Corner shape

[David Burgess]

When did it come into common use for navigation by the seafaring nations?

[Ken Pollard]

When did it come into common use for navigation by the seafaring nations?

I'm trying, I'm trying*.....and I only have a few more moments before I have customers in the shop...

Well, trusting Wikipedia, here's an 14th-century European example of a 13th-century compass with degree markings.

http://en.wikipedia.org/wiki/Compass

Scroll down to Medieval Europe. And Tycho Brahe was developing astronomical devices that apparently used degree markings, at least in the vertical plane, by the late 1500s. On the other hand, those were very expensive instruments.

On the other, other hand, this link seems to indicate that folks generally wanted simpler instruments for "on-the-street" work in surveying.

http://www.profsurv.com/magazine/article.aspx?i=2074

*Edit: Should have added in the -- because your question came in just as I was putting together some info I had found, including the navigatinal compass concept.

[David Burgess]

Sorry Ken, didn't mean to direct the question at you necessarily. Take care of your customers.

Looks like "quadrants" for measuring angles go way back. Basically it's a quarter of a circle with two flat edges, with a string and weight hanging from what would be the center of the circle. One of the straight edges can either be placed against an object, or sighted along, and the hanging string will correspond with a marking or printed number at the circumference.

Oh, used for telling the time of day too (angle of the sun in the sky).

[Ken Pollard]

Sorry Ken, didn't mean to direct the question at you necessarily. Take care of your customers.

Looks like "quadrants" for measuring angles go way back. Basically it's a quarter of a circle with two flat edges, with a string and weight hanging from what would be the center of the circle. One of the straight edges can either be placed against an object, or sighted along, and the hanging string will correspond with a marking or printed number on at the circumference.

Oh, used for telling the time of day too (angle of the sun in the sky).

Right -- and they also used the Zodiac to divide up a circle (12 parts) -- so it gets confusing to know what was used by who (or whom).

Learning that their Medieval to Renaissance-era high-precision instruments had degree markings was interesting. How much of that filtered into architectural design, etc, I don't know. I suspect that dividers were used far more than, say, protractor-like devices on the work benches.

I would also guess that not all sailing vessels had such intricate compasses -- fishing vessels versus battleships, for instance. We are lucky to live in a time when precise measuring instruments are so readily available.

[francoisdenis]

There is a distinction which remains in english between compass and divider which doesn't exist in French. The compass seems to be in relation with motion and trajectory. It's the the caracteristic tool of the astronomy and all move in relation of stars. The divider seems to be dedicate to the geometry, that means to the measurement of lenght surface...

I find this distinction interresting, could that be a reminiscence of the Quadirvium, (the same for the difference made between "one man" and "a man" )

What do you think of that ?

[robertdo]

There is a distinction which remains in english between compass and divider which doesn't exist in French. The compass seems to be in relation with motion and trajectory. It's the the caracteristic tool of the astronomy and all move in relation of stars. The divider seems to be dedicate to the geometry, that means to the measurement of lenght surface...

I find this distinction interresting, could that be a reminiscence of the Quadirvium, (the same for the difference made between "one man" and "a man" )

What do you think of that ?

Yes I found it funny when I arrived in Uk. Their compass is our "Boussole" and their divider is our "compas". Les faux amis, comme on les appelaient a l'ecole. When I tarted in the lab I was always saying " I was going to do this EXPERIENCE" instead of experiment and what really made my supervisor laughing was when I talked about me having a high consommation of chocolate (I did learn that consommation was related to something else...)

[Ken Pollard]

There is a distinction which remains in english between compass and divider which doesn't exist in French. The compass seems to be in relation with motion and trajectory. It's the the caracteristic tool of the astronomy and all move in relation of stars. The divider seems to be dedicate to the geometry, that means to the measurement of lenght surface...

I find this distinction interresting, could that be a reminiscence of the Quadirvium, (the same for the difference made between "one man" and "a man" )

What do you think of that ?

That distinction is interesting, and could be a good clue -- or it could be that English tends to steal words from other languages, sometimes creating a distinction where none exists, for example, violin and fiddle.

And also that we, in English, use the word 'compass' to mean two related but different measuring devices.

I know many people have a hard time making the connection between angle-measurement and distance measurement, one being relative, the other absolute. And in some of my skimming over material yesterday, there seemed to be a difference in the way astronomers before the 1600s measured vertical (sky) angles and horizontal (earth) angles -- but I haven't had time to explore that concept, yet.

[Bob Spear]

I realize that I am coming late to the party on this topic, but little details like how the Cremonese finished their corners, how they determined the angle, etc., has long intrigued me. I worked out the geometry of the model G Strad a few years ago and decided to see if there was a simple and accurate way to fix the corners. Most of the time in my research I feel like someone in the dense jungle with a machete. When I do come upon a possible answer, I have no way of knowing how the ancient masters did it. All I can say is that when done in this way, the end result is quite consistent with what we see. My first attempt to upload an attachment, so let's see how it goes.

