Stradivari scroll compass method

[Andreas Preuss]

17 hours ago, David Beard said:

The old Amati traditon are based on straight lines to a greater extent.

Do you mean for the peg box?

Or at least I hope you didn7t mean the front view, because there the lines of a Amati (family) scrolls have IMO much more grace with beautifully flowing curved lines.

I never deeply analyzed the proportions of Amati scrolls, but the result somehow looks to me like copied by eye from a model scroll in the shop. (maybe just my wild imagination)

Strad on the other hand looks to me more like following rule instructions without concern for ultimate aesthetic finesse. So most of the time they get the 'Strad taste' but once in a while some weird scrolls are in the production. I actually think the scroll of the Viotti Strad pictured on the STRAD poster is simply ugly because the inner windings are out of center. 

[Bill Yacey]

I tend to be of the view that Amati scrolls are more graceful in general;  less angular and more gentle curves.

[David Beard]

1 hour ago, Andreas Preuss said:

Do you mean for the peg box?

Or at least I hope you didn7t mean the front view, because there the lines of a Amati (family) scrolls have IMO much more grace with beautifully flowing curved lines.

I never deeply analyzed the proportions of Amati scrolls, but the result somehow looks to me like copied by eye from a model scroll in the shop. (maybe just my wild imagination)

Strad on the other hand looks to me more like following rule instructions without concern for ultimate aesthetic finesse. So most of the time they get the 'Strad taste' but once in a while some weird scrolls are in the production. I actually think the scroll of the Viotti Strad pictured on the STRAD poster is simply ugly because the inner windings are out of center. 

Yes. The pegbox width shape.

Certainly the Amati pegbox shape is beautiful.  But it is also a simpler cleaner geometry.  Straight lines play a major role.  Nothing wrong with that is there?  It's beautiful.

After a while, I'll start posting some geomtry illustration in this thread.  But for now am focusing on the conversation about neck stops.

[David Beard]

This is primarily what I mean by saying the Amati front side box shape is based on straight lines.

 

 

 

 

First example is Andrea Amati, second is Ruggieri.

 

[Davide Sora]

@David Beard  You are right, but I would say that all Cremonese pegboxes are based on straight lines, including Stradivari.

[David Beard]

2 hours ago, Davide Sora said:

@David Beard  You are right, but I would say that all Cremonese pegboxes are based on straight lines, including Stradivari.

I agree.  Of course, the earlier Strad scrolls are just Rugierri's version of Amati.  But later he changes.  To me, his changes seem aimed at keeping the box wider for longer as we approach the volute.

[Davide Sora]

1 hour ago, David Beard said:

I agree.  Of course, the earlier Strad scrolls are just Rugierri's version of Amati.  But later he changes.  To me, his changes seem aimed at keeping the box wider for longer as we approach the volute.

Agreed. Stradivari keeps the walls of the pegbox straight anyway, but by widening at the A peg, a kink is created in the connection with the volute, while in the scrolls of Amati the straight lines continue in the volute with a better aesthetic solution, but less functional. Stradivari also slightly widens at the G peg compared to Amati, improving the clearence of the strings into the Pegbox without having to open up the inside walls as Amati did. Better functionality and greater resistance.

Function above the geometric rules, in my opinion the same thing happens for the shape of the soundbox (form design), decreeing the end of the times of geometric rules rigor. One of the reasons why it is more difficult to find geometric correlations in Stradivari instruments, the reasons why it is more difficult to find geometric correlations in Stradivari, because he did not attribute to them the same importance that the Amati tradition probably carried forward from generation to generation without bothering to innovate.

[David Beard]

50 minutes ago, Davide Sora said:

Agreed. Stradivari keeps the walls of the pegbox straight anyway, but by widening at the A peg, a kink is created in the connection with the volute, while in the scrolls of Amati the straight lines continue in the volute with a better aesthetic solution, but less functional. Stradivari also slightly widens at the G peg compared to Amati, improving the clearence of the strings into the Pegbox without having to open up the inside walls as Amati did. Better functionality and greater resistance.

Function above the geometric rules, in my opinion the same thing happens for the shape of the soundbox (form design), decreeing the end of the times of geometric rules rigor. One of the reasons why it is more difficult to find geometric correlations in Stradivari instruments, the reasons why it is more difficult to find geometric correlations in Stradivari, because he did not attribute to them the same importance that the Amati tradition probably carried forward from generation to generation without bothering to innovate.

Well, we sort of diverge here.

For over ten years I've been working hard to be able to read the geometry in all the generations of old Cremona.  I don't see any of the main makers ever stepping out of the rules.  Instead, they push things around within the rules.

