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Joaquín Fonollosa

Geometría fabrorum

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I continue to explore the side of guitars-
I am now studying three Voboam guitars in Paris
I have good photos and also ... measurements
Here is an example of a match between a good definition photo and real measurements. (the camera was in a wrong axe)
I repeat, be careful with photos

1668714737_Capturedecran2019-10-12a12_03_52.thumb.png.0d5b49ba2448b3dd5489ed1ee0873def.png

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I have tried to follow this thread but am unable to grasp what the point of it is ?

Is it suggesting that Cremonese luthiers were closet mathematicians who devised incredibly complex ways of making simple shapes instead of just drawing them freehand ?

And how does using a complex mathematical formula make for better shapes than merely observing the shapes and forms in nature and modifying them freehand ?

I get the use of dividers, they have been common for thousands of years and can be used to tidy up an inspired freehand drawing, but is it really necessary to go beyond using this simple tool to make a violin ?

 

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Everyone is free to ignore the results.

But, what I'm saying is that once you understand the patterns and the way they were used, then all the Old Cremona stuff from A Amati through Del Gesu and Bergonzi, and quite a bit more N Italian instrument making, ALL the FEATURES show consistent patterns or recipes behind their shapes.  'Always use Vesici in this spot'.  The vesici here should generally be like 4:4:4, 4:3:4, or 5:4:5, with the three divisions of the bout equal or the middle division differing by only one part. Etc.

Once you understand the recipes that were traditional adhered to in each part, the whole design can be 'read'.

You can 'read' exactly the recipe behind the brothers Amati piccolo violin of 1613, and you can 'read' the recipes in the A Guarneri tenor, the 1714 Soil, Del Gesu's Lord Wilton.

And you can see exactly how and where the recipes are identical, and where slightly different options within tradition were used.

We can read these recipes in any instrument made within such traditional methods of divider use.

We can also then make in such methods, either copying all the choices in an example to make a 'twin', our we can take the extra step to do as they did and make by taking choices within the traditional recipes at each step.

Certainly, none of this is relevant unless one wants to follow or understand the classical examples.

It isn't the easiest way to go.  And it isn't all that obvious how it might matter.

But, understanding these things opens a powerful to observe the old work.

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3 hours ago, David Beard said:

Everyone is free to ignore the results.

But, what I'm saying is that once you understand the patterns and the way they were used, then all the Old Cremona stuff from A Amati through Del Gesu and Bergonzi, and quite a bit more N Italian instrument making, ALL the FEATURES show consistent patterns or recipes behind their shapes.  'Always use Vesici in this spot'.  The vesici here should generally be like 4:4:4, 4:3:4, or 5:4:5, with the three divisions of the bout equal or the middle division differing by only one part. Etc.

Once you understand the recipes that were traditional adhered to in each part, the whole design can be 'read'.

You can 'read' exactly the recipe behind the brothers Amati piccolo violin of 1613, and you can 'read' the recipes in the A Guarneri tenor, the 1714 Soil, Del Gesu's Lord Wilton.

And you can see exactly how and where the recipes are identical, and where slightly different options within tradition were used.

We can read these recipes in any instrument made within such traditional methods of divider use.

We can also then make in such methods, either copying all the choices in an example to make a 'twin', our we can take the extra step to do as they did and make by taking choices within the traditional recipes at each step.

Certainly, none of this is relevant unless one wants to follow or understand the classical examples.

It isn't the easiest way to go.  And it isn't all that obvious how it might matter.

But, understanding these things opens a powerful to observe the old work.

I have read some of your theory on your webpage, but it is very long and would take days to go through.

Is this a personal theory or a widely accepted fact ?

Is it not just as possible that Amati was artistic by nature and came up with a nice looking shape one day and people liked it and so he made more.

And then others copied around his shape and made more.

And then Stradivari copied around the same shape and tweaked it  etc ?

 

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1 hour ago, Delabo said:

I have read some of your theory on your webpage, but it is very long and would take days to go through.

Is this a personal theory or a widely accepted fact ?

Is it not just as possible that Amati was artistic by nature and came up with a nice looking shape one day and people liked it and so he made more.

And then others copied around his shape and made more.

And then Stradivari copied around the same shape and tweaked it  etc ?

 

It probably sounded good too.

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Oh. It's possible a Cremona apprenticeship might have taken more than a few days.

What is complicated?  

Every bit of the geometry is just bits of divider arcs.  The proportions can all be walked out by simply stepping the dividers.

