Jump to content
Maestronet Forums

Curtate cycloids revisited


catnip

Recommended Posts

Extract of Waiting for Godot - The parts Beckett edited out: 

 

 

 

VLADIMIR: Oh ... nothing very definite, curtate cycloids
ESTRAGON: A kind of curtate prayer. 
VLADIMIR: Precisely. But not precise, evidence of curtate cycloids. 
ESTRAGON: A vague supplication, yes very vauge. 
VLADIMIR: Exactly. 

VLADIMIR: Oh ... nothing very definite, but oddly cycloidic

ESTRAGON: A kind of prayer, pray for curtates? 
VLADIMIR: Precisely, or is it precise? Or even curtatish. 
ESTRAGON: Does Godot have the Templates? 
VLADIMIR: Exactly, templates, lucky if he has plates. 

VLADIMIR: Oh ...

ESTRAGON: A kind of plate? 
VLADIMIR: Tems really. 
ESTRAGON: A vague plate or curtate? 
VLADIMIR: Exactly.

 

 

Found in Becketts notebooks with lines drawn through. 

Link to comment
Share on other sites

  • Replies 121
  • Created
  • Last Reply

Top Posters In This Topic

The Luthier's Library would throw a cycloid over the kitchen table if they had one. No one has said they fit every violin ever made, and even in Cremona maker quality and instrument quality varied quite a bit.

 

Direct measurement is fine if you like second or third (fourth? fifth, even?) generation resolution, but where are you going to get an undistorted 300 year old violin?

Well, cc's either fit, weren't well fitted, or are the wrong model.

And unless I missed something (often happens... ) direct measurements are the only real data, excepting Guadagnini's arching templates, taken from a presumably undistorted Strad. The rest is hypothesis, which brings us back to space aliens. In terms of a practical, functional approach, well, you've outlined the limitations of cycloids and direct measurement already. Which makes cycloids a useful tool, but not THE answer.

Link to comment
Share on other sites

300 year old violins are almost all distorted, therefore are not perfect cycloids any more, therefore do not sound optimal.

 

or

 

Starting out as a cycloid infuses the wood with special properties that distortion can not destroy.

 

or

 

 

Which makes cycloids a useful tool, but not THE answer.

 

 

We all know THE answer is 42, but we don't know what the question is.

Link to comment
Share on other sites

I do often wonder why when these conversations come up that we talk of "arches" and the plates as if the roles and functions that the back and top serve are the same.

 

The top is loaded and serves as an arch to form a carrying bridge, whereas the back plate is loaded by the down force of the post pressure, transferred from the top load. The down force on the post is pushing on the back and undermining its strength by focusing down force on the "bottom" or underside of the arch, as it would be traditionally used to support weight from the topside. The back serves a completely different function that must work with the load from the top once vibration cycles begin.

 

So, however one be deriving there final form, these thing must be taken into account.

 

Again, violin makers who want to earn a living making copies of Italian master instruments should take advantage of templates in order to more perfectly copy known original shapes, at least  until they have it memorized . Graduations along with wood characteristics will effect the final tonal outcome. Luithiers who want to explore their own ideas can get from point A to B however they like, and I suppose when it comes down to it things either sound good or bad.

Link to comment
Share on other sites

300 year old violins are almost all distorted, therefore are not perfect cycloids any more, therefore do not sound optimal.

 

or

 

Starting out as a cycloid infuses the wood with special properties that distortion can not destroy.

 

or

 

We all know THE answer is 42, but we don't know what the question is.

 

1. I don't see that as an impossibility. 

 

2. The wood I couldn't say but it could make the geometry more tolerant to distortion through a couple of mechanisms.

 

3. That's the easy one : the question is if there was an original design and if that design still transpires through distortion and misunderstandings. That many makers interpreted loosely the original design because either they didn't understood it or didn't know about it ( and where forced to "copy" ) is irrelevant in this context.  

In the end it all comes down to how many variables one would like one's system to have. The better the maker, the more variables his system can tolerate. Up to a point, probably.

 

As David Burgess very nicely puts it, there are many successful makers employing other systems. They feel comfortable handling a larger number of variables from case to case. There is a lot to say about the "inside first" or the "bent sticks" methods to my mind which I believe add a new dimension of physical meaning to this problem. In the end, most every maker puts his personal touch on the tone and appearance of his violins - cycloids are a mechanical approach and they would hinder this sort of freedom.

Link to comment
Share on other sites

I was studying some things about curtate cycloids by searching the internet. I saw a good lead and clicked on  it. It turned out to be a MN conversation from 2012 in which all the prime suspects said exactly the same things they are saying in the current 'No templates' thread and this one. 

 

Funny stuff. 

This is true. As they say, change comes not through innovation, but through death [of the dinosaurs who are holding it back]. That's why I really enjoy teaching beginning makers: they come in with minimal prejudices and are genuinely open minded, rather than just using the concept as a slogan.