This business of the box with Strad is pretty much the single most 'free' change of geometry in the whole generations of traditional Cremona history.  And really it's not much of a revolution.  Others before him had already frequently used a break in the lines, where the lines in the box move at an angle, and then that angle changes in the approach to the top of the volute (looking from the front).

All Strad really changed initially was to set the main lines of the box straighter, and then move where the line angle changes to aim for the top of the volute.  Later, he adds some rounding and bulging based on these lines.  

But it's still organized by the lines, and then the proportions to give widths.  He does locate these differently to achieve a different purpose.  And this is where he shows his greater independence of thought than many of his colleagues, but still these changes are evolution and variation of the traditions, not revolution or abandonment of tradition or free new invention.

Same in Del Gesu.  He pushes against the boundaries of the tradition, and sometimes cheats in fully or properly carrying through some details, but he doesn't step away or free from the traditions. 

 

[Davide Sora]

53 minutes ago, David Beard said:

Well, we sort of diverge here.

....

  And this is where he shows his greater independence of thought than many of his colleagues, but still these changes are evolution and variation of the traditions, not revolution or abandonment of tradition or free new invention.

Same in Del Gesu.  He pushes against the boundaries of the tradition, and sometimes cheats in fully or properly carrying through some details, but he doesn't step away or free from the traditions.

Yep, I have misused the term innovation a bit...

Of course Stradivari inherited and continued in the tracks of tradition, but with much less respect of the canons then his predecessors. Del Gesù even more (he was younger and reckless to worry about similar things). If you start from a form (Amati) that has already been in use before, all the tradition is there, but if you change it even a little by eye, you necessarily go outside the geometric canons, even if only slightly. So then, many years after, people will start to go crazy to connect the Cs with the tips, or to find the 2: 3 ratio of the handle, being forced to resort to "liberties at the margins" to make things work.

Don't be mad, I appreciate the work you are doing and I find it really interesting, but I can't follow theories when they resort to approximations (not just your case). I know, it's my limit, I'm probably too rooted in the modern time and I can't think like a 600/700 artisan, perhaps...

[David Beard]

Sorry if I come across angry, not my intention.  I see you meant now.   Sure, Strad is very free and creative, just still within the structures and resources he inherited.

Please, I wish people could look at this liberty at the margins not as me taking license as an observer, but as the makers taking an inherited system that dictates to them 'pick one of these three ratios' to measure here, and they are back at that system.  They are saying, oksy, okay, I'll use the traditional ratio. Okay, but I want this part to be just a little bigger this time.  So, I'm gonna that from here to here instead.

The liberty at the margins gave them a little more room to steer as the liked, while still staying within proscribed tradition.

[Andrew Victor]

To my eye the Fibonacci sequence creates the perfect scroll pattern and if the maker carves scroll widths of 1, 2, 3, 5 back and forth across a diameter it will appear!. I have one violin that measures that way and it is surely the most attractive.

[Andreas Preuss]

5 minutes ago, Andrew Victor said:

To my eye the Fibonacci sequence creates the perfect scroll pattern and if the maker carves scroll widths of 1, 2, 3 5 back and forth across a diameter it will appear!. I have one violin that measures that way and it is surely the most attractive.

Would you mind to illustrate this, because from your description I can't really figure it out. (Maybe my lack in English)

[David Beard]

Fibonacci makes a kind of spiral.  You might prefer it, but very definitely not the Cremona volute.

[David Beard]

This thread began asking about the circles and geometry governing the widths of the fluted underside ot the pegbox, and wrapping around up to the widest point of the volute just at the far end of the pegbox.  But we can see also two other rather independent areas of 2D geometry governing the total 3D carving.  These are the widths of the pegbox and volute as seen from the front of the instrument.  And, the curved outlines for the head and volute as viewed from the side.

We actually can't fully discuss the geometry the OP focuses on first, because those widths key off the widths from viewed from the front.    And we can't start tjese front wodths either, because they key off heights from the sideview geometry. 

******

So let's start where we need to, with the sideview geometry, and how we might orient our observations.  

In most examples, the old necks have been replaced with new necks spliced onto the old scrolls and heads.  These splices generally protected most of the head's integrity, including the heal under the nut, however the internal end of the pegboxes were destroyed, as well usually as the top edges of the pegbox nearest the nut.  

While we can expect that most of these resets attempted to preserve as much as possible, we can not rely on the height of the box near the nut, the lengths of the neck compared to the lengths of the head, nor the angle relationship between the head and scroll versus the neck.

