Thomas Coleman

Violin geometry references

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Some historical images of dividers.  In most of these pictures some sort of straight edge also appears, most frequently as a square.

 

 

In the artisan's work place:

68e993168061d4794232f7de9349d623--le-roman-la-rose.jpg.dc18f574b2c63a5439dd1f900a302612.jpg

 

6f06d430a6a9b3441908724bf7d7530d--medieval-life-medieval-art.jpg.41de4a262df175d929b9fcedc839c5e0.jpg

 

4150afcb0c11350324b1f6c8d14dd50f--woodworking-furniture-woodworking-tools.jpg.2cc5317a3edf9de32ed57744735af40e.jpg

 

 

426239dcc45966b795fe5343f72fe245.jpg

Jacobo-da-Ponte-1574-Noah_s.jpg.e467ffb4af74f601e61e48e98f579231.jpg

size1.jpg.866756ee4ebd45ec1c2359b862b19131.jpg

temple05.jpg.7e6c58cd1732eb559887bf601edce757.jpg

 

And as part of the general workshop tool set, extending up to modern times:

cbab1f6e04dc0e468bc83f78fae4c2dd--woodworking-furniture-woodworking-tools.jpg.0f8b5946e42b1399d3ba645cde73f326.jpg

 

Woodworking_Hand_Tools.thumb.jpg.13d922fbc35f7c34ce35486a639e859f.jpg

526b9909b954a9e7834d3bacf0ed6cdc.jpg

 

 

We don't readily recognize the importance and pervasiveness of such tools in earlier times.  Dividers were made small and large.  Strings, chains, and trammel systems could be used to allow compass arcs of any size desired.   Small tools were often made with great care.   And many elaborations of the dividers were developed.   In a very real sense, proportional dividers were the calculating machine of the day, all the way until modern times.

Various dividers:

2c387b8edf33eaef3d57603b85051ce1.thumb.jpg.12a9156e3290fdff749157bf4412cdb8.jpg

4b98e6447f29570b5af740b041563a9a--compass-tool.jpg.0617316a8ce7601e80bb6349fa30c727.jpg

61b33548ea8c984f950ab8ea025111c8--stahl-wooden-bowls.jpg.e35cfd22a058340874bd3bf26c01b04b.jpg

 

And the compass acquired additional symbolic meaning, representing order and harmony, as well as creation and design.  It also sometimes acquire more political and social overtones:

5a052226710b5_medievalcompass.jpg.bce53f5800fca0938b647b2c6508e8ce.jpg

frm_009.jpg.66329115c21e5c09c7f8174b6d370b68.jpg

xl_geographer.thumb.jpg.81bf809bb8d1ebfe507bbf12fed8e7a2.jpg

Pends_L_sil_Ment_-_copie-1.jpg.c9a33b7e87763bf345cb2237fcfe1b02.jpg

5a0523aec9971_Drer_Melancholia_I.thumb.jpg.5543dc7ee8182b6a3d135f63ab5b988b.jpg

 

And, since Pythagoras and therefore the roots of western thought, proportion and harmony have been inseparably associated.  And dividers are the natural tool for carrying proportions into physical form:

monochord.thumb.jpg.fabd2416462df0e2ffc871d6d2c283bc.jpg

 

******************************

As both Ben and Francois have alluded to in this thread, there is an ancient notion running through western design that is sometimes expressed with the word harmony.  The idea is that the various parts and the whole of a work should all relate to each other.   The simplest way to create this while designing or building something is to take the size of one part using your dividers, and again use your dividers to produce the size of anther part through simple ratios.

 

********************************

 

Holbein.jpg.1704a25cdd1a6dfd12e50e5ead2542b1.jpg

 

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14 hours ago, David Burgess said:

Dang it, I only got about half way through before running out of whiskey, and I can't go out and get more, because I'm above the legal limit to drive. What do I do now? :lol:

I don't see them as being in opposition, nor am I more in support of one or the other. What I would suggest though is that practically speaking, to a contemporary maker, it doesn't matter. If one wants to come close to what has been done in the past, they can copy. Or they can imitate what they see as an attractive empirical theme, without strictly copying, but rendering their own interpretation. Or they can do something closer to freehand, should they be adventurous enough.  Or they could use some sort of drafting system which appeals to them. There are lots of options.

