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Geometría fabrorum


Joaquín Fonollosa
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1 hour ago, Joaquín Fonollosa said:

En efecto, son diferentes. Yo soy yo y Stradivari no. No trato de analizar a otros, solo dibujo. 

I can agree with you here.  Your spirals are a fine way to make your own individual violin designs.

They just aren't the way to make the kinds of designs used by Amati, Guarneri, Stradivari, and other families.      

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5 hours ago, Joaquín Fonollosa said:

En efecto, son diferentes. Yo soy yo y Stradivari no. No trato de analizar a otros, solo dibujo. 

You were asked by the moderator to post in English, the forum lnaguage, and that would be useful for those of us who don't speak Spanish.  Easier for you to translate than having many readers translate . Yet now you continue to not post in English.

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21 minutes ago, l33tplaya said:

El moderador le pidió que publicara en inglés, el idioma del foro, y eso sería útil para aquellos de nosotros que no hablamos español. Para usted es más fácil traducir que tener muchos lectores traducen. Sin embargo, ahora continúa sin publicar en inglés.

You are right. Excuse me. Sometimes one tends to respond quickly, and does so in his own language.

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Possibly quite similar method to the four circles method, using the golden ratio to calculate the lengths of each bout. The widths were already sorted out, so I needed to find the right radius- vesica piscis for the lower bouts, the same radius for the upper bouts, and I freehanded the c bout. The corners I added with a compass by feel. I will send photos when I get the chance

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Yes. It is very easy to get violin shapes just by using the tradition geometries: vesici, etc.

However, to get classical results, one must also stick with a large number of traditions about which ratios and guides are appropriate to each feature.

So for example, Body length to width should traditionally always be one of 5::9, 4::7, 3::5, or with lira or others sometimes 2::3.  And you are free to measure one or both from either the outer edge or purf.

In classical Cremona work, phi is not actually used. Though the fibonacci ratio aproximation occur at times: 2:3, 3:5, 5:8

 

 

.

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2 hours ago, David Beard said:

Yes. It is very easy to get violin shapes just by using the tradition geometries: vesici, etc.

However, to get classical results, one must also stick with a large number of traditions about which ratios and guides are appropriate to each feature.

So for example, Body length to width should traditionally always be one of 5::9, 4::7, 3::5, or with lira or others sometimes 2::3.  And you are free to measure one or both from either the outer edge or purf.

In classical Cremona work, phi is not actually used. Though the fibonacci ratio aproximation occur at times: 2:3, 3:5, 5:8

 

 

.

My Aug. 25 post showed how the upper/lower bout width ratio and Lower bout/ length ratio of Strad's violins varied greatly.  This shows Srad did not use simple ratios like 4/5  and 5/9.

With regards to Stradivari's molds Stewart Pollens(1) said  "...there is little evidence that any of the Cremonese violin makers (ranging all the way back to Andrea Amatil) adhered to a strict proportional system."

"By comparing the measurements of bout widths, overall length, and 'stop' it becomes evident that Stradivari did not employ fixed proportions in his designs." ...."The variations in dimensions and proportions of the violin forms-coupled with the lack of geometric construction marks-provide convincing evidence of Stradivari's pragmatic method of design."

Pollens suggested that Strad's pragmatic method of designing violins was to simply trace an older successful one to make a mold pattern.  If he wanted something a little different this pattern was then shifted or tilted around for making a newer shape as illustrated from outline overlays of his molds.

 

1.  "The Violin Forms of Antonio Stradivari",  Peter Biddulph, 1992  pages 21&22 'Proportional schemes and measurement standards'

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5 hours ago, Marty Kasprzyk said:

My Aug. 25 post showed how the upper/lower bout width ratio and Lower bout/ length ratio of Strad's violins varied greatly.  This shows Srad did not use simple ratios like 4/5  and 5/9.

With regards to Stradivari's molds Stewart Pollens(1) said  "...there is little evidence that any of the Cremonese violin makers (ranging all the way back to Andrea Amatil) adhered to a strict proportional system."

"By comparing the measurements of bout widths, overall length, and 'stop' it becomes evident that Stradivari did not employ fixed proportions in his designs." ...."The variations in dimensions and proportions of the violin forms-coupled with the lack of geometric construction marks-provide convincing evidence of Stradivari's pragmatic method of design."

Pollens suggested that Strad's pragmatic method of designing violins was to simply trace an older successful one to make a mold pattern.  If he wanted something a little different this pattern was then shifted or tilted around for making a newer shape as illustrated from outline overlays of his molds.

