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Corner shape


Don Noon

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Likewise, if one cannot do without decimal numbers, it's simple enough to compute the arctangent of 0.5000 (or as many zeros as you want), to come up with 26.57 degrees.

There are multiple ways of making parallel lines, some of which are unintentional, such as flipping templates and filing the same angle. That may look right because it follows our classical definition of design, which is an educated, not inherent, concept.

There's design, lay-out, and artistic interpretation. And I think most of us would agree there are probably Monday corners and Friday corners.

And certainly more than one way to skin a cat.

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There are multiple ways of making parallel lines, some of which are unintentional, such as flipping templates and filing the same angle. That may look right because it follows our classical definition of design, which is an educated, not inherent, concept.

In my case, it wasn't exactly unintentional. It just seemed like the quickest and most efficient way to make all four corner angles about the same. Later, that must have no longer looked right to me, because I find that now (upon checking), I make the upper and lower angles different. The same technique could still be used, just rotate one template a little before filing. That way, all four end curvatures are still automatically the same, while the upper and lower angles will be different.

There are more complicated ways to get the same result, but why bother?

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Thanks for sharing.

I think you can start out with a determined angle for the corners, but in the end, the intervention of the violinmaker and his artistic contribution to the final finishing touches to the instrument goes beyond anything that any measurement could ever give us.

I like things that are not completely predictable or somehow not quite precise. A truly great violin does not have to be absolutely precise. Let yourself go a little. Develop your own tastes. In the beginning it's about having a set of reference measurements but once you are able to reproduce those measurements doesn't mean that you are at the end of your exploration in violinmaking or aesthetics.

Bruce

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In my case, it wasn't exactly unintentional. It just seemed like the quickest and most efficient way to make all four corner angles about the same. Later, that must have no longer looked right to me, because I find that now (upon checking), I make the upper and lower angles different. The same technique could still be used, just rotate one template a little before filing. That way, all four end curvatures are still automatically the same, while the upper and lower angles will be different.

There are more complicated ways to get the same result, but why bother?

Fair enough. But one's understanding of what is complicated depends on how they were taught to think of things. Today, we often think of things such as 25 degrees, 30 degrees, $3.05 per gallon, 14 and 1/16 inches, 32 mm, 3.1415926... and so on, and it seems natural to us. Back in the classical violin-makers' day, it would have been more natural to think of things in terms of ratios, or fractions, such as 1 to 2 and 3 to 4.

And then there is the distance between the design and the finished product that kinda mucks it all up! :) (Edit: Bruce said it better.)

If it was simply random, or artful, though, perhaps we might see pointed corners, or corners cut parallel to the centerline, circular corners, or corners at random angles. I'm sure all have been tried, but they never look quite 'right' to us. To my mind, it indicates an underlying design, which would be based in the way design was done in those days.

And I don't know -- just what seems right to me. Certainly a product of the way I was taught.

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I think you can start out with a determined angle for the corners, but in the end, the intervention of the violinmaker and his artistic contribution to the final finishing touches to the instrument goes beyond anything that any measurement could ever give us.

I like things that are not completely predictable or somehow not quite precise. A truly great violin does not have to be absolutely precise. Let yourself go a little. Develop your own tastes. In the beginning it's about having a set of reference measurements but once you are able to reproduce those measurements doesn't mean that you are at the end of your exploration in violinmaking or aesthetics.

Bruce

Bruce,

I got similar advice (wisdom) from another pro this weekend, but I have to learn what the basic ground rules are before I can spread my wings and fly. I need to develop my artistic eye first (if I have one.)

Once I am told that I am there, I will take your advice and soar.

Stay tuned.

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Bruce,

I got similar advice (wisdom) from another pro this weekend, but I have to learn what the basic ground rules are before I can spread my wings and fly. I need to develop my artistic eye first (if I have one.)

Once I am told that I am there, I will take your advice and soar.

Stay tuned.

