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Geometría fabrorum


Joaquín Fonollosa
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On 08/18/2019 at 7:07 AM, Joaquín Fonollosa said:

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On the design of the instruments at the time of Stradivari, Roger Hargrave writes:

“(Stewart) Pollens suggests that the absence of geometric construction marks in Stradivari molds is due to the use of paper templates. In the Stradivarian Museum collection, there are several folded paper templates, guitars, lutes, pochettes, violas da gamba and violas. Those templates, like the molds, have no obvious construction marks on them. Pollens concludes that the molds were probably marked using folded sheets of paper, which were cut to create a symmetrical template. The use of paper templates may well have been the method with which empirical adjustments were made. From a given standard design, a slight alteration with the scissors could have created a smaller violin, a larger one, a wider model, a long model and so on. The templates may even have been responsible for accidental variations; At a time when paper was an expensive product, it is likely that a modest slip with scissors would have been more tolerated than today. It is certainly reasonable to assume that empiricism, rather than a rigid geometry system, typified Stradivari's design technique, and that what was good for Stradivari was probably also good for Del Gesù. ”

 

I thought Strad's  bend shapes followed the shape of bent ribs. 

But that must be too simple.

A.jpg

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But bent ribs and spirals can follow the shapes, just not generate them through simple finite consistent patterns of choice.

 

French curves and bezel curves are other examples that can follow the shapes but can't generate them from simple finite choices, nor fit the many variations of the generations of historical examples in a simple consistent way.

Also, a workshop approach requiring only dividers and straight edge fits the broad cultural context.

Like with boatbuilding, the concept of 'yar' or 'fair' smoothing between geometrical determined control points and curve shapes does have a place in the plate arching.  And this concept of smoothing is legitimately and historically based on bent splines.

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On 8/20/2019 at 3:17 PM, Joaquín Fonollosa said:

no estoy de acuerdo en que el círculo sea la base del diseño de violines

Speaking of outlines shapes, your "spiral" is  more what the Ancients called a "volute" which means a serie of circles 

Spirals need a continious change of a radius value what typically you get when you round a rope on a round stick

rather than volutes have a discret serie of radius typically what you get when you round a rope around a polyedre shape

the spirale is what you get when the polyedres have an infinity of sides

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47 minutes ago, francoisdenis said:

Hablando de formas de contornos, su "espiral" es más lo que los Antiguos llamaron una "voluta", que significa una serie de círculos. 

Las espirales necesitan un cambio continuo de un valor de radio que normalmente obtienes cuando rodeas una cuerda con un palo redondo

en lugar de volutas, tenga una serie discreta de radio, típicamente lo que obtiene cuando rodea una cuerda alrededor de una forma de poliedro

la espiral es lo que obtienes cuando los poliedros tienen infinidad de lados

Oui monsieur, vous avez raison, la spirale est formée de quartiers de circonférence selon le système mis au point par Alberto Durero, et constitue une approximation de la spirale logarithmique.

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1 hour ago, francoisdenis said:

Hablando de formas de contornos, su "espiral" es más lo que los Antiguos llamaron una "voluta", que significa una serie de círculos. 

Las espirales necesitan un cambio continuo de un valor de radio que normalmente obtienes cuando rodeas una cuerda con un palo redondo

en lugar de volutas, tenga una serie discreta de radio, típicamente lo que obtiene cuando rodea una cuerda alrededor de una forma de poliedro

la espiral es lo que obtienes cuando los poliedros tienen infinidad de lados

Yes sir, you are right, the spiral is formed by quarters of circumference, according to the instructions of Alberto Dürer, and is an approximation to the logarithmic spiral. But the resulting curve must be referenced to the point towards which it converges. At that point I call Him the Eye of God. By joining these points in the upper and lower module we obtain the position and length of the harmonic bar.

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10 minutes ago, Joaquín Fonollosa said:

Yes sir, you are right, the spiral is formed by quarters of circumference, according to the instructions of Alberto Dürer, and is an approximation to the logarithmic spiral. But the resulting curve must be referenced to the point towards which it converges. At that point I call Him the Eye of God. By joining these points in the upper and lower module we obtain the position and length of the harmonic bar.

So using circles... you should say that circles are the basic of your outlines .Why do you state the opposite?

What is the issue? What do you want to defend here? 

You  could advantageously take profit  that "volute" (or more exactly "scotia" which the form you used actually), are easy to draw which is not the case of the oser curves

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2 minutes ago, Joaquín Fonollosa said:

Anyway I renew my offer If you have a complet and free access documentation to your approach

I will add it to my online documentation (under construction)

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Again, tracing shapes is not generating them.

And,  for historical evidence, we have hundreds of existing Cremona instruments, from many families and generations of makers.  A system claiming historical merit must generate the actual shapes of this whole body of evidence, with the differences resulting in straight forward sensible ways.

Careful examinations have shown simple circle geometry and ratio methods running through this whole body of examples. And the methods are simple, consistent, and fully account and accurately account the whole range of the actual examples.

 

 

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4 hours ago, francoisdenis said:

Entonces, usando círculos ... deberías decir que los círculos son la base de tus contornos. ¿Por qué afirmas lo contrario?

¿Cual es el problema? ¿Qué quieres defender aquí? 

