Thomas Coleman

Violin geometry references

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I know of several resources concerning violin geometry.  I'll list what I know and maybe some of you could fill in the blanks?  Any comments or suggestions about any of the material would also be welcome. 

Francois Denis,  I've studied a bit and have made one drawing using his method.  It is my understanding that his method mostly relates to Strad?  correct?  Worth buying?  I haven't seen it in awhile.

Henry Strobel has a few things in maybe The art of violin making (or one of his books anyway).  Anybody care to give insight into his method?

Ake Ekwall The art of drawing a violin.  I know nothing about it and it's hard to find info.  Is it worth hunting down?

Kevin Coates.  I have briefly perused his book but that's it.  It seems like more of a general, historical overview as opposed to practical.  correct?

Kevin Kelly vids.  really enjoy them and have been dinking around with AutoCad and his videos (actually why I started this thread).  What's your opinion on his methods?

Sergei Muratov book.  I have a pdf of it.  Havn't really looked at it a whole lot.  Are his methods sound?

Anything you care to comment on or add would be helpful and appreciated

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If you want the Ekwall book, try olle.g.ekwall@gmail.com.  I haven't spent enough time on the whole subject to venture an opinion as to where it ranks in all this.  I would guess not very high.  There's probably a pretty steep drop-off from the Denis-Kelly[-Coates class of material and the rest.  That certainly would be good in terms of concentrating your time.

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3 hours ago, Thomas Coleman said:

I know of several resources concerning violin geometry.  I'll list what I know and maybe some of you could fill in the blanks?  Any comments or suggestions about any of the material would also be welcome. 

Francois Denis,  I've studied a bit and have made one drawing using his method.  It is my understanding that his method mostly relates to Strad?  correct?  Worth buying?  I haven't seen it in awhile.

Henry Strobel has a few things in maybe The art of violin making (or one of his books anyway).  Anybody care to give insight into his method?

Ake Ekwall The art of drawing a violin.  I know nothing about it and it's hard to find info.  Is it worth hunting down?

Kevin Coates.  I have briefly perused his book but that's it.  It seems like more of a general, historical overview as opposed to practical.  correct?

Kevin Kelly vids.  really enjoy them and have been dinking around with AutoCad and his videos (actually why I started this thread).  What's your opinion on his methods?

Sergei Muratov book.  I have a pdf of it.  Havn't really looked at it a whole lot.  Are his methods sound?

Anything you care to comment on or add would be helpful and appreciated

In addition to the ones you’ve already listed for compass and straight edge constructions:
 
V. Baginsky, “Construction of a contour and arch with use of the golden section”, translate. by F. Liden, Stockholm, 1996

D. Woodrow “The Shape of Stradivari Forms and Violins”, Taunton Press, Oxford, 1991

Simone Saccon, “The Secrets of Stadivari, Translated by Andrew Differ and Cristina Rivroli,  Eric Blot, Cremona, 2000

Robert Spear, “The Stradivari Model G, the Golden Section, and Modern Violin Design”, Journal of the Violin Society of America VSA Papers, Volume xxii, No 1

 

If you believe true ellipses do an easier job of matching violin geometry than circles I suggest:

George L. Hersey, “Architecture and Geometry in the Age of the Baroque”, The University of Chicago Press, Chicago, 2000
 

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22 hours ago, Thomas Coleman said:

Francois Denis,  I've studied a bit and have made one drawing using his method.  It is my understanding that his method mostly relates to Strad?  correct?  Worth buying?  I haven't seen it in awhile.

Denis also wrote an article called The geometric principles of string instrument-making in Brescia.   (You can also find this included in the book "Liutai in Brescia").   I used this approach successfully for my last instrument.

Ed.

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I think that almost any drawing or drafting system can be superimposed on violins, if one tries hard enough.

Do I think it means that the superimposed system was original, or that it matters? No.