********

And we aren't being proscriptive.  Noone is saying 'this is how you should work today'.   Instead we're saying 'look, we can follow the clues and see what they did.  This is how the Old Cremona makers worked'  

It's exposed now.  We can 'read' the choices they made.

Do with it as you will.

 

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This topic began with Joaquin Fonollosa's post suggesting that Joachim Durer's spiral and associated rectangle could be the basic element of violin design. And to myself it looks pretty convincing, although I'm not sure how it might best be applied. I get the impression that using such a rectangular template the same width of the waist of the proposed violin's inner form, placed in the right way, is all that is required to get the relevant position of corners, length of body, width of bouts, &c.

If that approach was invented/used by Amati senior, or any other geometric method achieving the same outcome, then apart from corner shapes, there would originally have been a standard violin design or shape. I'm sure that would have been considered desirable by makers at the time, and many makers now for that matter. After all the outline shape is visually important and can be tricky to get right, but it probably has little to do with the sound qualities of the instrument.

 

 

 

 

 

 

 

 

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Joaquin Fonollosa's idea of using the spirals is important because it shows that proportions alone are not adequate.  How the shapes of the rectangular proportions are  rounded off is a key point of attractiveness.  Circle arcs of constant curvature are not very appealing whereas Joaquin's spirals are.  If you use many circular arcs they can approach Joaguin's spirals beauty but why bother?

Attached is a rectangular drawing showing the bout and length proportions for a typical violin.  If you round off the corners with simple circular arcs it doesn't look very attractive to me.  Also attached is a Strad guitar outline and then drawn with the same proportions with circular arcs.  That doesn't look good to me either.

violin proportions.jpg

Simple circle violin ◊ Layer-1 ◊ 1 _ 1.jpg

Rawlings and circle guitar .jpg

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Good. 

Marty and Dennis,

You're asserting that spirals would be a simpler, better, more attractive system.

I can't argue with such an opinion, though I don't share that opinion.

 

But, I will continue to assert that we can demonstrate that the Old Cremona work observably displays the circle geometry and ratios I've been pointing to, and not something else.  

I will continue providing evidence for this position as need be.

 

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I totally agree. If Joaquin's spirals can reproduce the outlines of the upper and lower bouts given a form waist measurement the design problem is largely solved. I'm just not sure this is the case, I haven't tried it. The same figures can be made using splines, as I have done myself. But although they can comply with all the relevant points they still can be varied in shape quite a bit. It depends on how the carbon fibre splines are manipulated. Which is not a bad thing because it means different outlines can be created. Doing it myself I've noticed that you can not get too far away from the near-circular at the widest sections of the upper and lower bouts before things go wrong. But it is self evident that there are no sections of a violin's outline that are circular. I suppose that those advocating using circle geometry are are not saying that, but as you say, curves produced by carbon fibre are very attractive, it is just a matter of controlling the process.

 

 

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If an outstanding question here is whether Stradivari's outline was built from circles or spirals, this question has a definite answer, there is software that can answer it, and I have thrown the software at the question. The answer is circles, WITHOUT A DOUBT. The same process precludes the use of splines, as well. In fact, I would go so far as to say that the nature of splines and spirals is such that there is not way that they could ACCURATELY recreate a Stradivari mold, even if you were going the "wrong" way, backwards from the originals.  

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23 hours ago, Delabo said:

incredibly complex ways

"incredibly complex ways" ....Sorry but these means nothing-  

English is "incredibly complex" for me is it for you too?

complexity is a relative concept as soon as it is connected to ignorance

Seven different measurement of the foot were used at the same time by the stone carvers to built the Cathedral of Chartres

would you says that it is an "incredibly complex way" ?

 if you answer "Yes" your thought is addressed to our nowadays commun sens - for us, it is obviously a "complex way"

if you answer "No" your thought will be addressed to our capacity of understanding this is where the place of complexity is.

Explaining of our ignorance can be a hard work-  

I understand and respect the motivations of people who prefer the reassuring idea that there is nothing to understand but here, I see nothing more than a confortable opinion founded on ignorance.

It is a very normal behaviour ,ignorance, peace of mind and certainties are good friends of all of us. 

