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Geometría fabrorum


Joaquín Fonollosa
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Joaquín!

Estoy seguro de que cuando los antiguos crearon el primer violín, lo diseñaron siguiendo algún método parecido al que tu has creado y los siguientes simplemente heredaron el diseño haciéndole retoques "a ojo" para probar cosas nuevas. 

Por lo tanto es prácticamente imposible que todos las formas entren en un sistema de diseño geométrico. 

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19 minutes ago, Riodifirenze said:

Joaquín!

Estoy seguro de que cuando los antiguos crearon el primer violín, lo diseñaron siguiendo algún método parecido al que tu has creado y los siguientes simplemente heredaron el diseño haciéndole retoques "a ojo" para probar cosas nuevas. 

Por lo tanto es prácticamente imposible que todos las formas entren en un sistema de diseño geométrico. 

Así es. No todas las formas pueden entrar en el mismo diseño geométrico. Ni siquiera todas las formas se corresponden ni con curvas aúreas ni con círculos. En cualquier caso, un violín visto desde el exterior, tomando medidas externas, me dice poco. Pero de alguna manera, la normalización impuso el criterio único. Y el propio Stradivari asentó su standar y la fabricación en serie. Más tarde, el negocio consistió en copiar modelos.... Y en esas seguimos, y casi nadie se plantea cómo lo hicieron. 

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In this, history seems to disagree with you.  While there were some peripheral Italians making from outside these traditions, it appears that whole almost five centuries of bowed stringed instrument development in Northen Italian was unified under a broad tradition, approaching all the design using circle and line geometry and simple ratios.  ( see Coates)

These basic tradition of design approach give structure, but remain flexible enough to cover all the lute family explorations of N Italy up into the second half of the 18th century.

Different regions and families developed their on variations on the choices made within the tradition, but remain firmly in the genersl principles.  

On same version of these methods covers the full range of variation in Cremona classical work.  It covers stout dancr master violins, lira, violins, violas, cellos, and yes, all the molds.

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3 hours ago, Joaquín Fonollosa said:

Me encantan sus argumentos, señora. La burla siempre fue un recurso fácil y expeditivo. Y, en la plaza pública, muy efectivo. Gracias y enhorabuena. 

Que encantador Sarcasmo español! Mi comentario fue sobre cuán cerca de la magia siempre parecen llegar estas discusiones.  :)

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20 hours ago, MikeC said:

¿Es solo una expresión artística? En realidad no se puede diseñar una forma de violín de esta manera.    

por cierto, todos ustedes saben que estos recortes de medio círculo tienen un propósito, ¿verdad?   

 

recortes.png

 

Ten cuidado con ese pentagrama ... 

No, no es solo una expresión artística. Es el resultado de supurponer sobre un molde la plantilla de medida con las diagonales de los rectángulos trazadas. Se intersectando formando esa figura en el módulo superior. 

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2 hours ago, David Beard said:

In this, history seems to disagree with you.  While there were some peripheral Italians making from outside these traditions, it appears that whole almost five centuries of bowed stringed instrument development in Northen Italian was unified under a broad tradition, approaching all the design using circle and line geometry and simple ratios.  ( see Coates)

These basic tradition of design approach give structure, but remain flexible enough to cover all the lute family explorations of N Italy up into the second half of the 18th century.

Different regions and families developed their on variations on the choices made within the tradition, but remain firmly in the genersl principles.  

On same version of these methods covers the full range of variation in Cremona classical work.  It covers stout dancr master violins, lira, violins, violas, cellos, and yes, all the molds.

I think you're using circular reasoning by referencing Kevin Coates ("Geometry, Proportion and the Art of Lutherie", Clarendon Press, Oxford, 1985).  

Coates made drawings of various old instruments using his circle drawing technique.  He then superimposed these circles on his drawings and wow--the circles match the outlines of his drawings!  Thus showing the reader that the instruments must have been originally designed with circles.

He would have been more honest if he superimposed his circles onto photographs of the instruments.

I've read the book and attached is a review by Mark Lindley

Review_of_Kevin_Coates_Geometry_Proporti.pdf

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Not referencing him as proof. His book profides merely a broad casusl survey of the circle geometry in a wide range of instrument.