Sticking closely to some formula doesn't seem to be that important for sound. This is perhaps most clearly demonstrated with violas, which can be all over the map, without this necessarily causing a reduction in sound quality. Even with violins, dimension or shapes or proportions can be tweaked quite a bit, with no apparent damage to sound quality.

You paraphrase here Durër's thought (quoted above) when he talks about the techniques to know to draw a line. One can always copied empirically existing profiles but that's not the question. The question is: how did the creators of these profiles operate? What knowledge have they referred to and what can we understand?
The answer to this question should not evoke the beliefs but the facts.
If you think that a rational project originates these profils you must be able to state it according to sources. If you do not agree with the analysis of these sources or if you have reservations, you must be able to say why the analysis of these sources is at fault. One can not dispute (like some do here) the existence of things and ideas with the sole argument that one does not need them.
(Let's leave aside the acoustic which is another topic)

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8 hours ago, Addie said:

How many people who don't know music theory do you think are admitted to master classes?  :P

I don't think the same is true for VM classes.  Even at the master level.  Good workmanship does not require drafting from scratch using anyone's reconstructed Cremonese secret... 


Dear Addie This is the current situation but you are probably aware of the only document we have which give us the content of a master luthier exam. This happens in Toledo at the turn of the sixteenth and seventeenth centuries. It states that to become maestro the luthier will draw a violin to the rule and the compass and also drill all the ankles freehand. So at that période to pretend to be a maetro you should get both theory and practice.

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8 hours ago, Ben Hebbert said:

It's difficult to get our modern heads around the medieval idea of "Harmonia" which was an obsession for abut 1000 years of Western thought, and gives understanding of why a theoretical, mathematical reasoning of music was important not to musicians and instrument makers so much as to the foundation of all scientific thought. 

Early philosophers recognised that the natural ratios appearing in music were the same ratios that described the cosmos, and the same ratios - as per Vitruvian man - that described the proportional nature of the human body, and as we are made in God's form, therefore, Divine form. That these ratios describe many other occurrences in God's Creation merely reinforced the concept of the divine nature, so easily demonstrable through the harmonics of a vibrating string - 2:1 Octave, 3:2 Perfect Fifth, 4:3 Major Third, 5:4 Minor Third... hence the study of Harmonia was the understanding of how God created the earth, of understanding nature, and hence to understand how to create new things in the same vein, which is what music itself constantly does. If you studied the quadrivium at a Medieval or Renaissance University - or even into the eighteenth century,  this was fundamental to how you progressed to learn other things: It was a mandatory part of education whether you were musical or not. If you didn't but were schooled to any level by people who had studied the Quadrivium, it was essentially a robust part of the European curriculum. Being a musician - at least an elevated musician - meant that you essentially had to be steeped in an understanding of this as a way of validating your performance or simply your claim to be musical. Hence Thomas Morley's Plaine and Easie Introduction to Practicall Musicke, (1597) and after the 1650s, innumerable editions of John Playford's Introduction to the Skill of Musick

These attitudes are totally incompatible with our modern notions of musicianship. They seem utterly otherworldly, bizarre and unnecessary and yet they represent the bulk of musical thought as we know it throughout the 16/17/18th centuries... If musical instrument makers played a part within these communities they surely had to play to the same rules to one extent or another. If only conscious that former generations had done the footwork for them and they could be content simply copying forms, which perhaps accommodates David Burgess's view as entirely compatible with past attitudes as well - at least if many regional makers did apply rigid rules of geometry and proportion, they would have done a pretty dismal job, to judge by the relative ugliness of their work.

 

Morley's 1597 Plaine and Easie Introduction to the Skill of Music of 1597 is available here in its 1771 reprint. It's curious that a few violin makers are in the subscribers list for it... sowhatchathinkthattellsya? It's also worth a bottle or two of whisky whilst reading it... or scanning it just to understand the complexity of it.  In original form, it is purposefully by the same printer as Dee's Euclid's Elements, the same frontispiece and format and very definitely intended to be an associated work.

 

 https://books.google.co.uk/books?id=ZvG6loTD7OsC&pg=PA31&dq=morley+musicke&hl=en&sa=X&ved=0ahUKEwjH3KK-4rLXAhWjLMAKHSR4AvIQ6AEIRjAF#v=onepage&q=morley musicke&f=false

 

Totally off subject, but here's a 1580s illustration by Mathew Baker, a royal shipwright in England. I like to think its pretty close to what I'd see in a violin maker's workshop of the same era...