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People who seem to have nothing in common .......
... "The luthier Max Möckel, who worked at the end of the 19th century in St. Petersburg and Berlin, did not rest until he had investigated the true origin of the architectural and sonic beauty of the violin. His idea was to investigate whether, in the light of knowledge of the Renaissance, it might be possible to discover what role Leonardo da Vinci, Luca Pacioli and Alberto Durero had played in the instrument construction revolution, so he began to look for clues to support his hypotheses in the works of these great artists, and he came to The following conclusion:

    Is there really an Italian secret? Yes and no. If we think of this as some kind of recipe, hidden somewhere in an old trunk, then no. . . We must move to the time when the violin was invented, and to the ideas with which the old masters created their works. . . The most important minds, to name two of them, Leonardo da Vinci and his friend Luca Pacioli, had been interested shortly before, in their work of so many facets, in mathematical problems, and when they saw the triangle and the pentagon, they did not see them merely as simple geometric figures, but they saw in the pentagon, for example, the secret eye of God, a living sensitive image, with its infinite number of relationships, for all that is appropriate.

With this hypothesis as a starting point, Möckel developed a procedure to build the violin, the viola and the cello, whose model was what Luca Pacioli called the divine proportion (in the divine proportion, the division of a line or a geometric figure is such that the smallest dimension is the largest, as the largest is the whole). Since then, he built many excellent instruments with this method. "

https://archive.schillerinstitute.com/newspanish/InstitutoSchiller/Arte/MusiParadojaPitagoras.html

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Some new of the Strad Guitar...

The actual measurements of the Strad Rawlins guitar has been given by Pollens and, good news, the variations with respect to the dimensions of the photo are remarkably low (1.5 mm in length and 3/10 ° in width which is excellent) - We can therefore consider that the analysis that I previously posted here is well founded :)

Moreover Pollens always seems angry with the relative measurements since the three ratios W / L (body max width / length)  are bad ....
"Guistiniani" W / L = 2.24 "Hill" W / L = 2.2 and "Rawlins" W / L = 2.08

the correct ratios are :

"Guistiniani" W / L = 1.758 "Hill" W / L = 1, 74 and "Rawlins" W / L = 1,644

Given these surprising errors in calculations Pollens's conclusions are faulty - it does not have a 5/11 ratio and the 5/9 ratio is only found on one paper template ...

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36 minutes ago, francoisdenis said:

"incredibly complex ways" ....Sorry but these means nothing-  

English is "incredibly complex" for me is it for you too?

complexity is a relative concept as soon as it is connected to ignorance

Seven different measurement of the foot were used at the same time by the stone carvers to built the Cathedral of Chartres

would you says that it is an "incredibly complex way" ?

 if you answer "Yes" your thought is addressed to our nowadays commun sens - for us, it is obviously a "complex way"

if you answer "No" your thought will be addressed to our capacity of understanding this is where the place of complexity is.

Explaining of our ignorance can be a hard work-  

I understand and respect the motivations of people who prefer the reassuring idea that there is nothing to understand but here, I see nothing more than a confortable opinion founded on ignorance.

It is a very normal behaviour ,ignorance, peace of mind and certainties are good friends of all of us. 

"Incredibly complex"  - relative -   to what seems a simple task.

It is "relatively" easy to see how a seemingly simple shape can be drawn by someone on a piece of paper.

Various curves could be drawn using dividers - rulers - triangles etc and cut out with  scissors and used to make a violin pattern on wood.

A person with above average intelligence who excells in maths might wish to make this simple task "incredibly complex" because they like doing maths.

Are you suggesting Amati, Stardivarius, Guarneri were of this ilk ?

 

 

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18 minutes ago, Joaquín Fonollosa said:

People who seem to have nothing in common .......
... "The luthier Max Möckel, who worked at the end of the 19th century in St. Petersburg and Berlin, did not rest until he had investigated the true origin of the architectural and sonic beauty of the violin. His idea was to investigate whether, in the light of knowledge of the Renaissance, it might be possible to discover what role Leonardo da Vinci, Luca Pacioli and Alberto Durero had played in the instrument construction revolution, so he began to look for clues to support his hypotheses in the works of these great artists, and he came to The following conclusion:

    Is there really an Italian secret? Yes and no. If we think of this as some kind of recipe, hidden somewhere in an old trunk, then no. . . We must move to the time when the violin was invented, and to the ideas with which the old masters created their works. . . The most important minds, to name two of them, Leonardo da Vinci and his friend Luca Pacioli, had been interested shortly before, in their work of so many facets, in mathematical problems, and when they saw the triangle and the pentagon, they did not see them merely as simple geometric figures, but they saw in the pentagon, for example, the secret eye of God, a living sensitive image, with its infinite number of relationships, for all that is appropriate.