Link to comment
Share on other sites

I was studying some things about curtate cycloids by searching the internet. I saw a good lead and clicked on  it. It turned out to be a MN conversation from 2012 in which all the prime suspects said exactly the same things they are saying in the current 'No templates' thread and this one. 

 

Funny stuff. 

Funny how history repeats itself.

 

Let me throw out a couple of thoughts. First of all, there are many different functions (equations) that can simulate the cross arch, but it remains to be proven that there is a physical reason underlying the match. See Kevin Kelly's remark.

 

Next, is there the historical basis for using a certain function such as c-c's ? Namely, did designers of Strad's time use that function on a regular basis to design instruments or structures? They may have known about c-c's but what is the evidence that they used them to make violins?

 

Moreover, what truly irks me is that we had a discussion of Francois Denis' "Golden Arches" article in The Strad, but to my knowledge no one here has tried to fit a curve to his vault framework and compare those arches to some instruments. Denis is telling us that the old makers were not using cross arches to construct instruments. Test out that idea!  <_<

 

Finally, I was alluding to Don's questions as being rhetorical because I believe it does not matter what the shape is (within reason). If the shape is reasonably close to a family or group of smooth arches, we get a decent sound-producing plate. The proof of that theory is the range of arches we see in instruments that produce good tones. If there was one magical shape, there would be a lot poorer sounding instruments. I know someone will pull out the old stinking red herring that Strad's violins sounded unique. Did they? Now, that is another rhetorical question.  ;)

 

Mike

Link to comment
Share on other sites

I was studying some things about curtate cycloids by searching the internet. I saw a good lead and clicked on  it. It turned out to be a MN conversation from 2012 in which all the prime suspects said exactly the same things they are saying in the current 'No templates' thread and this one. 

 

Funny stuff. 

“Student: Dr. Einstein, Aren't these the same questions as last year's [physics] final exam?

Dr. Einstein: Yes; But this year the answers are different.”

 

Ok, the answers are still the same but I like when old topics resurface.  Even if the answers and peoples perspectives are the same, I've changed.  I have a better understanding of how much I don't know now, than I did in 2012.  If I keep learning, I'll know even less in 2017.  :D   

 

This is a great thread.  I'm glad MD has thrown his hat back in the ring.

 

Cheers,

Jim

Link to comment
Share on other sites

That's why I really enjoy teaching beginning makers: they come in with minimal prejudices and are genuinely open minded, rather than just using the concept as a slogan.

In Kindergarten, I accepted and believed everything my teacher said. By the end of first and second grade, I was beginning to understand that this isn't always the best way.

 

I still remember my first incident of discovering that the teacher wasn't always right. There was a rather heated argument between the teacher, and a rather brave (impertinent?) student, during which the teacher insisted repeatedly and emphatically that a tomato is a vegetable. I could read by then, and we had a couple of sets of encyclopedias, and a few dictionaries at home........

 

Later, when I started to become more involved in teaching, I tried to keep experiences like that solidly in mind.

 

Yes, it can be much less challenging to teach beginners, than those who have some experience, and reasonable level of prior success.

Link to comment
Share on other sites

There's one del Gesu we had at B&F that had an unusually scooped arch. We wondered why, and eventually someone noticed the tailings of what must have been a huge tear-out. Whoops! Better cut that out! And thus the strange arch. That's why I stress the idea of an underlying design--the idea that if you know what they knew, then you at least have a starting point for experimentation. If you don't admit to any underlying design, you're pretty alone. 

 

Also with some understanding of what the concept was, we can develop an understanding of how they morphed and changed, and the parameters they were willing to compromise on vs the aspects they felt always had to be there.

 

Regarding the superiority of their system, I've worked with several well-known makers who had problems like being commissioned to copy an instrument but wanting to reconstruct the arch. As one of them told me, "I've been making for 30 years, and this is the first one of my instruments that could be said to be 'Cremonese' sounding." After just one copy he was talking about completely revamping how he approached arching.  Others have noticed, on their own, how when they put more care into keeping to the templates, the results improved suddenly and radically. The reason I keep pushing on this is how definite the results have been for other people who've tried the strategy, in proportion to how well and accurately they work it--not just for me.

 

This isn't something I've been keeping to myself--I've taught quite a few people to use it, with good results for them. I think there may be a misconception that I'm in this alone. More to the point is the number of people who've told me that I should keep this all quiet. But as you can see from these threads, there's no threat to them. :-)

 

If you do it, and do it carefully not casually, the result can be remarkable. Part of the reason I believe that Stradivari violins are more consistently good is that my templates always fit his instruments more closely than they do on other makers' violins, makers who were being more casual about what they were doing.