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1 hour ago, David Burgess said:

I think that almost any drawing or drafting system can be superimposed on violins, if one tries hard enough.

Do I think it means that the superimposed system was original, or that it matters? No.

That's why I think the Hersey book is worth reading.  It gives a good sense of the principles that undergirded what The Ancients saw around them every day and indirectly supported the training of the eye they all underwent as they made and examined instruments.  Whether the geometric principles influencing the makers were of the everyday variety or specific design methodologies, I think it is useful to understand the basics because one way or another, they were part of the world in which these folks lived.  For my own part, I made a conscious decision that my own making would be better informed by making and making some more.  We all prioritize.

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My work tries to answer a simple question:  If you only use the simplest and most wide spread tools of the 16th century, how would you make what we see in classical Italian violins?       

I started making the work public last year, in a series of blog posts.

As much as possible, I started from what had already been accomplished in the works of Hargrave, Sacconi, Denis, and Coates.

Does any of it matter?   Certainly it doesn't if you don't regard the old classical making as something to aspire to.   And even if you do believe we would do well to understand and at least match their achievements, even then the usefulness of these methods can fairly be questioned.   For myself, I'm game.  I want to figure out how to 'do as they did' to as great an extent as possible.

And there are quite a few layers to emulating the old work: Materials, tooling and work methods, and design methods.  These three are rather separable in study, but must work together if you want to walk down their road.

Hargrave and Sacconi most of all helped in the arena of tools and working methods.  Materials are difficult to study beyond a certain level.  I'm glad that there are people working on these issues currently.  For my own work, I concentrate on using materials that were prevalent in the time, and how to use them to finish instruments with as much consistency to historical example as I can muster.

Coates' work is to me the most significant.  Sacconi had echoed the idea that the old designs might be based on geometry, but gave a bogus and confused/confusing illustration.   This knowledge had echoed down the generations, and has been hinted at many times over, but always vaguely and generally offered with no detail, or confused false details.   Coates was the first to demonstrate specifically that such circles and line geometry plays out across old Italian instrument making, not just the violin family -- and ties back to earlier Arabic instruments.  I don't remember if he demonstrates the link to old Roman methods, but regardless, Coates shows the breadth of this geometry in old making.  Though he doesn't show much about the ratios pervasively associated with the geometry constructions.

My work has mostly been on the design methods, and how they interact with the building process.   As far as I know, Denis was the first to offer a system that can generate some classical instrument outlines from scratch.  That accomplishment deserves great notice.  However, I believe that fully understanding the old methods, and understanding the diversity and freedom of the old Italian making, requires stepping outside the framework Denis outlines.  This is the work I've taken on, as well as expanding the concepts to embrace the full design of an instrument.

Considering the flexibility of the old methods, we again come back to the question 'does it matter'?   At this point, I believe I see primarily three large differences between prevalent modern methods and the old Italian methods I've been researching that likely do matter.    First, modern copy methods tend to encourage controlling the wood and avoiding wood movement.  The old methods seem to go to extremes in the opposite direction.  Nothing is done to avoid wood movement, and then the old design methods actively respond and adapt to whatever variances arise during the build process.  This old/new difference also encompasses the use of water.  Modern making tends to need to work dry to keep control of the wood.  Old woodworking traditions ubiquitously use wet processes. This includes sizing and staining, as well as other uses.   Second, the old methods put a relation between certain key parts ahead of others, and ahead of concerns for symmetry or specific measure.  These key relations are preserved even as they experiment with details of design.  The 'kit' or 'collection of methods' are very traditional, and while considerable experimentation in the exact implementation of the 'kit' from one instrument to the next is part of the tradition, changes to the actual 'kit' only develop or evolve much slower.  This insures that the most important deeper relationships among elements of design are highly protected.   Third, the 'kit' of methods provides a fine grain capacity to copy or subtly vary any combination of features from instrument to instrument, while keeping the most important and deepest embedded aspects of the design most protected.  This results in a powerful and well structured path for individual and community learning about what does and doesn't work well in the instruments.   This last might well be the most significant aspect of the method, and how it most powerfully contributed to the historical success of the old Italian making.