Here is an example from a neck splice on a 1671 Girolamo II Amati 351mm violin where the angle of the head and scroll appear tipped downward a few mms compared to the line of the neck.

So, a reasonable first question is to see what we can about the traditional relationship of the neck line and the head and scroll work.

If we look at unmolested examples where the original neck and head are still joined as they were, we consistently see a straight line from the neck to the top of the scroll.

1613 Bros Amati piccolo:

 

1664 Andrea Guarneri tenor

 

1690 Strad tenor

 

1721 Strad Lady Blunt

1793 Mantegazza viola

 

And, in fact, most of the splices reasonably well preserve this line relationship, though certainly not all.    We will hypothesize that this was the proper normal relationship in Cremona work.

But, we remain uncertain when looking at a reset example.   Do these few well preserved examples give us any more clues that might help us orient our observations in reset examples?

We can make a start by observing that most of the examples show the 'underturn' beneath the pegbox is placed 1/2 the height of the volute, when viewed at 90º from the neck line orientation.

In the Strad tenor:

And we see this repeated in more examples:

1664 A Guarneri tenor:

 

1613 Bros Amati piccolo:

1721 Strad Lady Blunt:

 

And, if we are careful to check orientation, we will find this relationship protected and still very clearly and obviously presented in a great many examples that actually have reset necks.  Here are just a few such examples:

   

              

 

Across the generations and families we see clean surviving examples of placing the underturn at 1/2 the volute height, even continuing into late Del Gesu.

 

You may have noted however, that these pegbox heights can appear rather on the stout side to the eye.

Since all other aspects of the overall observable old Cremona use of geometry and ratio leave the makers significantly in charge and able to steer, let's consider how one of the old makers might approach setting a less stout pegbox height, while characteristically staying completely within the system's traditions?

In all other features, the larger scale variations are created by choosing a different ratio, and the smaller scale variations are made by the maker manipulating the 'liberties at the margins'.   So lets look at these potential steps to obtain skinnier box heights.

The 'margins' in the head and scroll work are the chamfers.  In some locations, these are a significant percent of the general scale of dimensions, like in the volute as we approach the eye.   But for the large outlines of the head, these chanfer are quite minor compared to the general measures of height.

But let's look at the Lady Blunt example again.

The other 1/2 volute height examples were very clean.  But here, the fit is poor. Stradivari has either cheated on this ratio to get a skinnier box, or worked quite inaccurately, or used a typical 'liberty at the margins' choice to get his result.

And, we can see that if he used the camfer line at the bottom of the volute height as a 'liberty at the margin', then his work appears as an accurate use of the 1/2 volute height tradition. 

So what do we have in this example?  Is it proof of Strad using 'liberty at the margins'?  Is it an example of Strad working with poor accuracy?  Or is it proof that this whole proposed system is wrong? Proof that so many instruments just accidentally end up near 1/2 volute height, rather than that being an actual intended use of a traditional ratio.

Well, so far, it is only one example. So we can punt on deciding it's ultimate meaning.

Lets consider if a maker wanted to vary the box height more significantly from the common 1/2 ratio by using a different ratio.   

1/3 might be an option, but that probably makes the box just too skinny.  4 parts doesn't help at all.  We either get even skinnier with 1/4, or exactly where we started with 2/4 = 1/2.  But 5 parts looks more promising.  By 3/5 gives us a much less dramatic reduction of the box.  

If we extend this idea to ratios that put us near 1/2, but make the box height a little skinnier, we can try using other odd number divisions in the same way.  So, 4/7, 5/9, 6/11.

You might of noticed I didn't yet show the box heights from our well preserved Mantegazza and Storioni examples.  That's because these are skinnier boxes that show use of the 5/9 ratio instead of the 1/2 we looked at first.

 

 

 

I had intended to go further in this post today, but I'm getting tired and will wrap up for now.

The thing to observe next is how the volutes are proportionately framed.

Generally, once the neck angle and underturn are squared away, we will see then that the all the volutes are worked with in either a 4 by 5 or 3 by 4 frame.

Yet, we are presented with a choice again. Accepting 'liberty at the margins' allows us to view classical making as consistently and accurately  proportioned. 

Do we believe there is actually no proportional tradition present?  Do we believe these makers were frequently inaccurate in framing the volutes to a tune of 1 or 2mm?  Or, do we recognize that the makers granted themselves a final opportunity to manipulate the results when honor a traditional ratio to frame the volute by allowing themselves to decide to exclude a chamfer from the measure when it suited them.  

Do we accept 'Liberty at the margins'?

