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Marty Kasprzyk

Inflection points of polynomial cross arch shapes

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28 minutes ago, Dennis J said:

I think your approach and my approach are aimed at the same outcome, but yours is a working method where the inflection point position is to some extent optional.

I lock in the position of the inflection points of all the cross arches where I want them to be by manipulating the variable elements of the geometric construct. And I can use the arching profiles produced to make arching guides.

If there is such a thing as a Cremonese arching shape my guess is that it is simply due to the fact that they used a geometrically correct method to make the arching. Especially at the corner arch positions where a strong recurve is necessary.

I don't want a system to be more proscriptive than actual Cremona practice was.

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Actually it's not. I've found that, with the inflection points in a reasonable place, reconciling the upper convex curve and lower curve through the inflection point is not hard to do with french curves.

However there is an anomaly in the geometry between the circular arc and flattened curve of the long arch which leads to the centre arch inflection point as calculated to be a little higher at the centre bout, and the upper and lower corner arch points lower than is ideal.

It's only a matter of about 1 mm, so now I just adjust the path of the arching profile a little below the marked inflection point at the centre bout, and a little higher at each corner arch when I shape the template.

And while I use french curves to mark the template blanks I wipe the ink line out when I get close to the line and just rely only my eye.

 

 

 

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1 hour ago, Dennis J said:

Actually it's not. I've found that, with the inflection points in a reasonable place, reconciling the upper convex curve and lower curve through the inflection point is not hard to do with french curves.

However there is an anomaly in the geometry between the circular arc and flattened curve of the long arch which leads to the centre arch inflection point as calculated to be a little higher at the centre bout, and the upper and lower corner arch points lower than is ideal.

It's only a matter of about 1 mm, so now I just adjust the path of the arching profile a little below the marked inflection point at the centre bout, and a little higher at each corner arch when I shape the template.

And while I use french curves to mark the template blanks I wipe the ink line out when I get close to the line and just rely only my eye.

 

 

 

Again, I think it's great you've create a system you enjoy using.  But I don't think it is a reasonable candidate for what might have been actually used in Old Cremona.

 

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On 10/3/2020 at 7:14 PM, David Burgess said:

I can't quite relate to all the mindphucking that goes on. Most of the better makers I am acquainted with use oblique lighting to quickly and easily recognize arching shapes. Some also use templates taken from a historically successful instrument, or from one of their own which has been successful, to finalize their arching.

That's what I do too.

I have also tried using a single candle or oil lamp flame as the oblique light source,  testing the notion that Stradivari may have worked beyond daylight hours. The single flame source revealed even more than the electric lights I usually use.

I do sometimes wonder if some people on the left and right coasts of the US (and even Finland) use too much "happy smoke". :D

I doubt if Stradivari did much carving in the gloomy part of the year. That would be the best time to cut the wood in preparation for all the work to come later. The highly intensive work of sawing all that wood kept him from freezing his nuts off. And all the off cuts went on the fire which kept 'er indoors 'appy.

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9 hours ago, sospiri said:

I doubt if Stradivari did much carving in the gloomy part of the year. That would be the best time to cut the wood in preparation for all the work to come later. The highly intensive work of sawing all that wood kept him from freezing his nuts off. And all the off cuts went on the fire which kept 'er indoors 'appy.

Or perhaps the darkest times of the year were the best times to do archings, using a "single" point oblique light source, rather than diffuse light coming in through a northern-facing window.

Do you really think that Antonio spent much of his time doing highly intensive rough-sawing of wood, when he had two (three) less skilled sons to do that?

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One of the problems with a violin plate arch shape is that it acts like a dome.  If you push down on it, like from the string force on the bridge, it will want to spread out latterly as shown in the attached sketch.  Architects have learned over thousands of years to add a "tensile rim" to the base of domed buildings to prevent this spreading as shown in another sketch and in the attached photos of a government building and a product it inspired.

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18 hours ago, David Burgess said:

Or perhaps the darkest times of the year were the best times to do archings, using a "single" point oblique light source, rather than diffuse light coming in through a northern-facing window.