None of this need have any relevance to makers that are pursuing a path of modern innovation in making.  Nor to anyone that doesn't decide to make it important.

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2 hours ago, David Burgess said:

I think that almost any drawing or drafting system can be superimposed on violins, if one tries hard enough.

Do I think it means that the superimposed system was original, or that it matters? No.

Haven't noticed that. Most "drafting systems" seem to work only for the violin the author bothered with. 2-3 iterations later it starts looking like Chupacabra. 

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I think it's fair to say that given the tools and mathematical knowledge available at the time, some form of geometric construction would have to have been employed to arrive at the shapes we see in classical violin making. I appreciate any sincere attempt to approach that matter. Without considering the antique instruments we treasure from a design perspective with an intent to comprehend, we are stuck either copying successful models of the past or going back to the drawing board and attempting to reinvent a tool that is considered by the users of our time to have been perfected shortly after it's conception.

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I would very much like to see some of D. Beards work posted here.

I don't recall ever seeing a photo of your work in the ten years I've been here.

I've looked at your website and did not find any examples of your work. Why is that?

I find your writing interesting but there is nothing to compare your work to modern copyist models.

I mean no offense...but come on give us a glimpse of your work....Whadda say David?

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I've only made a handful of instruments to date, and most have been in the way of experimenting with parts of these ideas.  I am back in the workshop now.  Admittedly slowly, I'm now working on a pair of violins that I hope will both embody a full representation of these ideas, and be successful good instruments.

I undertook this research because when I set my sights on making, I found that no one had before me given a sufficiently complete picture of old methods to enable to make without recourse to copying or guessing.  So all of this has happened as part of the first steps in my journey into making.   Theory, research, and practice don't always travel in perfect synchronized equality.  For a while now, my research as led my way, and the making has been limited and largely experimental.   I do hope that soon I will have good instruments to show to all.  That's certainly the purpose of the research, and my aim.   But I remain more interested in the quality and nature of the work I eventually arrive at, rather than how fast I get there. 

I know that doesn't satisfy the current request to see my work.  But it's how things are for now.    Please understand however that showing outstanding work would neither validate nor invalidate my research.  And neither would showing poor work.    

 

I also didn't show my research until more than six years into it.  It's very much my desire than in another few years everyone will have seen plenty of both.

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David Thanks for explaining. I look forward to your instruments not to judge but to learn from them. And to see if the old methods of design, wood and varnish work really do make a difference when compared to the modern copied approach.

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Steward Pollens wrote a book about Strad forms and he is against the idea of highly complicated formulas for designing the molds:

"Paper body patterns preserved in Cremona may have been preliminary studies for the wood forms. Like the wood forms, the paper patterns lack construction marks associated with a formal system of design. Remmants of rather crudely sketched oulines remain on the perimeters of the paper patterns, suggesting that the designs were freely sketched. Central folds may have been used to asses or adjust left-right symmetry (the sketched outlines often appear to wander on either side of the trimmed edge. A drawing for a viola d'amore (MS no. 344) is quite irregular, though it's outline could have been made symmetrical if folded and cut out." (page 13).

"... ... there are no indications of how new proportions were established or how curves were drafted... ... The relative lack of geometric construction marks on the wood forms and paper patterns is indeed surprising and casts doubt upon theories that propose that Stradivari emplyed complex geometric schemes in generating the outlines of his forms.