More later...

     

[Davide Sora]

@David Beard Thanks for posting.

Your considerations on the relationship between the neck line and the volute correspond to my observations as well.

[Marty Kasprzyk]

These look nice but but some have a lousy design because the pegbox sometimes cracks along the wood grain direction through the A string peg hole.  

[David Burgess]

Do either Francois Denis or David Beard have a geometric or ratio construct for boobies, which probably generate more interest and attemtion from more people than anything else on the planet?

I am referring to the wild birds, of course.

[David Beard]

Good one David.  

[David Beard]

4 hours ago, Marty Kasprzyk said:

These look nice but but some have a lousy design because the pegbox sometimes cracks along the wood grain direction through the A string peg hole.  

I leave improving on the old masters to you.

I'm only trying to see if we can understand 'what' they did fully enough to allow those who wish to 'Do as They Did'.

If you want to 'Out Do What they Did', that's a different game.

[Marty Kasprzyk]

3 hours ago, David Beard said:

I leave improving on the old masters to you.

I'm only trying to see if we can understand 'what' they did fully enough to allow those who wish to 'Do as They Did'.

If you want to 'Out Do What they Did', that's a different game.

From your illustrations the scroll on the right has a longer distance a crack has to propagate through the A string peg hole than the scroll on the left.  Appearance and proportions are a consideration but strength is also important.

[David Beard]

Hi Again,

We already looked at the alignment between neck and scroll, the box height as either 1/2 the volute height, or as a ratio making it somewhat skinnier.  We saw 4/9th examples.  And, we saw the examples of the 3 by 4 frame ratio for the volute.

So let's continue by surveying these choices in a range of examples.

To begin, let's look at a Zanetto Micheli viola scroll from Brescia.   Though commonly dated 1580c, we don't really know.   This scroll could readily be significantly earlier.     Early Brescian viola work has its own geometry use that is related to but distinct from what we see Andrea Amati do in Cremona.   I think it very likely that the Brescian geometry was known to Amati, and provided a precedent for his work.

In this distinctly old Brescian scroll, we see the volute frame and the box height use the same patterns familiar in Cremona work.

  

Curiously, the first generations of Cremona examples all (or nearly?) apply the 3 by 4 volute frame excluding 1 or 2 of the camfers.  As in the Andrea Amati 'Kurtz' small violin example here.

 

But, by Nicolo Amati's time, we do see examples of the 3 by 4 frame applied to the outer edges all around.  As in this 1645 example.

  

Particularly in the earlier generations, we see a 4 by 5 frame sometimes used for larger instruments.  Here is the Witten viola from Andrea Amati.

  

 

And this is what we see in all the Cremona examples.   The 3 by 4 frame is strongly favored.   But, the 4 by 5 occurs occasionally.   Application of the frame often excludes 1 or more camfer.    And, the ratio for the box height is also at times applied excluding a margin.

 

Now, let's briefly look at the options if a maker wanted a skinny volute.   After all, for most uses they seemed to consider the 4 by 5 frame a bit too wide.  The 3 by 4 is skinnier.    But if they want even skinnier than 3 by 4, the next 'a part less' ratio in this series would be 1 by 2, and that jumps too far.

Here I show these three potential ratio frames compared directly to each other.

  

 

The 1 by 2 ratio is just too skinny to use.

So we just don't see them jumping to this next ratio.  Instead, we see them maximize the 'liberties at the margins'.   The Molitor shows kind of an extreme example of Strad reaching for a 'skinny' take on 3 by 4,  but without breaking from the ratio!!

So how to apply 3 by 4 to maximize height versus width?  You let your measure take in the full width, and you take your 'liberty at the margins' on the top and bottom camfers to omit as much height from your measure as possible.

And, these are exactly the choices we see Strad taking with the Molitor from 1697.

The wide camfers he sets at top and bottom, and then excludes when applying the ratio!!

And then his relatively skinny volute as reward:

 

So from one extreme of the range to the other, here is a 1669 Andrea Guarneri cello, the Soyer, with the scroll showing a nice fat 4 by 5 frame choice.

 

 

Ok.  This has been very long.  So to wrap up, let's look at a late Del Gesu example.    He doesn't abandon the rules. But, he takes it simple, and he shortcuts.  Let's look at the Soldat from 1742.   No finessing with the margin choices, he's content with the simplest 3 by 4 frame and 1/2 volute box height.

 

 

 

Now, let's warm up some ideas to come back to later.  And take a peak at Del Gesu's short cutting, and why it doesn't completely fail.