Usted puede sacar provecho de manera ventajosa de que la "voluta" (o más exactamente "scotia", que es la forma que usó en realidad), es fácil de dibujar, que no es el caso de las curvas oser

I mean that, for me, circles are not a base because they don't give me details that my double spiral gives me. Tell me how you determine with circles the position and length of the harmonic bar, or the width of the bridge base, or the distance between ff on the bridge line.

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1 hour ago, David Beard said:

Circles plus ratios.

Ratios give those things.  Though the bar we use now differs from the older Cremona bars.

And the bar you show is neither in a current or old standard position or width 

I agree , following your proposition the bassbar seems to keep the relation between Lb and UB  (parallel to the tangent to LB and UB)

It is not the common ratio used in violin making (I don't know where you get this ) 

in other hand you find this specific ratio in the viol making

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On 8/20/2019 at 4:02 PM, David Beard said:

You do not present this clearly or consistently.  Often you veer toward statements that claim more than just a decorative playfulness.  You often appear to be claim to create violin shapes in this way, merely than just creating a visual jazz from them.

Muratov already made exactly the claim for spirals.

As this has been hashed through thoroughly elsewhere, I will not go into depth again.

Suffice to repeat here, families of spirals, and families of bent splint shapes are both sufficient to trace the shapes of classical Cremona violins to any degree of aproximation you choose, but will require an increasing number of spirals to continue improving the aproximation.

Circles however are the concept behind these Italian shapes. Only a finite number of circles are needed to idealize the design beyond the accuracy of the handwork.

Moreover, simply patterns of the circle choices can be observed running consistently across all the generations of Classical Cremona making.  And the slow evolution of the traditional choices can be observed.

Guides of circle geometry and aimple ratios govern all the features very thuroughly.  And the system they used generates the shapes through making simple choices within traditional options.

All the research for was done comparing the choice generated shapes directly to classical examples.  A very large number of instruments examples running across all the makers and generations of Old Cremona was used in the research.

 

That said, I do enjoy your work on a decorative level.

 

rightly said ,nothing to add

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On 08/21/2019 at 12:26 PM, David Beard said:

But bent ribs and spirals can follow the shapes, just not generate them through simple finite consistent patterns of choice.

 

French curves and bezel curves are other examples that can follow the shapes but can't generate them from simple finite choices, nor fit the many variations of the generations of historical examples in a simple consistent way.

Also, a workshop approach requiring only dividers and straight edge fits the broad cultural context.

Like with boatbuilding, the concept of 'yar' or 'fair' smoothing between geometrical determined control points and curve shapes does have a place in the plate arching.  And this concept of smoothing is legitimately and historically based on bent splines.

The traditional and successful way of making violins is to copy  previously made good ones.  

I believe Strad's paper outline patterns were tracings of previous violin rib structures which were then used for shaping his molds.

If he wanted something a little different a simple freehand sketch folded over i cut out was all that was necessary.  Or a sketching was done directly onto the mold for reshaping which is seen on one of his molds.

Freehand sketching is a traditional method for generating completely new shapes.  Sometimes these can be inspired from the shapes from bent splines, French curves, mathematical equations etc.

For example, my f hole shapes were inspired from the accidental bend shape of a garden hose laying on my lawn.  From this concept freehand sketches were made.  The shapes were repeatedly resketched and rescaled until I got the length and width and areas I wanted along with a graceful shape.

No compass or straight edge constructions were used.  No "simple finite consistent patterns of choice" was necessary.

 

Garden hose f hole.jpg

No 33 viola, No 31 violin.jpg

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My understanding of Sergei Muratov's book is that he was mainly interested in how different spiral forms could be applied to known instruments. But at the end of the book he outlines how early makers used splines along with  ratios to generate a form outline.

I've successfully made forms using this method. I found the best thing to use was carbon fibre, of different diameters, to generate curves for the Cs and upper and lower bouts. I would bet that early makers would have used gut strings in the same way. He also showed how arching shapes followed spiral configurations. But my experience making arching templates tells me that using splines is not practical or necessary.

 

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I've used both thin music wire and real small diameter carbon fiber rods for outline shape bending experiments.  Both work equally well for generating the  outlines but the black and less light reflective carbon fiber is better for making photographs.

French curves use various mathematical spirals.  They have differing rates of curvature changes to give different tight to long shallow curve shapes sometimes with reversed direction curvatures for inflections.  I think they were invented as a drafting aid  to avoid the hassle of generating a bunch of spirals all the time. But I believe they were invented after the time the violin shape had already been established.  They (and their older spiral origins) can match the smooth outline shapes of violins more closely than a series of a few constant curvature circles.

Quite some time ago (30y ?) violin maker Fred Nitchy thought the violin arches could also be generated with bent sticks (splines).  I don't know if he ever published his work.  Attached is one of his back plate arch illustrations.

 

Fred Nitchy's back plate-1.jpg

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My arching experiments result in a different result than the Nitchy diagram shows. It looks as though there is not much geometry there. With both the uppermost and lowest arches the inflection point is about 13-15 mm from the edge with nearly all of the arch convex. At the narrowest arch position of the waist the same applies. But at the bridge and corner arches there is a longer recurve. However the arching shape stands alone as all of the inflection points should be arranged along a regular arc both in horizontal and vertical position.

 

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