 

442_4.thumb.jpg.b40ed781525e681f7c2693ed077ebdff.jpg

Hi Ben   Nice illustration, new for me :) . It's good to explain how all these profiles and architectural drawings made during the Renaissance are related to the thought of Quadrivium. It is striking that even simple craftsman like the musical instrument maker strive to comply with these rules

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7 hours ago, Violadamore said:

What are we supposed to think?  I can read your text, but not your mind.  You began by deprecating grammar, then began using "elite" in a vague way which does not indicate which particular superior or difficult-to-join group you are attempting to show contempt for.  I'd say you're digging a good hole for your own argument.  :P:lol:

But I was not deprecating grammar, or showing contempt for elite language. You made that part up. ;)

I was speaking only about its usefulness or utility, just as I was when speaking about ways of making a violin.

1 hour ago, francoisdenis said:

One can not dispute (like some do here) the existence of things and ideas with the sole argument that one does not need them.
(Let's leave aside the acoustic which is another topic)

Who was disputing the existence of anything?

Yes, I did question whether one needs them.

Funny thing: In the various violin making competitions I have judged, I have never ever heard another judge say something like, "Uh oh, this doesn't look like these arcs were drawn with a compass". Or, "These dimensions look like they might have been transferred with a a ruler, rather than a compass". I don't think I have even heard any widely regarded fiddle expert say something like that in any venue. :)   I don't think I have ever heard a musician say anything like that either.

However, I won't claim that being able to say something is done a certain way couldn't have some marketing value.

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14 minutes ago, David Burgess said:

[...]. .    "Uh oh, this doesn't look like these arcs were drawn with a compass". Or, "These dimensions look like they might have been transferred with a a ruler, rather than a compass".  [...]

And here I was thinking that was the technical translation of Testore and early Guadagnini scrolls look 'rough'.:lol:

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1 hour ago, francoisdenis said:

Hi Ben   Nice illustration, new for me :) . It's good to explain how all these profiles and architectural drawings made during the Renaissance are related to the thought of Quadrivium. It is striking that even simple craftsman like the musical instrument maker strive to comply with these rules

 

To follow from this... 

 

Here is a quinto acuto arch, like Bruneleschi's dome in Florence, which relies on a proportion of 5 parts width and the compass placed on the 4:5 point. Very simple medieval - renaissance geometry.

5a0580be51560_Screenshot2017-11-1010_34_08.thumb.png.32a824364b3ef8de5219fcb27b88fef2.png

To translate this, to make the kind of "composite" gothic tracery that you see in Medieval church windows, instead of using any kind of complex maths, I simply change the angle of the carpenter's rule from dividing the width from five parts to, in this case, 6 parts. 

 

5a05819b3f80e_Screenshot2017-11-1010_37_51.png.ff15e65ea57f33410e2cd3f29e2ec6b8.png

- the rectangular base, for what it's worth is a standard golden ratio constructed as you can see here.. 

5a0581e567987_Screenshot2017-11-1010_39_16.png.7f0c3965266f65e9968b16d161287ea3.png
 

So as you can see there is nothing sophisticated or particularly scientific in laying out the tracery of something like this... 

5a05822a2fb36_Screenshot2017-11-1010_40_22.thumb.png.810e92bcf7cf5036526765ec3a3777b8.png

... which you see on every single church in Britain.. (not actually that one, I'm being lazy ... you get my point though)

... when I was thinking about translating proportion in terms of English viol geometry - any idea had to be contingent on the simplicity of the tool to do it. I very quickly understood that dividing and multiplying any measured unit was too complex, and it had to be something using dividers, carpenters rules, etc. 

The basis of all my geometric-proportional ideas is a calculator for super particular ratios, i.e. whole number ratios of 1:2, 2:3, 3:2, etc. It could be scribed on your bench, wall or on a piece of vellum and looks like this.. 

5a058343cd5b0_Screenshot2017-11-1010_43_58.thumb.png.18f5ac7c5bdf5fd58eb05b4ec871428a.png

With the help of a square, to reduce an arbitrary measurement by say 3:2, you move your dividers to where they meet on the III line, and reduce down accordingly.

5a0583ad04551_Screenshot2017-11-1010_46_41.thumb.png.6cfa480524a32c5f1c288f69dcfb83cc.png

 

Whatever philosophical, scientific, magic, divine ideal sits behind what you are doing, and irrespective of whether you feel it is important or not to the outcome, it is just simply easier to work in proportions as a craftsman, and if you have the smallest belief that proportions make things look 'well proportioned', 'proportionate' etc. etc. etc. .... then you are working in a tradition that every stone mason and every craftsman was vaguely aware of even if they hadn't the slightest notion of who Euclid and Pythagoras were. 