Do you really think that Antonio spent much of his time doing highly intensive rough-sawing of wood, when he had two (three) less skilled sons to do that?

I think that without electricity their lives would have been different to the point that they must have had to plan their year differently with a seasonal system.

If I had to live like that, I would use the winter to split saw up the logs for all the different items they were going to make. I guess it would have been several weeks of labour intensive work.

I don't know about your candle light idea. I don't understand why arching is so mysterious to do. To me the mystery is in what effect different arching has on the sound and they were probably just as intrigued as we are.

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I would quicker think they worked at most phases of violin making at all times of the year.  And at any time of day they wanted, using the best light available the time.

But who can know?  We lack evidence to look over thier shoulders to such an extent.

I can see and talk about the shapes they left in the instruments, but how am I to see what lighting they used to get there, or if they took a working familt vacation to harvest spruce, or just bought from wood specialists?

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I think this is all reasonably well documented. The trade in tonewood was established, and we can see from dendro that the wood used in Cremonese instruments came from a very narrow source, essentially one valley, probably wholesaled through Venice merchants. 

I really don't think Stradivari was out in the Italian Alps all winter chopping up wood to keep himself warm ...

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52 minutes ago, martin swan said:

 

I really don't think Stradivari was out in the Italian Alps all winter chopping up wood to keep himself warm ...

He had plenty of work on his hands splitting and sawing the supplies he had at home though didn't he?

 

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4 hours ago, David Beard said:

I would quicker think they worked at most phases of violin making at all times of the year.  And at any time of day they wanted, using the best light available the time.

But who can know?  We lack evidence to look over thier shoulders to such an extent.

I can see and talk about the shapes they left in the instruments, but how am I to see what lighting they used to get there, or if they took a working familt vacation to harvest spruce, or just bought from wood specialists?

Did he go to a market in  Venice or did the supplier come to him? Or both? 

 

 

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The earlier and on going making in Brescia should make us suspect that at least some instrument wood likely came from up stream/hill of there.

Who in their right mind would tote logs up to Brescia.  

It's also tempting to guess that at least some wood supliers might have run the materials through Cremona on the way to larger markets via the Po.

But who knows? What's very hard for me to imagine is for these maker familes to take big breaks to go into the forests and cut their own trees.  Maybe they also traveled down to the isle of Chios to collect and process mastic?

There was active trade and commerce in many 'materia'.

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Interesting comments from Peter Ratcliff here: https://maestronet.com/forum/index.php?/topic/340572-where-did-stradivari-get-his-wood/page/3/

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Here's a little game to help show how the system I'm proposing as the concept behind old Cremona arching depends heavily on the idea that the luthier has choices within the system.

Below, I showing 5 pairs of archings.  In each pair, different choices are used, but all within the suggested system.  In each pair, the two archings have the same plate and edge heights, and the same distance from edge to center.  The differences in the arches are due to the difference in choices used.

The game though is that in each pair, one was created directly from a real example of old Cremona work.  They other was made by altering a few of the choices.

Can anyone tell which is which?

I'll post up illustrations showing the originals in a few days.

 

1564.thumb.jpg.0f9f0e11f37e0d1267155b186c2f7531.jpg

 

1620c.thumb.jpg.07fb9821977bc61db90d6a3b66bb5162.jpg

 

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1715.thumb.jpg.f3a0c4daa5f69aeca7ac558dceafb20e.jpg

 

 

 

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1564 N Amati

420749179_A1564NAmativln.thumb.jpg.341322b301108d22b82cd6a507d5eb9d.jpg

The first example - A

 

1620s Bros Amati viola Estense

1112524417_A1620cBrosAvlaEstense.thumb.jpg.72b4f7a7fbfd4c3dca58b73b1100d01e.jpg

The first example - A

 

1700 Strad cello Christiani

1463325636_B1700StradclChristiani.thumb.jpg.60b2e9f1018f870a4d3a1fbcf41f05bd.jpg

The second example - B

 

 