 

1.  "The Violin Forms of Antonio Stradivari",  Peter Biddulph, 1992  pages 21&22 'Proportional schemes and measurement standards'

No. He did use them. But it is often to width on the purf verus body on the outer edge, or similar.

When the measure is on the purf, it is always on a 3purf width in set from the edge.

The accuracy of the original work was not super high. Accurate to perhaps a 1/3 a purf width on this overall ratios.

Also to remember, tops have been repeatedly taken on an off, which can lead to splaying of the top further obscuring the basic ratio relation.

Further, reported numeric measures of plate dimensions are very inconsistent.  Until very recently, it was common to measure with a tape measure over the contour of the arching.  Such measures are worthless for this purpose.

There is also the matter of edge wear. 

If you study the plate dimensions graphically, overlaying frames of the standard ratios, you will find:

* Most examples appear to reasonably to execellently well

* Some fit only poorly 

* a small percent don't in current condition appear to fit. But also tend to more compromised examples

* best preserved example tend to fit very cleanly.

 

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Some examples of the body to width ratio in classical work.  

These also show the somewhat forgiving method I used to visually check for the ratios.

 1574 A Amati small violin

4to7 outer edge both width and length  

530756082_1574violinsmallAndreaAmati.thumb.jpg.3b8bb075768c7619dbea71cb08a219e6.jpg

 

1596 Bros Amati violin

Again 4o :: 7o

1938774260_1596BrosAmativiolin.thumb.jpg.f4d37170de54a00d7c71294521e2fbfa.jpg

 

 

Maggini 1610 cello.  Here the stouter shaped 3to5 ratio is chosen. And to make just a smidge stouter without breaking the ratio, the maker chose to calculate the length on the outer edge, but the width on the purf.

3p :: 5o

1092019699_1610Magginicello.thumb.jpg.6c7266a07fa77fdacacecd5353b9eb33.jpg

 

For their 1613 piccolo violin, the Bros Amati chose the skinnier 5:9 ratio, carrying out on the purf as 5p :: 9p

 

2059820374_1613BrosAmatipiccolo.thumb.jpg.dd06424b659b2d31629984caa3656328.jpg

 

In their 1620c viola at RAM, they used 5p :: 9o

990969302_1620cviolaBrosAmati(RAMuncut).thumb.jpg.a123e54dc4679255b8453934c025776e.jpg

 

In this 1624 violin, N Amati made the very typical Cremona violin choice to use a 4o :: 7o ratio.

584619649_1624violinNicolaAmat.thumb.jpg.c702c8ac3b11b5f2dae385401ec355cc.jpg

 

 

In the 1714 'Soil, Strad chose the only very subtly stouter  4p :: 7p ratio.

291425632_1714violin358StradSoil.thumb.jpg.867d6180c22be36f2b96749f64220ec5.jpg

 

In Del Gesu's 'Kreisler', we again see 4o :: 7o

97307072_1730ne1733violin355DelGesuKreisler.thumb.jpg.2c540e2a5edd0cb32c3de88e86bd788b.jpg

 

For his stout 1735 'Chardon', Del Gesu choose his ratio as 3o :: 5p

 

1060356334_1735violindance239DelGesuChardon.thumb.jpg.5947afb86e7a0357e636a71317bd0376.jpg

 

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15 hours ago, David Beard said:

No. He did use them. But it is often to width on the purf verus body on the outer edge, or similar.

When the measure is on the purf, it is always on a 3purf width in set from the edge.

The accuracy of the original work was not super high. Accurate to perhaps a 1/3 a purf width on this overall ratios.

Also to remember, tops have been repeatedly taken on an off, which can lead to splaying of the top further obscuring the basic ratio relation.

Further, reported numeric measures of plate dimensions are very inconsistent.  Until very recently, it was common to measure with a tape measure over the contour of the arching.  Such measures are worthless for this purpose.

There is also the matter of edge wear. 

If you study the plate dimensions graphically, overlaying frames of the standard ratios, you will find:

* Most examples appear to reasonably to execellently well

* Some fit only poorly 

* a small percent don't in current condition appear to fit. But also tend to more compromised examples

* best preserved example tend to fit very cleanly.

 

Pollens' studies of Strad's actual molds led him to conclude that Strad wasn't using simple low integer ratios to generate their proportions.

Attached is a plot of the length/lower bout width of all of Strad's violin molds in the sequence that Pollens thought they were made.  Also shown on the plot are the simple ratios 9/5, 7/4, and 5/3 which shows that only three out of the twelve Strad molds (an ironic simple 1/4 ratio) had a simple length to width ratio of 7/4. 