I'm and still several years away from presenting my research in a full and formal way.  But for my own satisfaction, I've spot check the basic principle in various instruments outside my main focus on Cremona work.  

Compass work and divider work with ratios were normal things at the time.  It really is very simple and straightforward for them to have worked in these methods. And the exisiting evidence shows they did.

 

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2 hours ago, Marty Kasprzyk said:

Creo que está utilizando el razonamiento circular haciendo referencia a Kevin Coates ("Geometría, proporción y el arte de la Lutherie", Clarendon Press, Oxford, 1985).  

Coates hizo dibujos de varios instrumentos antiguos utilizando su técnica de dibujo circular. Luego superpuso estos círculos en sus dibujos y wow, ¡los círculos coinciden con los contornos de sus dibujos! Mostrando así al lector que los instrumentos deben haber sido diseñados originalmente con círculos.

Hubiera sido más honesto si superpusiera sus círculos en fotografías de los instrumentos.

He leído el libro y adjunto una reseña de Mark Lindley

Review_of_Kevin_Coates_Geometry_Proporti.pdf Obteniendo 1.46 MB · 3 descargas

Esto es muy clarificador. Gracias.

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The review alludes to the locations of the circles not always being obvious.  This is undoubtedly also way he does not more consistent show ratios.

This broad N Italian tradition approach is not about convining the volition the makers' design work, but rather about structuring the design, and giving a mechanism to repeat and vary designs.  So through the tradition, there is a combination limits and liberties. 

In many instances, a maker will have a choice of the natue 'will I calculate this from the margin or from the edge.' Etc.  This kind of choice was very much left as a freedon for the maker in each instance.

So for example, for upper and lower bouts in violin family instruments, a vesici construction of overlapping circles was always used in the Cremona tradition.  No one broke this rule. And the centers the vesici circles always divided the bout line in some simple proportion, like 1:1:1 or 2:1:2.  No one every broke or ignored this.  But, they did have some freedom in choosing the ratios from instrument to instrument.  So a violin's lower bout might be made in a 1:1:1 vesici proportion for the last ten instruments. But the maker was still free to use 4:3:4 on the next 5 violins if he wanted to try that slightly rounder choice.

There was even greater freedom for the maker to calculate his vesici from the outer edge or from the purf line at will.

 

So these kinds of liberties add a bit of conplication. Nevertheless, once you know the traditional patterns, it isn't difficult to work backwards and find the geometry and ratio choices used in any example made within these traditions.

 

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The golden section in violin making

 

Excerpt from the lecture: The golden section – by Wolfgang Schiele

 

At the beginning there was the color red. It is the first color that was ever named by mankind. In some languages the word “colored” is identical with the word “red” as in Spanish “colorado” for example. God as the light figure is the origin of the color. Red means blood as well as fire; blood is the vital force and in many cultures it is supposed to be the place where the soul is situated. In Hebrew, the words blood and red come from the same source: red is called “dm” and blood is called “dom”. To dye or paint something red means the revival of life. The most used color in the varnish of ancient Italian stringed instruments was red as well, which underlines the symbolical reverence of God.To music lovers and connoisseurs alike the question arises how, in the early baroque era, the “perfect” shape of the violin could have developed. Perfect, on the one hand, because it survived unchanged all efforts at improvement during 19th and 20th centuries; perfect, on the other hand, up to the present day as by craftman’s skills highly esteemed work of art as well as musical instruments with exceptional qualities have been created. Following, the two basic requirements will be described, which in their amalgamation where responsible for the creation of work of art in architecture, painting as well as instrument making.Searching to (re-)construct the shape of the violin, I have deduced an ideal design from instruments by the violinmakers Nicolo Amati, Andrea Guarneri and Antonius Stradivarius from around 1650 1670. Starting with the overall length of the instrument, all its measurements are in specific proportional relation to each another.

