Thursday, September 28, 2017

Constructing a Bergonzi violin mold from scratch

Here's a very detailed example of classical violin geometry in application.   Here, the shapes are all created by simple compass arcs and straight lines.  And every part is sized with simple ratios from other parts. 

It's a rather dense presentation to wade through.  But it shows the complete design process behind a violin form by Stradivari's apprentice Bergonzi.   This gives the shape for a form that Bergonzi cut in a walnut board, approximately 14mm thick.  Using this inner form, Bergonzi bent the ribs for many of his wonderful violins.


I'll put three stages of work in each picture.
The first illustration shows adding the long arcs to the center line.    In this case the lower long arc has a radius equal the full length of the mold.  While the upper long arc has a radius of 2/5 the mold length.    These aren't unusual choices compared to other classical molds or instrument outlines.   The common choices for the lower long arc are radius of 3/5, 4/5, 2/3, or full body length.  For the upper long arc 1/3 or 2/5 body are most common.  3/5 body is also sometimes seen.
The second drawing shows setting the bout widths for the mold.  In this case, the lower bout is 4/7th the mold length, the center bout 2/7th, and the upper bout is 4/5th the lower bout.   Again, these are very common classical choices.

For this mold design, Bergonzi also worked with the anticipated outline size in the upper bouts.  To get requires estimating the inset.   Though not exactly so, the mold line tends to approximate the line 3 purf widths in from the outline in almost all cases, which is the inset.   There is no way to be certain of the inset calculation Bergonzi used in this mold.  But the most common choices my research has found in classical work are 1/90, 1/80, and 1/100 the body length.  I've used 1/90th in this case as it is probably most common, and sort of mid way in the range of choices seen most frequently.   Even if he actually used another ratio, this should come rather close in practical application.   The long arc for the outline is also drawn in as it will be needed.
The 2nd picture shows another three stages of the construction.  The first shows drawing the main vesici constructions in.   The lower vesici is based on dividing the mold width in equal thirds, a 1::1::1 vesici if you will.   The vesici is drawn tangent to the planned width lines and to the long arc.    In the upper bout area, a 2::1::2 vesici is constructed, but based on the planned outline width instead of the mold width.  This is why we needed to anticipated the inset. 
The middle drawing here shows how lines through the vesici centers provide bounds for the long arcs.   The final drawing in this panel adds in the upper vesici for the mold.

The first drawing in this third panel shows setting the corner levels.   In the upper bout area, this is set as 1/3 the mold length.   In the lower bout area, this is set by a 5:7 proportion with the mold width.   It's also common to see the lower corner set by 2/5 the body length, or 3:4 or 4:7 ratios used with the bout widths for either the upper or lower corner levels.   Some other ratios are less frequently seen for corner levels in classical molds and instrument outlines.
The middle drawing shows the main circle diameter for the center bout curve set as 6/5th the lower bout width.   This is unusual.   In most cases this diameter equals either the upper or lower bout.   Apparently Bergonzi wanted a flatter curvature through the center bout, thus resorting to this recipe for a wider diameter.
The last drawing in this panel shows sizing for the inner corner circles.   In Cremona molds, this particular sizing as 1/5 the main circle for the upper corners and 1/4 for the lower is extremely characteristic.  But it isn't normal in the instrument outlines.
This panel shows the work to place the corner circles in this mold. 
In the first stage, arcs are drawn down from the main bout lines to intersect the lines for the corner levels.  The arc in the upper bout is based on the outline width, in the lower bout on the mold width.    The second stage uses arcs of the same radii as the corner circles to locate the centers for the corner circles.   The last draw just completes the work on the other side of the mold.
The hard work is done now.  The first two drawings of this panel show adding in the planned corner circles, and then the main circle to give the center bout shape.  In the last drawing of the panel, risers are add from the bouts up toward the corners.   In this mold, Bergonzi has used arcs from the centers of the upper and lower bouts to construct the risers.  But risers centered on the vesici centers or other logical points on the bout line aren't uncommon in classical work.
This last panel of the construction shows setting the 2nd lines for the corner block notches.   In this case, Bergonzi has set these using divisions from the corner work.   His choices here are not the most common, but also not unique. 
This drawing highlights the mold outline achieve from the geometry construction.
And finally, the construction is compared to Bergonzi's actual form.   

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