Pollens pointed out that the plates used with these molds would be about 8mm wider to take into account rib thicknesses and plate overhang.  He recalculated the length to width ratios and I also plotted these. He showed that his estimated violin plates were even farther away from having a simple 7/4 ratio.

 

Woodrow studied the dimensions of actual Strad violins.  Like Pollens he was very concerned about making accurate measurements.  A  length to lower bout width plot from Woodrow's data also shows that almost all of Strad's violins did not have a simple integer ratio.

It appears that Strad was using several differently proportioned molds simultaneously during the last few decades of his work.

 

Strad's L-W from Woodrow.jpg

Strad's L-W from Pollens.jpg

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Here is the 1708 G mold as example.

The mold portions are based on 5::9. 

 

994146212_1708Gmold.thumb.jpg.70c3b2d466006e8d8e6efb6df6ea925e.jpg

 

In concept, the mold line corresponds to the 3p width purf line of the outline. So this mold is proportioned based on a projected 5p::9o instrument proportion.

But, with classical methods the sides can be pushed and pulled around some once off the mold.  There is no reason to assume a straight connection from mold design to final instrument design.  In fact, analysis shows a fair independence of outline design front to back, and in some examples even treble to bass side.  So, this rather implies an outline was worked up for each plate during building, accommodating any variances that had already developed in the build. This then implies only an indirect relation to the mold.

 

(N.B.  The choices shown here in projecting a planning outline for the mold are typical in Cremona work.  The centers for the long arcs connecting the vesici circles use radii 2/5 and 4/5  of body here.  Almost all Cremona work used 3rds or 5ths of body length for these.  The insets from mold to outer edge are also typical.  1/80 of Body(p) is perhaps most typical.)

 

 

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On 8/27/2019 at 7:36 PM, Marty Kasprzyk said:

My Aug. 25 post showed how the upper/lower bout width ratio and Lower bout/ length ratio of Strad's violins varied greatly.  This shows Srad did not use simple ratios like 4/5  and 5/9.

With regards to Stradivari's molds Stewart Pollens(1) said  "...there is little evidence that any of the Cremonese violin makers (ranging all the way back to Andrea Amatil) adhered to a strict proportional system."

"By comparing the measurements of bout widths, overall length, and 'stop' it becomes evident that Stradivari did not employ fixed proportions in his designs." ...."The variations in dimensions and proportions of the violin forms-coupled with the lack of geometric construction marks-provide convincing evidence of Stradivari's pragmatic method of design."

Pollens suggested that Strad's pragmatic method of designing violins was to simply trace an older successful one to make a mold pattern.  If he wanted something a little different this pattern was then shifted or tilted around for making a newer shape as illustrated from outline overlays of his molds.

 

1.  "The Violin Forms of Antonio Stradivari",  Peter Biddulph, 1992  pages 21&22 'Proportional schemes and measurement standards'

With all respect due to the great researcher, if there is one area in which Mr Pollens  illustrates his limits, it is surely the one of proportionality.
So I will not pay attention to his conclusion on this domain.Actually many other ratios than the major third major 4 to 5 provide values close to those of the Woodrow table and other ratios that 4 to 7 provide numbers close to 1.7.(see some of them on attached file.)

In fact, any number has a rational or irrational geometric construction that approaches it sufficiently for the violin making (+/- 0.5 mm). We can imagine dozens of solutions to trace all kinds of violins.
Moreover, at all times  instruments that do not precisely follow proportional or geometric systems have been made. This is not surprising. From ancient times it is said that make a template and use it are two different things (to the point that Vitruvius complains about the bad habits of the workers which weaken the outlines  by copying the templates rather than drawing them ) .
So the idea of copying is a old story…
A trace of this process (used a template to create another one) is found on the majority of Stradivarius forms. I seem to have demonstrated this for a while already and finally my conclusions only prolong the statement already made by Pollens on this subject.
However, we should definetly admit that the design of an instrument is a simple thing if we stick to the common sense. First the format of a surface (maximum lenght and width), then a partition in 3 parts in the height and 5 parts in the width. This being defined, the drawing of the outline is a "piece of cake". Dürer's recommendation in his introduction to "geometrica deutsche" is excellent: "used the process you master" and Durër quotes 3, rules and compasses, point by point, free hand. But nevertheless that circles have been used in the first traces of the Amatis is, however, a fact difficult to contradict.

Capture d’écran 2019-08-31 à 15.21.45.png

Capture d’écran 2019-08-31 à 15.21.56.png

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14 hours ago, David Beard said:

???   I don't see what you mean?

As I see it there are two important measures; the internal measure between the upper and lower blocks, and externally the body length. The first measure relates to the (baroque) string length, and the second to the player's body size.

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