Notice below where there's a bump at the red arrow.   This is where he didn't join two circle arcs very well.     And then at the green arrow, the curves go from pretty decent to totally nuts.  This is precisely where he stops following the traditional compass arcs for the outer volute shape.  This is where he begins cutting the arcs freehand.  This is something which can be done skillfully and well for the smaller curves of the mid and inner volute curves.  But he does a very bad job with freehanding these curves.  Why doesn't it totally fail??  Because he does a fair job of placing and checking in with more or less traditional boundaries for these curves, indicated by the green lines.

 

 

More later.

 

[David Beard]

Before diving fully into the complexity of geometry and proportions working together to make the head and volute outlines, it might be good to warm to these materials but taking a freer look at how these things work separately and in concert.

Once again, the 1690 Strad Tuscan tenor and the 1721 Lady Blunt make good initial examples as they are very clean, and the relation of neck to head are original.

 

1690 tenor:

 

1721 Lady Blunt violin:

So we're winding up toward looking at how all  these shapes are made from smoothly joined circle arcs, and here and there a segment of line.   The placement and sizing of these component elements involves a little further geometry, and the use of simple ratios.

I apologize if some of this intro is too basic for some, but I think it's worth review.

Two points define a line, but not a circle.

 

To define one specific circle takes a bit more info.  So, two points plus knowing one of them is the center, or a third point.

 

But mostly, we're going to be concerned with how circles and lines join together smoothly.    For this we have to pay attention to where things join.     So, lines can join smoothly with circles, but at the point they join, the line will always be at a right angle with the circle's radius.   And we can always find a line that joins smoothly between two circles.

 

The most important bit for Cremona geometry however is how to smoothly join circles.    The one thing that makes this work is for the point where the two circles join to lay on the line between their centers.

 

Now, usually we will be concerned with arc portions from a circle instead of the full circle, but the geometry implied by an arc is the geometry of the full circle it comes from.

 

So how can any of this help us look at a scroll?   For one, we can easily spot some of the horizontal and vertical lines that must have arc centers on them.   These are the right angle lines to tangents that we an easily spot at the tops, bottoms, and sides of curves.    As here in a circle illustration:

 

In the same way, we can eyeball a number of visually obvious lines for some for some of the arc centers in the 1690 tenor.

 

As easy as these lines where to identify, and we can easily see more of these continuing toward the volute eye, we already know for certain that arc centers for our geometry sit along exactly these lines.   There are only two possibilities with these visually obvious lines.  Either, one arc center sits on such a line.  In which case, an arc from that center swings through the intersections we marked.  Or, two arc centers sit on such a line.  In that case, one arc with swing to one side, and the other to the opposite side.   Illustrated here:

 

With these techniques, we can take first preliminary looks at the underturns on these examples.  But we will need to go quite a bit further with our looking to find any sort of understanding.

1690 tenor

 

Lady Blunt:

 

 

 

 

 

[Torbjörn Zethelius]

On 11/9/2020 at 1:54 PM, Wood Butcher said:

I’ve seen pictures of the templates for marking out the back of the scroll in the Sacconi book, so I understand the principle of how it works.

I have never seen anywhere information on how it is generated.
Does anyone know the position of the compass locations? Presumably the chin is the starting point, and it works from there. How do you work out the changing distances between the points, and how to work out the widths of the circles for a violin scroll?
 

Any help is appreciated.

I wrote an article about how to measure out the scroll and pegbox in The Strad's Trade Secrets. If you manage to follow it then from there it should be easy to make a template. Strad's templates were made for a busy workshop IMO. A lone maker doesn't need it. I have made a storey stick with the essential measurements, the same as marked out in my article.

Carving a scroll using angular templates.pdf

[Torbjörn Zethelius]

On 11/12/2020 at 7:06 PM, Davide Sora said:

@David Beard  You are right, but I would say that all Cremonese pegboxes are based on straight lines, including Stradivari.

They are straight looking to the eye, but not necessarily by the straightedge.

[MikeC]

56 minutes ago, Torbjörn Zethelius said:

I wrote an article about how to measure out the scroll and pegbox in The Strad's Trade Secrets. If you manage to follow it then from there it should be easy to make a template. Strad's templates were made for a busy workshop IMO. A lone maker doesn't need it. I have made a storey stick with the essential measurements, the same as marked out in my article.

Carving a scroll using angular templates.pdf 1.18 MB · 4 downloads

Hi TZ,  I read that article.  I have a question,  how do you determine the first turn on the back?  See the circled area.  The rest of the scroll is easy but that part I just kind of eyeball it.