All the divisions in this drawing are on the golden section. The arc used for reference for the upper corners has its center on the upper horizontal line at the centerline, and the process is flipped upside down for the lower. Notice that the radius of the arc is determined by the inward-facing extent of the corner blocks. It's pretty clean, and the diagonals for the corners even respect the edge overhang used on the rest of the body. I do like to put a very slight arc on my corners; I think it looks more refined. But it starts out square. Just have to remember to finish them.

[Torbjörn Zethelius]

Hi Bob, it might work for somebody else but I believe the angles are wrong for Stradivari.

[JimMurphy]

I know many people have a hard time making the connection between angle-measurement and distance measurement, one being relative, the other absolute.

I wonder whether any of those Cremonese were proficient at Radian Measure.

It is both Math & a lost Art.

Jim

[Don Noon]

Since early on, I've mostly drawn and edited an outline until I liked it, including the corner angles.

I'll bet someone could take your final drawing and impose some sort of golden triangle or other mathematical construction process on it. Humans are really good at looking for and finding patterns, everywhere, even though they might not really exist.

[Ken Pollard]

I'll bet someone could take your final drawing and impose some sort of golden triangle or other mathematical construction process on it. Humans are really good at looking for and finding patterns, everywhere, even though they might not really exist.

Don, we're talking about violins here, not seashells or pinecones. A human invention made during a very specific time.

http://www.paradoxplace.com/Perspectives/I...AW4827AR900.jpg

[Ken Pollard]

I realize that I am coming late to the party on this topic, but little details like how the Cremonese finished their corners, how they determined the angle, etc., has long intrigued me. I worked out the geometry of the model G Strad a few years ago and decided to see if there was a simple and accurate way to fix the corners. Most of the time in my research I feel like someone in the dense jungle with a machete. When I do come upon a possible answer, I have no way of knowing how the ancient masters did it. All I can say is that when done in this way, the end result is quite consistent with what we see. My first attempt to upload an attachment, so let's see how it goes.

All the divisions in this drawing are on the golden section. The arc used for reference for the upper corners has its center on the upper horizontal line at the centerline, and the process is flipped upside down for the lower. Notice that the radius of the arc is determined by the inward-facing extent of the corner blocks. It's pretty clean, and the diagonals for the corners even respect the edge overhang used on the rest of the body. I do like to put a very slight arc on my corners; I think it looks more refined. But it starts out square. Just have to remember to finish them.

Hi Bob,

How did you locate the apex at the top, the angles that define the lower corners? It appears that you have simply flipped the angle that defined the upper corners, thus maintaining the paralllel line idea, but it's likely I'm missing something.

I have no experience with Stradivari instruments outside of photos I've seen, but your angles appear much steeper.

Ken

[Don Noon]

I'm just suggesting the possibility that the old guys could have tweaked and modified things to what looked or worked good... an evolutionary process that would not necessarily have adhered to precise mathematical design.

[Ken Pollard]

I wonder whether any of those Cremonese were proficient at Radian Measure.

It is both Math & a lost Art.

Jim

Hi Jim,

I don't understand what you're getting at. I did mention radian measure in a post above (#148). I don't know if it was used by the Cremonese or not, but it is commonly taught today.

Ken

[Ken Pollard]

I'm just suggesting the possibility that the old guys could have tweaked and modified things to what looked or worked good... an evolutionary process that would not necessarily have adhered to precise mathematical design.

Ah, ok. I think most of us agree with the tweaking concept, both intentional and not. It's the basic, underlying design that interests me. I think it existed.

[JimMurphy]

I don't understand what you're getting at. I did mention radian measure in a post above (#148).

That explains it, Ken. [i missed your earlier reference].

Thanks,

Jim

[Bob Spear]

Hi Bob,

How did you locate the apex at the top, the angles that define the lower corners? It appears that you have simply flipped the angle that defined the upper corners, thus maintaining the paralllel line idea, but it's likely I'm missing something.

I have no experience with Stradivari instruments outside of photos I've seen, but your angles appear much steeper.

Ken

Greetings, Ken-- the center of the arc for the lower corners for some reason did not come out as boldly on the diagram I uploaded as it is on the original.

If you look closely at the drawing between lines E and C, you'll see a dotted normal line. On the right side where this line meets the bounding box is the label "body GS," which means the golden section of the entire body length. The intersection of the dotted line and the vertical centerline is the center of the circle from which the arc is taken. The compass point goes there, and the lead goes on the centerline of the lower blocks at the bounding box line Yt - Zt. This horizontal centerline of the lower blocks is the dashed line between G and D. The arc is swung upward until in intersects the vertical centerline. That's the apex of the triangle. The drawing has a dashed green arc showing this; it's just very hard to see.