I've said it before but a good way to get these things into your head is to draw or sketch them as often as you can. It trains your eye/hand coordination and forces you to become critical about detail. In the beginning you might want to copy something that you've seen and after a while you might try to sketch it out without looking at the original. The old saying is: "If you can't draw it you can't make it."

Bruce

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Ken,

I think your Arctan(0.5) is on the money. It's a simple geometrical layout.

Nevertheless, I suspect that Strad et al. were finessing their violin shapes because of the limitation of making by hand. The molds, for one, are so asymmetric from wear that I would throw them out. But these guys knew how to bring them back to artistic beauty.

That's my two cents.

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I've said it before but a good way to get these things into your head is to draw or sketch them as often as you can. It trains your eye/hand coordination and forces you to become critical about detail. In the beginning you might want to copy something that you've seen and after a while you might try to sketch it out without looking at the original. The old saying is: "If you can't draw it you can't make it."

Bruce

Now that I am doing and agree 100%.

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For me, the 'Betts' Stradivari's corner work is the epitome of beauty in design and I don't think it could be done without a thorough understanding of geometry.

That's the way beautiful or captivating music is created too. Can't be done without a thorough understanding of the applicable math, and a good education in musicology. :)

Hey, a violin is shaped a little like a female, isn't it?

If more women had been makers around the time of the genesis of the violiin, I wonder if violins would look different? :)

Why do my violins look like sheep? :)

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Fair enough. But one's understanding of what is complicated depends on how they were taught to think of things. Today, we often think of things such as 25 degrees, 30 degrees, $3.05 per gallon, 14 and 1/16 inches, 32 mm, 3.1415926... and so on, and it seems natural to us. Back in the classical violin-makers' day, it would have been more natural to think of things in terms of ratios, or fractions, such as 1 to 2 and 3 to 4.

And then there is the distance between the design and the finished product that kinda mucks it all up! :) (Edit: Bruce said it better.)

If it was simply random, or artful, though, perhaps we might see pointed corners, or corners cut parallel to the centerline, circular corners, or corners at random angles. I'm sure all have been tried, but they never look quite 'right' to us. To my mind, it indicates an underlying design, which would be based in the way design was done in those days.

And I don't know -- just what seems right to me. Certainly a product of the way I was taught.

For sure, Del gesu would have not existed without a solid tradition of making supported by few perfect geometrical model.

Violin making is one example among others of this type of inventive creations were based on well constructed archetypes (the history of the drawings of the typo provides us another example where you find very few geometrical archetypes beside numberless free interpretations of them)

Unfortunately for the violin making, the lost of the inital rules has disturbed the ancient relation between the perfect ideal model (like god) and the real object (imperfect, like human). Today this distance appears like a contradiction but it was not he case by the past.

Francois

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Ken,

I think your Arctan(0.5) is on the money. It's a simple geometrical layout.

Nevertheless, I suspect that Strad et al. were finessing their violin shapes because of the limitation of making by hand. The molds, for one, are so asymmetric from wear that I would throw them out. But these guys knew how to bring them back to artistic beauty.

That's my two cents.

Michael,

Well, my Arctan(0.5) comment was from Francois' post in this thread #117, where the sides of the triangle have the 1:2 ratio. As you know, if you want 30 degrees, you just make the ratio of the short side to the hypotenuse 1:2. Conceptually, though, I think that represents some of the difference in the way we think (degree measurements and standardized units of length) as opposed to folks back in the 1600s (small-integer ratios).

We (math, science types) often get accustomed to thinking of trig functions as black-box mathematical functions, instead of, in a basic interpretation, as simply ratios of sides of triangles. In addition to Francois' fine book on the subject, you can find a pretty nice description of it in Rudolf Wittkower's _Architectural Principles in the Age of Humanism_, specifically Part Four, "The Problem of Harmonic Proportion in Architecture". The concept of ratios of small integers is interesting to consider in design.

Again, that is the design part of it. Where the violin-maker goes from there is interesting, too.