1704 Strad vln Betts

279455834_B1704StradvlnBetts.thumb.jpg.9235e50be18013b09da34266de263d9a.jpg

The second example - B

 

 

1715 Strad vln  Titian

1456651782_B1715StradvlnTitian.thumb.jpg.c70272b08c26e55af2fc953855841ff6.jpg

The second example - B

 

 

 

 

 

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The persistence of the cross arching "rule", the flexibility of the system, and the results I've gotten from actually using it are compelling. To those that wonder at the utility of Beard's research, why not take it to the bench before you decide whether or not it works? I say the same about Darnton's cycloid half templates. If you haven't given it a go, what's stopping you? 

I'm planning to make and try some of Dennis's templates, and if they get me where I want to go faster and better than what I'm doing now, I'll switch. I have to eat, which means I have to make. If any method doesn't produce quality results efficiently, it's not for me. But if I haven't tried it I can't say whether or not is has value.

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The illustrations below show how someone who carves the arching mostly be eye and experience might use the '1/2 fall in 2/3 run' to easily check if the rate their arching begins falling from the center toward the edge is on track.

 

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two.thumb.jpg.d97adc28c2f944275bc55f05f3ec5307.jpg

 

 

 

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26 minutes ago, Marty Kasprzyk said:

Here's a photo of my dog's leash hanging to dry.   I noticed the cross arch  inflection point changes depending on how wet the leash is.  

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I suppose you might just be jesting, but that is an interesting sort of shape.

Toward the center, the shape approaches the catenary that a risistance free chain takes naturally under gravity.  Which is also the shape needing to conatining within thw physical thickness of any free standing arch to carry its own weight or a center load to the ends without buckling or collapsing.

However, the chord you show is not resistance free. Any wetness will change this resistance.  In turn, this effects how the cord shapes around the pegs it hangs on, and affects the boundary comditions for the center 'near catenary' shape.

Very interesting in its way.

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18 hours ago, David Beard said:

I suppose you might just be jesting, but that is an interesting sort of shape.

Toward the center, the shape approaches the catenary that a risistance free chain takes naturally under gravity.  Which is also the shape needing to conatining within thw physical thickness of any free standing arch to carry its own weight or a center load to the ends without buckling or collapsing.

However, the chord you show is not resistance free. Any wetness will change this resistance.  In turn, this effects how the cord shapes around the pegs it hangs on, and affects the boundary comditions for the center 'near catenary' shape.

Very interesting in its way.

This natural shape is a catenary with some bending stiffness.  It can be analytically described and its shape often seen in the laying of undersea cables, pipe lines, and bridges.

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6 hours ago, Marty Kasprzyk said:

This natural shape is a catenary with some bending stiffness.  It can be analytically described and its shape often seen in the laying of undersea cables, pipe lines, and bridges.

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Yes.  As a physical concept of what makes arching shapes actual work or not work, I believe stiff catenaries are actually spot on.

But, I don't believe this is how the old masters actually worked.  It isn't friendly for a workshop. Not from 1550 to 1750, not even today.

However, the system I propose is completely workshop friendly.  And it keeps you in shapes that mimic approproate catenaries quite well.

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18 hours ago, David Beard said:

Yes.  As a physical concept of what makes arching shapes actual work or not work, I believe stiff catenaries are actually spot on.

But, I don't believe this is how the old masters actually worked.  It isn't friendly for a workshop. Not from 1550 to 1750, not even today.

However, the system I propose is completely workshop friendly.  And it keeps you in shapes that mimic approproate catenaries quite well.

If the  goal is to use a practical method of generating the cross arch shapes that could have used long ago then a simple way is to bend some thin wood strips.  Attached is a photo of two wood strips held together with rubber bands at their ends and then spread apart with a single spacer piece in the center.  The "bulginess" of the shape can be increased and the inflection point moved farther out by pushing spaces closer to the end as shown in another photo and in another photo showing the inflection point changes.                                                   

These aren't new ideas and they've been used for a while. One example is seen in a photo of a birch bark canoe made by Native Americans.

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