Lastly, here are examples of Daisywheel graffiti, which appears in churches on stone and wood, and seems to have been a way that the slightly pagan English - up into the Renaissance period - would ward off any evil spirits that God couldn't cope with. You see them absolutely everywhere on church furniture and on the fabric of the buildings... 

In terms of mysticism, the simple idea that the compass creates an entirely autonomous and divinely perfect line, can probably be seen through medieval and primitive eyes as something miraculous outside of human control - essentially using a magic wand to invoke a spell. Amati & Chums weren't that primitive - anything but, so understanding what the lowest common denominator is for geometric fascination puts them well within the ideological reach of things. It also reinforces how ubiquitous the idea of a compass (or two fixed points) would have been to our ancestors.

blogger-image--1920493546.jpg.38503b69fa9410f401b2135613091ada.jpgwp7122f227_06.png.882239f5d6f1eede2f0ba5efe0414212.png

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29 minutes ago, David Beard said:

And here I was thinking that was the technical translation of Testore and early Guadagnini scrolls look 'rough'.:lol:

Rough can be nice. :)

It may be a special challenge to make it look good though, on a fully-varnished non-antiqued violin.

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7 hours ago, francoisdenis said:


Dear Addie This is the current situation but you are probably aware of the only document we have which give us the content of a master luthier exam. This happens in Toledo at the turn of the sixteenth and seventeenth centuries. It states that to become maestro the luthier will draw a violin to the rule and the compass and also drill all the ankles freehand. So at that période to pretend to be a maetro you should get both theory and practice.

Dear M. Denis, yes I am indeed aware of that requirement.  Please don't take my moments of flippancy seriously.  Sometimes, like Melville's Ishmael, one impulsively feels like knocking off hats (especially on a cold November day) rather than discussing the teleological intent of craftsmen who have been dead for hundreds of years.  :)

I am, in fact, intensely interested in craft tools and techniques of the past, and am, of course, an admirer of your work. :wub:

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The problem with the Socratic method is that it assumes all the facts are known, or discoverable whilst chatting in the shade of an olive tree...  ^_^

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Interesting conversation. Personally I am a big fan of a geometrically assisted and informed design concept, but not in any way that is dictorial , more of a way to explore,and define ideas. The daSalo I did fit bueatiful into the ratios described by F.Denis , but there seemed to be room left for interpretation of the final curves and new ratios to play with, da Salo used several ratio schemes to do his work. Even combining them .If I were Strad and had not served an apprentice with Nicole, might be easier to just cop a form.....The M .... And simply go from there vs the geometric recipe needed to get the form. Hard telling not knowin. Certainly good fiddles from both camps, probably the best all take some or considerable liberty to whatever school they ascribe to. 

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Another example of utility, versus sticking to a concept:

How many of us shape the top of the bridge by using a compass to draw an arc on the bridge, and then fudging that arc a little looser at the ends to make it look more like we are used to, so it doesn't give the impression of being "slope-shouldered"? Why would we, when it's so quick and easy to trace a pattern onto the bridge? 

How was the pattern originally generated? Perhaps by drawing a compass arc, and then fudging the shape at the ends, but that doesn't mean that one needs to go through the process each and every time one makes a bridge. 

Is a bridge where the compass is used directly on the bridge superior to one which is traced from a template? I don't see why.

Not that I wish to diminish in any way to contributions of the scholars and researchers. Just trying to add the perspective of someone who has spent nearly a career lifetime "in the trenches".

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2 hours ago, Addie said:

The problem with the Socratic method is that it assumes all the facts are known, or discoverable whilst chatting in the shade of an olive tree...  ^_^

It helps if the olive tree is conveniently placed between the taverna and the library.  :)

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1 hour ago, David Burgess said:

Another example of utility, versus sticking to a concept:

How many of us shape the top of the bridge by using a compass to draw an arc on the bridge, and then fudging that arc a little looser at the ends to make it look more like we are used to, so it doesn't give the impression of being "slope-shouldered"? Why would we, when it's so quick and easy to trace a pattern onto the bridge? 

How was the pattern originally generated? Perhaps by drawing a compass arc, and then fudging the shape at the ends, but that doesn't mean that one needs to go through the process each and every time one makes a bridge. 