Cheers,

Ken

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Michael,

Well, my Arctan(0.5) comment was from Francois' post in this thread #117, where the sides of the triangle have the 1:2 ratio. As you know, if you want 30 degrees, you just make the ratio of the short side to the hypotenuse 1:2. Conceptually, though, I think that represents some of the difference in the way we think (degree measurements and standardized units of length) as opposed to folks back in the 1600s (small-integer ratios).

We (math, science types) often get accustomed to thinking of trig functions as black-box mathematical functions, instead of, in a basic interpretation, as simply ratios of sides of triangles. In addition to Francois' fine book on the subject, you can find a pretty nice description of it in Rudolf Wittkower's _Architectural Principles in the Age of Humanism_, specifically Part Four, "The Problem of Harmonic Proportion in Architecture". The concept of ratios of small integers is interesting to consider in design.

Again, that is the design part of it. Where the violin-maker goes from there is interesting, too.

Cheers,

Ken

That's the way to draw a corner with a 30° angle (rather exceptionnal) 25° or less is the standart guide

post-29143-1271228242.jpg

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Francois, I like your drawings. Yes, indeed, these illustrate what I was referring to above, yet your drawings still give me different ways of thinking about the constructs.

I don't have any firm belief in 25 degrees or 30 degrees or any other degrees, except that the old builders didn't think of the corners in terms of degrees.

Thank you,

Ken

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Hi Ken,

Hi Ken,

Regarding the corners shape, it's probable that commun triangles in relation with a simple construction were the first in used. These kind of constructions are at the origine of the style we like. Note that rules like that one are not in contradiction with the artistic touch (for those who are annoyed by these geometrical stuff) I would say that it's exactly the oposite. It's easier to do something different keeping the control if you know them.

If degres were not in use at that time do you know which kind of measurements existed by th past ? I never studied the history of the measurement of the angles. Do you have references on this topic?

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Hi Ken,

Regarding the corners shape, it's probable that commun triangles in relation with a simple construction were the first in used. These kind of constructions are at the origine of the style we like. Note that rules like that one are not in contradiction with the artistic touch (for those who are annoyed by these geometrical stuff) I would say that it's exactly the oposite. It's easier to do something different keeping the control if you know them.

If degres were not in use at that time do you know which kind of measurements existed by th past ? I never studied the history of the measurement of the angles. Do you have references on this topic?

Hi Francois,

It is a good question that I don't have a good answer for off the top of my head. Certainly degrees are an old measure, but my memory seems to be that it wasn't common in Europe of those days. I will look into it and see what I can find. I have not many of my math books left, but I did find this 1587 image in one book on my shelf.

post-24063-1271276519.jpg

It clearly shows angle measure. This does not mean degree measurements, because we certainly can measure angles in fractions of a circle, as in radian measure, such as pi/2 or pi/3 or pi/4 or pi/6, all of which are angle measurements still commonly taught in trigonometry classes today.

But more closely to what I had intended was that I don't believe degree measure was used in architectural or violin design of the era, rather, as you mentioned, the use of triangles, and in particular triangles with small-integer ratios of various sizes. Perhaps it is prejudice on my part. Some 30 years ago, when I worked as a carpenter, we would square-up a corner, or make a 90-degree angle, in words, but in practice we measured out a 3-4-5 triangle. That method seems to me, therefore, to be a good workshop solution.

Ken

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Apparently, degree measurements go back as far as Babilylonia, sourced in a 360 day calender and astronomy.

Is the info in this this link any good?

http://en.wikipedia.org/wiki/Degree_%28angle%29

I question whether the term used to describe the angle of a violin corner is important though, as long as a worker has some method of reproducing angles, and communicating them to other people.

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Apparently, degree measurements go back as far as Babilylonia, used in a 360 day calender and astronomy.

Is the info in this this link any good?

http://en.wikipedia.org/wiki/Degree_%28angle%29

David,

A quick glance, it seems reasonable information. Ancient Babylonians certainly are credited with the 360-degree division, but whether it was in common, workshop use in Europe at the time of violin development is the question. And I don't know that answer.

Ken

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