 

The Cremonese ell, which was the existing measure since the 11th century in this North Italian region, is used as basic measure. It is still visible carved in stone on the clock tower of Cremona. For the design, the geometric elements that come into use are the circle, the equilateral triangle, the hexagon and a square in a semi-circle that demonstrates the Golden Section on the diameter in a very special way. These elementary elements of geometry have been known for 5,000 years. They became the basis and part of a Greek philosophy regarding the view on harmony and cosmos. Harmony in their view was not only a valuable, nice and useful quality but also an objectively well founded one. By the consolidation of the Pythagorean science of numbers, there was in addition the discovery of the reciprocal equivalent of intervals and numbers. In the Middle Ages, these geometric elements represented symbolic meanings: the circle stands for the heavenly or divine unity; the equilateral triangle represents the Trinity on different levels, e. g. father, mother and son; the triple nature of the universe; heaven, earth and man; Man as body, soul and spirit. The symbolic meaning of the square is the earth as opposed to the skies for the circle. The hexagon, the double triangle, the Star of David, indicates that every true analogy has to be applied inverted, as above so beneath; it is the unification of opposites as male and female, positive and negative. In Christian symbolism it means: perfection, completion, the six days of Creation. During the renaissance era, there were many studies of and theories about proportions of humans. It was the time when people considered the human being to be God’s image, the godlike perfect. Consequently, architecture aimed at developing a clear and harmonious relationship between all parts of a building and to base them on both human dimensions, as divine proportions, and on the ideal proportions derived from the Golden Section.

 

Because humans appear to be “designed” based on the golden section, and also because nature makes extensive use of the same ratio, it seems conclusive that humans too find exactly this ratio of proportions harmonious, even simply from an optical standpoint. For instance, all pentagonal five-leafed flowers, as well as hexagonal honeycombs or snowflakes are directly related to the golden section. Consequently, buildings, pictures and sculptures based on these laws, whether consciously or unconsciously, are found to be balanced.

 

In 1509, the mathematician and theologian Luca Pacioli introduced the term “divina proportione” for the first time as the title of a printed work, which he used to define the golden section. “Divina proportione” for him stood symbolically with its three parts for the holy trinity. Leonardo da Vinci (1452 – 1519) is said to have coined the term “sectio aurea” (golden section), others claim however that this term only originated in the 19th century.During the reform of the Catholic Church in the 15th – 17th centuries, geometry and religious development met. For the praise of God and for the celebration of ceremonies as encouragement for the attractiveness of the Christian Church, more and more music appeared in church during the renaissance. In the beginning, there was only vocal music and then the organ and stringed instruments were added, which subsequently led to a higher demand for instruments. I find it highly exciting that, given this background, it is possible to completely reconstruct the shape of the violin solely by geometric means. Also the design and position of the f-hole as it is known from Stradivarius can be reconstructed; even the “third dimension” – the height of the ribs, back and top as well as the positions of the bassbar, soundpost and bridge – can be inferred. All these constructed dimensions correspond to the measurements we find on historical instruments. And the constructed positions of bassbar, soundpost and bridge correspond to those that are good positions by today’s experience of sound.

 

How could such common and approved knowledge of violin making vanish? The explanation lies in the general political development of the North Italian region. After two years of famine from 1628 to 1630, the plague and the taking over of Northern Italy by the Spanish during 16th and 17th centuries, with the end of the Spanish war of succession Cremona became Austrian in 1714. All this led to a deep economic depression from 1730 to 1750; only with the beginning of the 19th century the Industrial Revolution starting in England would eventually change the economoc situation. Unfortunately, the end of the three great violin maker dynasties fell exactly within this period: Hieronymus II Amati died 1740, Antonio Stradivari 1737, Omobono Stradivari 1742, Francesco Stradivari 1743 and Guarneri del Gesu in 1744. Carlo Bergonzi, the last violinmaker who can be considered to have been same level as his predecessors died in 1747. As to why the work of his son Michel Angelo does not show the knoweledge and the qualities of his fathers work we can only speculate.

 

As far as I know, the relation between geometric elements, proportional ratios and the used color to the symbolic and religious meanings has never before been pointed out. The power of geometry makes it obvious that the shape of the violin cannot be improved as it has been tried many times over the past several hundreds of years. So if one can take controlled use of all the sound-affecting components like the proportion and dimension of an instrument, the choice of wood, the form of the arching with corresponding thickness, the sizing of the wood and the varnish, then the result of contemporary instrument making is a very valuable one for a musician.