If a formal geometric system of construction was not used to generate the outlines of the forms or paper body patterns, how were they designed? From physical evidence it may be impossible to provide a definitive answer for all the form; however, when tracing of certain forms are overlaid it becomes clear that Stradivari copied sections of earlier designs (the upper-and certer-bout regions, for example) and changed other areas (such as the lower bouts) to create new models. The design technique was certainly used in the altered forms, where parts of the initial desing were left intact and other areas modified. As mentioned above, a number of designs appear to have been quickly sketched on a folded sheet of paper and then cut out - creating a symetrical pattern wich was then transferred to a wood plank used to make the form." (page 14 of Pollens' book)

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You may want to look at my work on viola da gamba. In essence, I think that the English makers of the 16th-early 17th century were interested in the same general philosophy, but approached design as "Proportion" rather than "Geometry" (which makes much more sense if you read things like Euclid's elements. So, you can't make a violin this way, but it adds to the general idea. 

I left this work "as is" years ago. Frankly it's a headache to put stuff together, so I thought it better just to put the concept out there... if anyone ever wants to revisit it and take it further, I'll be delighted!

https://www.academia.edu/149099/The_Geometry_of_Early_English_Viols

This is about the best sequence I could come up with... :)

https://www.academia.edu/1119976/The_Geometry_of_the_English_Viol_Geometrical_Sequence_for_a_Treble_VIol_by_John_Hoskin_s_1609

 

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4 hours ago, MANFIO said:
Steward Pollens wrote a book about Strad forms and he is against the idea of highly complicated formulas for designing the molds:

"Paper body patterns preserved in Cremona may have been preliminary studies for the wood forms. Like the wood forms, the paper patterns lack construction marks associated with a formal system of design. Remmants of rather crudely sketched oulines remain on the perimeters of the paper patterns, suggesting that the designs were freely sketched. Central folds may have been used to asses or adjust left-right symmetry (the sketched outlines often appear to wander on either side of the trimmed edge. A drawing for a viola d'amore (MS no. 344) is quite irregular, though it's outline could have been made symmetrical if folded and cut out." (page 13).

"... ... there are no indications of how new proportions were established or how curves were drafted... ... The relative lack of geometric construction marks on the wood forms and paper patterns is indeed surprising and casts doubt upon theories that propose that Stradivari emplyed complex geometric schemes in generating the outlines of his forms.

If a formal geometric system of construction was not used to generate the outlines of the forms or paper body patterns, how were they designed? From physical evidence it may be impossible to provide a definitive answer for all the form; however, when tracing of certain forms are overlaid it becomes clear that Stradivari copied sections of earlier designs (the upper-and certer-bout regions, for example) and changed other areas (such as the lower bouts) to create new models. The design technique was certainly used in the altered forms, where parts of the initial desing were left intact and other areas modified. As mentioned above, a number of designs appear to have been quickly sketched on a folded sheet of paper and then cut out - creating a symetrical pattern wich was then transferred to a wood plank used to make the form." (page 14 of Pollens' book)

There are realities that one should be familiar with when dealing with geometry in the Renaissance period.
Among them it should be emphasized here that:
 - From antiquity to the end of the Renaissance, geometry and measurement are synonymous. Thus the texts use indifferently one or the other term. So to doubt that we used geometry is to doubt that we used measurement. This makes no sense.
 -There is no confusion between relative measurements and metrological measures at least as long as, according to Euclid, unity is not a number.

The fading of the Ancients principles  I have just stated, was possible thanks to the work of remarkable mathematicians. The old concepts  become obsolete. What we call "the quarrel of the ancients and the moderns" is a trace of this period (XVII°) precursor of our modernity, science and technology.

 Thus, our understanding of measurement is fully dependent on the theoretical advances of the seventeenth century and consequently, what the school teaches does not make it possible to understand well the thought of a craftsman of XVI ° S.

That's a bad new for us.

Luckily, there is a XV ° S manuscript containing a technical lute drawing. I showed that:
- the deep meaning of this drawing is understood only if one takes into account the principles mentioned at the beginning of this post.
- that at that time, any well designed project respects these principles
-that the violin does not escape this rule.