Tobjorn, I must respectfully disagree. I just sacrificed my poster of the Titian Strad for the sake of knowledge, and the correlation of the triangles both to the extents and the angles of the corners is quite good. Yes, the corners on this violin are quite rounded. For someone like Strad who was constantly experimenting with the violin's form, this should not be surprising. However, I found the rounding to be generally consistent, although there is plenty of evidence of rounding caused by wear.

[Ken Pollard]

Greetings, Ken-- the center of the arc for the lower corners for some reason did not come out as boldly on the diagram I uploaded as it is on the original.

...

Thanks, Bob. I've printed it out and will play with it.

I'm never quite sure what to think of Golden Section arguments. Used to like them. Then didn't. And now I just don't know. One possibly interesting thing is that back when I taught math classes, I would generate the Golden Ratio on the chalkboard using a right triangle with sides of 1 and 2. Refer to Francois Denis' post #117 in this thread -- perhaps just a coincidence to me, and maybe a confusion. Actually, probably a confusion on my part.

Now back to the bench for more unintentional tweaking of the design!

Cheers,

Ken

[David Burgess]

I'm just suggesting the possibility that the old guys could have tweaked and modified things to what looked or worked good... an evolutionary process that would not necessarily have adhered to precise mathematical design.

That may work fine for rocket science, but the process is too sophisticated for your average wood dinker.

[francoisdenis]

I'm just suggesting the possibility that the old guys could have tweaked and modified things to what looked or worked good... an evolutionary process that would not necessarily have adhered to precise mathematical design.

Hi Don,

Except that, specially speaking of the Renaissance it's exactly the opposite that we observe. Even at that time basic mathematics were crucial to the reliability and acceptability of the concepts which supported the aesthetic. Just one example which concern us here; think to the evolution of the division of the musical scale. There is no acceptance of any "equal" division of the scale prior the possibility to calculate 12 proportionnal means. Difficult to be spectical on that point. Mathematic progress create the possibility of a new expression and you don't need to be able to calculate these means to play the music with. Calculus is tied to concepts and styles has been seen by some good art expert of the XIX° century, as the nicer expression of those concepts.

About the empirical approach of David, don't forget that he is not the inventor of the violin. As he is a good one, he is able to refound the correct place taking account of hours passed to studied the old masters. I know that is puzzling for many to admit that rules have existed because they have the experience that they don't need them. But actually, those who have a good intuition are just doing an empirical reproduction of the correct form.

Think about this example of the parallel lines to set the angles of the corners, when you know the process, you will never forget it... I guess.

[Bob Spear]

Thanks, Bob. I've printed it out and will play with it.

I'm never quite sure what to think of Golden Section arguments. Used to like them. Then didn't. And now I just don't know. One possibly interesting thing is that back when I taught math classes, I would generate the Golden Ratio on the chalkboard using a right triangle with sides of 1 and 2. Refer to Francois Denis' post #117 in this thread -- perhaps just a coincidence to me, and maybe a confusion. Actually, probably a confusion on my part.

Now back to the bench for more unintentional tweaking of the design!

Cheers,

Ken

Hi, Ken--

I'd heard so much about how the violin was not designed on the golden section that I just wanted to see if I could design one using only the golden section. When Tom King published his work about the placement of the f-hole, I thought that the case was considerably strengthened. I've known Tom for years, and we tested our theories against each other and found a great deal of agreement. I just took it from there and ran with it. The outline of the violin I posted has since been refined; I just didn't have an uploadable drawing of it handy. I've also worked out the f-hole, which I think is placed according to the golden section but not designed on it. And the scroll-- well, that's another story. It works with about 85% golden section so far.

I think we (the generalized violin-making world "we") are prone to get into "either - or" states about this point. I don't see much evidence that the Cremonese were hung up on it. I find it a lot of fun, but it can get to you at times. I recall that Francois Denis mentioned in an article how the problem would keep him awake at night. Believe me, I've been in that state myself.

--Bob

[Torbjörn Zethelius]

There is so much more to geometry and geometric design than the golden section. Why limit yourself to only that aspect?

[Eric Brooks]

There is so much more to geometry and geometric design than the golden section. Why limit yourself to only that aspect?

Excellent observation ! The golden section is just a tool amongst other...

[Ken Pollard]

Well, I am coming to the conclusion that the concept of degrees was well understood and used in Europe by the time of the of the Cremonese violin design.

Here's one example, a tech manual from the late 1300's.

http://www.fordham.edu/halsall/source/chaucer-astro.html

I can't verify that it is accurate, but it appears to be. It also appears to be consistent with other readings I have run across. What I liked about this one was that it is a practical application of the degree concept, and does not appear to talk of it as some new method.

I'm still clinging to my belief that in workshop situations, builders and designers would be more likely to use straight-edges and compass-dividers. They're just easier and faster than something such as a protractor. But I have no 'smoking gun' to support my belief.

So far!

We do, I think, agree that length measurements were not standard throughout Europe. That adds a certain set of complications to design.