins to draw yourself up a new model.

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Any other issue aside, the immediate problem I see with Yapkv's drawing is that the upper and lower bouts are short one circle, each--there should be a junction to a different curve right at the widest part of both upper and lower bouts. Cremonese violins have a slight discontinuity there, and a different curve above and below those points. There appears to be a problem with the shape of the c-bouts and corners, too, less easy to specify.

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You could just photocopy all of Strads forms, they are all in a very big book somewhere.

Then you can take the photocopy (life size) and stick it to a board and prick around it.

Cut out the board and all the others, then proclaim yourself a genius.

However, you'll then realize that the original Strad forms are not totally symetrical, so you'll go bonkers for a week and make your own nice new symetrical ones instead.

Cheers.

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Is it possible to simply trace the Stradivari "P" form in the museum and sell copies of the tracing?

I'd buy...

Yes, as Ben notes, there are two books you could buy. One is Denis' book, which has laminated "placemats" of all of the molds that you could work from. The other is Stewart Pollens' book, which has life-size photos of each mold.

http://www.amatibooks.com/cgi-bin/bookfind.pl?file=13900016

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I haven't done the math. Frankly, I have yet to wade through Denis' book, which is wonderful and dense, and doesn't mesh well with my math handicap. The book, and its conclusions, are great, though.

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I have to ask this.

Why not simply copy an existing Strad, or is that considered too easy?

Why would anyone feel that they had to "re create" something that already exists, and where much of the design may well be the end result of purely aesthetic considerations?

You could even alter the design, if there was some particular that you didn't like.

Is this like the mountain you have to climb simply because it is there?

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