I agree that that is difficult to assimilate. But our difficulty here is the mark of our culture and our education. It is silly to reject what is difficult for us to understand with the argument that the craftsmen could not have been satisfied with such a difficulty (often confused with complexity). Many things are difficult for me and not for others like speaking Chinese for example. I do not understand anything in Latin but I do not doubt that this language has been spoken without difficulty. It's the same with the concept of measurement except that we do not pay attention. The list of authors who understand this is much easier to train than the other way round. To stay in the field of violin Pollens and Coates for example are off topic when they talk about measurement (which they incorrectly call "proportions"). At no moment does they succeed in getting rid of a metrological representation of the measurement.

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4 hours ago, MANFIO said:
Steward Pollens wrote a book about Strad forms and he is against the idea of highly complicated formulas for designing the molds:

"Paper body patterns preserved in Cremona may have been preliminary studies for the wood forms. Like the wood forms, the paper patterns lack construction marks associated with a formal system of design. Remmants of rather crudely sketched oulines remain on the perimeters of the paper patterns, suggesting that the designs were freely sketched. Central folds may have been used to asses or adjust left-right symmetry (the sketched outlines often appear to wander on either side of the trimmed edge. A drawing for a viola d'amore (MS no. 344) is quite irregular, though it's outline could have been made symmetrical if folded and cut out." (page 13).

"... ... there are no indications of how new proportions were established or how curves were drafted... ... The relative lack of geometric construction marks on the wood forms and paper patterns is indeed surprising and casts doubt upon theories that propose that Stradivari emplyed complex geometric schemes in generating the outlines of his forms.

If a formal geometric system of construction was not used to generate the outlines of the forms or paper body patterns, how were they designed? From physical evidence it may be impossible to provide a definitive answer for all the form; however, when tracing of certain forms are overlaid it becomes clear that Stradivari copied sections of earlier designs (the upper-and certer-bout regions, for example) and changed other areas (such as the lower bouts) to create new models. The design technique was certainly used in the altered forms, where parts of the initial desing were left intact and other areas modified. As mentioned above, a number of designs appear to have been quickly sketched on a folded sheet of paper and then cut out - creating a symetrical pattern wich was then transferred to a wood plank used to make the form." (page 14 of Pollens' book)

Or the paper forms might have been quickly traced afterwards, from the actual work, to document and keep.     I don't believe such freehand creation as you describe would give whats seen in the instruments.  Nor such consistent fit with geometry constructions as it does.

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In "underweissung" Albretch Durër introduces the drawing of curves as follows. He says (I quote from memory) that a curve is drawn freehand or point by point or with a compass. It is recommended to use the most appropriate means and the best control. Understood that if you are good enough not to use a compass then do not use it. This means that there is no opposition but rather complementarity of the drawing process. In addition, measurement procedures focus mainly on the construction of surfaces rather than outlines.

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On 10/30/2017 at 4:58 PM, David Burgess said:

I think that almost any drawing or drafting system can be superimposed on violins, if one tries hard enough.

Do I think it means that the superimposed system was original, or that it matters? No.

I believe the first instruments may have used simple triangular bouts (like the Russian Balalaika) but early players didn't like the sharp edges so they were sawed off.

More and more straight saw cuts were made until the bouts eventually looked like smooth rounded curves as shown in the attached constructions.  The last one is superimposed on the Titian Strad CT rib scan to prove what you said that anything works if you try hard enough.

1.jpg

2.jpg

3.jpg

4.jpg

5.jpg

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Back to this... :(

 

Many curve families can be caused to fit violin families.     But few can be cause to generate the shapes from simple initial choices, and as far as I'm aware there is only one solution that can generate the full range of classical Italian violin shapes from a simple consistent range of choices.

Add historical context and there you go.

But there is no hope of convincing everyone.

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On 10/31/2017 at 6:02 PM, David Beard said:

Or the paper forms might have been quickly traced afterwards, from the actual work, to document and keep.     I don't believe such freehand creation as you describe would give whats seen in the instruments.  Nor such consistent fit with geometry constructions as it does.