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Yes.  Everyone loves the idea of some single magic key!  And why not.the golden section?    It is a number that was know at the time, yet still somewhat special and exotic.

And, it's popular today in New Age kind of way, along A 432, and the number 420.

 

Certainly, as I began my research I was prepared to encounter phi.  I tested for that relation in countless circumstances.

But, as it turns out, the most accurate undersrand of Cremona design develops from leting go of that fetish and trusting just to simple integer relationships.  Phi is just not the Cremona way, not if you cleave to the evidence instead of current fashionable desire.

Nor are the integer ratios used in Cremona work special or meaningful.  I was also prepared to perhaps find them favoring musical ratios.  But the ratio actual present in execiting the Cremona work are very flat footed.  There just a way of measuring, relating, and locating things.

 

 

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Si bien podríamos remontarnos muy atrás hasta los antiguos griegos.......Y tener en cuenta todas las consideraciones filosóficas en torno a ideas.......La música, la geometría y la arquitectura comparten orígenes comunes y principios comunes. Para mí no hay contradicción entre procedimientos si el resultado es similar. Todos estos conocimientos son muy antiguos, no se trata de nuevas modas.

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Yo tengo un procedimiento para dibujar, partiendo de cero, un molde completo. Por supuesto, no puedo afirmar categóricamente que éste fue el procedimiento utilizado por los antiguos luthiers italianos, pero tampoco lo puedo descartar. Tampoco puedo descartar ningún otro sistema que desde cero diseñe el molde con todos sus detalles.

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6 hours ago, Joaquín Fonollosa said:

The golden section in violin making

 

Excerpt from the lecture: The golden section – by Wolfgang Schiele

>

>

I have deduced an ideal design from instruments by the violinmakers Nicolo Amati, Andrea Guarneri and Antonius Stradivarius from around 1650 1670. Starting with the overall length of the instrument, all its measurements are in specific proportional relation to each another.

 

>

>

I find it highly exciting that, given this background, it is possible to completely reconstruct the shape of the violin solely by geometric means.

>

>

The power of geometry makes it obvious that the shape of the violin cannot be improved as it has been tried many times over the past several hundreds of years.

>

Stradivari tried many different proportions over the length of his career.  He might have saved a lot needless experimenting if he had just used the proper geometry constructions at the start.

 

The attached graphs used data taken from David Woodrow's book "The Shape of Stradivari Forms and Violins", Taynton Press, Oxford, 1991

Strad's upper- lower bout ratio.jpg

Strad's lower bout-L.jpg

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There are more than a dozen historical molds exisiting with imaging on the web.

Ask yourself, does my 'system' generate all of these molds exactly in all aspects, as logical variations within one coherent method?

With circle geometry and simple ratios the answer is yes.

Be honest with yourself.  It isn't both circles and spirals. 

Circles and integer ratios get the whole job done in flying colors.  Since the design are indeed well structured, there will be other patterns that pop up incidentally.  But only the systems they actually used wel explain the whole range of examples in the simplest way.

*******

I understand you've found tantalizing fits with your spirals, so how can that not be the true method?

Concider this little exercise.  Smoothly join two circle arcs of different radii.  (Smooth join requires that both centers and the point where the join all sit on one line)

The two arcs are drawn as circles, buy will look much like a spiral: the small radius curve continuing in the larger flatter radius.

If you try, you will be able to find some spiral that reasonbly fits a portion of this drawing.

So shapes made a circles will automatic supply many partial but false fits to spirals.

 

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I see three images. The comparison image shows your drawing and the mold are completely different.     

Drawing shapes kinda of sort of similar to violins is not it.   

Again, the  circle geometry with integer ratios can be used to analyze and to generate the actual accurate shapes of the whole range of classical Cremona bowed strings and molds.

It took ten years of work to uncover the full extent of that old system.  But it ends up being a consistent system, with all the different resulting instruments being a matter of logical variations in the design choices within the system.

 

 

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