Is a bridge where the compass is used directly on the bridge superior to one which is traced from a template? I don't see why.

OK, how about this?   

You want to use a violin bridge template for a violin, cello template for cello, etc. and you may want to make the string heights higher or lower for some reason, etc. 

The template is already done because it’s been figured out how it works, and you can make whatever modifications you want and make your customer happy.

What i use is exactly that - a template that can be modified, so if you want to make something different you don’t have to start from scratch each time, and the result will always look “right”.

I'm moving my studio, so I can't take photos of stuff right now, but here are a few fiddles I made5a061aa01bb3e_n1carvedf.png.99f0cc72b64922205402784eefc61da5.png.  Can you tell these shape were drawn with a compass?

IMG_2484.thumb.JPG.9998c62f14ea94b02ef8d7a1ed85dd78.JPGN1_bench.thumb.JPG.8d0f95f1c62c1904ba112e7e56307dd6.JPG

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Kevin, those look like very nice fiddles, and I have never doubted your making ability.

People who use other methods have also made very nice fiddles.

I might make some small changes in the outline, to bring them more into line with my personal taste, or what I consider to be the "Cremonese" concept, but that's neither here nor there.

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24 minutes ago, David Burgess said:

Kevin, those look like very nice fiddles, and I have never doubted your making ability.

People who use other methods have also made very nice fiddles.

I might make some small changes in the outline, to bring them more into line with my personal taste, or what I consider to the the "Cremonese" concept, but that's neither here nor there.

:P

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I made my own bridge templates.  I think that brought me emotionally closer to Stradivari.  Or at least emotionally closer to Herdim and StewMac.  :rolleyes::lol:

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12 hours ago, David Burgess said:

But I was not deprecating grammar, or showing contempt for elite language. You made that part up. ;)

I was speaking only about its usefulness or utility, just as I was when speaking about ways of making a violin.

Who was disputing the existence of anything?

Yes, I did question whether one needs them.

Funny thing: In the various violin making competitions I have judged, I have never ever heard another judge say something like, "Uh oh, this doesn't look like these arcs were drawn with a compass". Or, "These dimensions look like they might have been transferred with a a ruler, rather than a compass". I don't think I have even heard any widely regarded fiddle expert say something like that in any venue. :)   I don't think I have ever heard a musician say anything like that either.

However, I won't claim that being able to say something is done a certain way couldn't have some marketing value.

So we still agree, not using (and by extension, not seeing, not recognizing, not saying and not hearing, things, ideas,relations etc ...) says nothing of their existence .
May be the secret of happiness :)

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7 hours ago, Addie said:

Dear M. Denis, yes I am indeed aware of that requirement.  Please don't take my moments of flippancy seriously.  Sometimes, like Melville's Ishmael, one impulsively feels like knocking off hats (especially on a cold November day) rather than discussing the teleological intent of craftsmen who have been dead for hundreds of years.  :)

I am, in fact, intensely interested in craft tools and techniques of the past, and am, of course, an admirer of your work. :wub:

No need for admiration, if you understand it, it is enough for me

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36 minutes ago, francoisdenis said:

So we still agree, not using (and by extension, not seeing, not recognizing, not saying and not hearing, things, ideas,relations etc ...) says nothing of their existence .
May be the secret of happiness :)

No, I don't see it that way, regardless of how you may wish to interpret my posts into some sort of skullduggery, or lack of intelligence.  Isn't there a level on a higher plane than casting insults ?

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so I do not understand you. Do you consider that, regardless of whether it is currently useful, recognized, seen etc ... It is important to understand how the violin was designed?

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31 minutes ago, francoisdenis said:

So we still agree, not using (and by extension, not seeing, not recognizing, not saying and not hearing, things, ideas,relations etc ...) says nothing of their existence .
May be the secret of happiness :)

Modern scientific method would state that the above says nothing of their NON-existence. But we should also NOT believe in their existence, or act as if they exist without good reason.

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1 minute ago, ctanzio said:

Modern scientific method would state that the above says nothing of their NON-existence. But we should also NOT believe in their existence, or act as if they exist without good reason.

Yes of course,  we need some of them and we have them

 

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3 minutes ago, francoisdenis said:
 

 

so I do not understand you. Do you consider that, regardless of whether it is currently useful, recognized, seen etc ... It is important to understand how the violin was designed?

I think that it's really interesting,

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