 

On 10/31/2017 at 1:32 PM, MANFIO said:
Steward Pollens wrote a book about Strad forms and he is against the idea of highly complicated formulas for designing the molds:

"Paper body patterns preserved in Cremona may have been preliminary studies for the wood forms. Like the wood forms, the paper patterns lack construction marks associated with a formal system of design. Remmants of rather crudely sketched oulines remain on the perimeters of the paper patterns, suggesting that the designs were freely sketched. Central folds may have been used to asses or adjust left-right symmetry (the sketched outlines often appear to wander on either side of the trimmed edge. A drawing for a viola d'amore (MS no. 344) is quite irregular, though it's outline could have been made symmetrical if folded and cut out." (page 13).

"... ... there are no indications of how new proportions were established or how curves were drafted... ... The relative lack of geometric construction marks on the wood forms and paper patterns is indeed surprising and casts doubt upon theories that propose that Stradivari emplyed complex geometric schemes in generating the outlines of his forms.

If a formal geometric system of construction was not used to generate the outlines of the forms or paper body patterns, how were they designed? From physical evidence it may be impossible to provide a definitive answer for all the form; however, when tracing of certain forms are overlaid it becomes clear that Stradivari copied sections of earlier designs (the upper-and certer-bout regions, for example) and changed other areas (such as the lower bouts) to create new models. The design technique was certainly used in the altered forms, where parts of the initial desing were left intact and other areas modified. As mentioned above, a number of designs appear to have been quickly sketched on a folded sheet of paper and then cut out - creating a symetrical pattern wich was then transferred to a wood plank used to make the form." (page 14 of Pollens' book)

I agree with Pollens.  Strad's  tenor viola wood form marked "TV" (MS no. 229) shows scribe marks for shortening the form.

Pollen says on page 16:  The sketchy quality of these scribe lines would indicate that the intended alteration was marked out without the use of a template or drafting aid."

Strad's scribe lines on the lower bout look reasonably attractive so I think he would have been a skilled enough to sketch a whole form.

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On 10/29/2017 at 7:27 PM, Marty Kasprzyk said:

In addition to the ones you’ve already listed for compass and straight edge constructions:
 
V. Baginsky, “Construction of a contour and arch with use of the golden section”, translate. by F. Liden, Stockholm, 1996

D. Woodrow “The Shape of Stradivari Forms and Violins”, Taunton Press, Oxford, 1991

Simone Saccon, “The Secrets of Stadivari, Translated by Andrew Differ and Cristina Rivroli,  Eric Blot, Cremona, 2000

Robert Spear, “The Stradivari Model G, the Golden Section, and Modern Violin Design”, Journal of the Violin Society of America VSA Papers, Volume xxii, No 1

 

If you believe true ellipses do an easier job of matching violin geometry than circles I suggest:

George L. Hersey, “Architecture and Geometry in the Age of the Baroque”, The University of Chicago Press, Chicago, 2000
 

I forgot to include an interesting article on drawing ovals which is attached.  It gives a good history overview of architecture and how ovals were used and how they were drawn by different methods.  Its bibliography is great if you like this stuff.

Serlio's construction of ovals.pdf

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Those who know me are aware that I am pretty pragmatic about instrument design and have used either patterns shared with me by my teachers or those derived from the outlines of existing instruments for a very long time. Also that my education did not include  much in the way of maths before learning  violin making. I have read or tried to read much of the literature on violin design for many years and have understood very little or found the constructions so complex that they were impossible to use. I have recently watched some of Kevin Kelly's videos, however, and  have finally understood how geometry could indeed result in the forms of the Amati family from which other models could have been derived by gradual modifications. The video suggested by  Juan Tavira above certainly makes sense to me and I will be looking at it again when I have more time to do some drawing.

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