With this hypothesis as a starting point, Möckel developed a procedure to build the violin, the viola and the cello, whose model was what Luca Pacioli called the divine proportion (in the divine proportion, the division of a line or a geometric figure is such that the smallest dimension is the largest, as the largest is the whole). Since then, he built many excellent instruments with this method. "

https://archive.schillerinstitute.com/newspanish/InstitutoSchiller/Arte/MusiParadojaPitagoras.html

Are you kidding ?

Have you read Max Möckel ?  You have to gave up with all these the XIX° century cliché 

time to move forward

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4 minutes ago, francoisdenis said:

Are you kidding ?

Have you read Max Möckel ?  You have to gave up with all these the XIX° century cliché 

time to move forward

No, I do not know the postulates of this German luthier.
Let's keep going!!

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8 minutes ago, Delabo said:

"Incredibly complex"  - relative -   to what seems a simple task.

It is "relatively" easy to see how a seemingly simple shape can be drawn by someone on a piece of paper.

Various curves could be drawn using dividers - rulers - triangles etc and cut out with  scissors and used to make a violin pattern on wood.

A person with above average intelligence who excells in maths might wish to make this simple task "incredibly complex" because they like doing maths.

Are you suggesting Amati, Stardivarius, Guarneri were of this ilk ?

 

 

Dear Delabo,

You're just arguing that Amati was not able to count to 12. Because you do not need to know much more than "complex math" to design a violin 

you did not read me well where I expressed myself badly

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14 minutes ago, Joaquín Fonollosa said:

No, I do not know the postulates of this German luthier.
Let's keep going!!

a glance ... I have the book if you want to dig in

IMG_1757.thumb.JPG.0373809cf4d3c44570cc6f4b541e3245.JPGIMG_1758.thumb.JPG.17a61cce2cff29fbe1776301e9a02ab5.JPG

IMG_1755.thumb.JPG.65b7bea5321550181a61b4c608213a73.JPGIMG_1756.thumb.JPG.23e7fc8b6422b1392f56a9d656710995.JPG

 

 

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5 minutes ago, francoisdenis said:

a glance ... I have the book if you want to dig in

IMG_1757.thumb.JPG.0373809cf4d3c44570cc6f4b541e3245.JPGIMG_1758.thumb.JPG.17a61cce2cff29fbe1776301e9a02ab5.JPG

IMG_1755.thumb.JPG.65b7bea5321550181a61b4c608213a73.JPGIMG_1756.thumb.JPG.23e7fc8b6422b1392f56a9d656710995.JPG

 

 

Mr. Max seems certainly complex. If it catches my attention it is because he wanted to see a link between Pacioli, Dürer, Da Vinci and Amati.

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It seems to me that the easiest way to resolve whether the circle/ratio theory is correct would be to take a random selection of Cremonese instruments and later copies of Cremonese instruments, carefully copy their outlines, purfling lines, and soundhole locations, then subject the images to analysis. The Cremonese instruments should - theoretically - all correspond to circle/ratio geometry, while the copies should tend not to (obviously, the possibility exists that a traced example would coincide).

It would require a bit of work, but perhaps it would put an end to the repetitious cycle we seem to have here...

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4 minutes ago, Three13 said:

It seems to me that the easiest way to resolve whether the circle/ratio theory is correct would be to take a random selection of Cremonese instruments and later copies of Cremonese instruments, carefully copy their outlines, purfling lines, and soundhole locations, then subject the images to analysis. The Cremonese instruments should - theoretically - all correspond to circle/ratio geometry, while the copies should tend not to (obviously, the possibility exists that a traced example would coincide).

It would require a bit of work, but perhaps it would put an end to the repetitious cycle we seem to have here...

No, that wouldn't do anything except create another data point to argue about :D I mean let's be real here, we're talking about violin makers, people, who if stuck on a desert island, would have within them the ability to create a most beautiful island with many clever solutions for all the challenges we might face, but you'd probably just find a pile of bodies and bones "over there" with gouges sticking out of the eye sockets with some crazy guy circling about muttering about "see! I knew I was right!" :lol:

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2 hours ago, francoisdenis said:

You're just arguing that Amati was not able to count to 12.

Quite the opposite.

I was asking if he was of of at least above average IQ or even more.

 

 

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