Michael,
 
If I understand you correctly, a suitable system of parametric design for violin family arches would include, but not necessarily be limited to, the constraint that the cross section of the upper surface of the arching of top and back match that of a specific instrument based on templates, probably tempered by the acknowledgment of distortion, with the interpretation from observation that those cross arches form a related suite of curtate cycloids allowing interpolation between known cross arches (e.g., those shown on posters).  Imagery including photographs and CT scans of the instrument being copied provide further constraints.
 
An implication of this is, if I understand the concept well, that a larger suite of constraints could, might, should match Cremonese archings and support development of a more general parametric design process involving those constraints.  Examples of such additional constraints that might apply, with more or less evidence supporting their historical use, and have been proposed include, but are not limited to:
- simultaneous fit to a geometric working method known to be used in the Renaissance, e.g., the various systems described by or pointed to by Francois Denis;
- use of specific longitudinal arches (e.g., circle segments - see Evan’s exposition);
- fixing of certain points on the cycloid suite to match interpretation of observed systems (e.g., channel low point, curtate cycloid inflection point); and
- formation of specific elements on the resulting arch (e.g., Zuger’s straight line tangents).
 
Any number of other constraints could be added, such as making the interior cross arch a specific shape such that when graduation is added the exterior is a curtate cycloid.  Constraints could also be lifted so long as a sufficiently close (within measurement and distortion error) match to the historical examples was achieved.  This could be something along the lines of curtate cycloid across the corners, but arcs of circles or other geometry between the F holes, or perhaps accommodation for special treatment of the area where cross arching does not work well, e.g., directly over the neck and end blocks.
 
Of particular note by its absence in the literature, specific forms of arch shape diagonal to the longitudinal axis could be integrated as a constraint.
 
Clearly some of these constraints might be incompatible with each other or the parametric design goal of producing a Cremonese arch.
 
The intended result, of course, being to generate an instrument that will produce more of the desired old Italian sound and character.
 
Just some thoughts on a Monday morning.  Back to writing this tedious brief!  We should discuss the role and design of the primary load bearing arches, those formed by the ribs at the upper and lower ends of the instrument.
Link to comment
Share on other sites

While the roll of curtate cycloid's as cross arching guides may or may not be workable, what I find interesting, even more, is the meshing of odd shaped teeth in this discussion... as if the two wheels will not roll, as a matter of established course.

 

That fact notwithstanding, the options available to us are unlimited! We can do anything we choose.

If we believe Michael, and this option as 'viable', what is there to stop us?

(Well, I mean what is there to stop me?)

Nothing. 

Link to comment
Share on other sites

If the shape is reasonably close to a family or group of smooth arches, we get a decent sound-producing plate. The proof of that theory is the range of arches we see in instruments that produce good tones. If there was one magical shape, there would be a lot poorer sounding instruments. 

 

First, I definitely agree that Cremonese-like arching, with cycloid-like crossarching, seems to work well according to the type of sound that is generally desirable.  And since it looks Cremonese-like, the aesthetics of today's buyers and critics won't find much to complain about.

 

That does not necessarily mean that other shapes can not sound good... unless you either have some physics/acoustics proofs, or have tried every other possible shape... neither of which has happened or is likely to happen. 

 

Unfortunately for me, this line of reasoning is leading into some ideas for some very bizarre shapes to test out... just to try and understand how it works, and possibly prove the existence of an alternative (functionally, but probably not aesthetically).  

 

 

... the options available to us are unlimited! We can do anything we choose.

 

Very true, although all factors need to be considered:

Need to make a living at this?  Then it might not be such a hot idea to stray too far from the tried-and-true stuff that sells.

Link to comment
Share on other sites

To answer a previous question about whether or not people of this time could use the curves, analytic geometry was being invented about the same time as the violin was evolving, and was quite the buzz in intellectual circles.  People were playing with curves.  Any of these, except a catenary,  can be easily constructed using compasses, rulers, and strings.  With a French curve, one can connect different curves to produce things not easily drawn or calculated.

 

Another curve which is, one supposes, as good as any for arching, and of the proper age, is this:

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

Link to comment
Share on other sites

To answer a previous question about whether or not people of this time could use the curves, analytic geometry was being invented about the same time as the violin was evolving, and was quite the buzz in intellectual circles.  People were playing with curves.  Any of these, except a catenary,  can be easily constructed using compasses, rulers, and strings.  With a French curve, one can connect different curves to produce things not easily drawn or calculated.

 

The cycloid is an extremely simple curve to generate mathematically, and it does appear that the math was up to the task at the time.

Link to comment
Share on other sites

Violin making is wood working. Arching templates made with curtate cycloid shapes are useful tools.

 

I've made and compared curtate cycloid templates to dozens of Cremonese arches, and I consider them to be so close to matching so often, that I have made them a part of my own work. At the moment I happen to not use templates, but I've found them useful in the past. I've often made just one, for the narrowest part of the arch, to help me get the right feel for a new viola model, for example. 

 

I believe that there are Cremonese instruments that do not fit cycloid templates, and also that there are lots of violins with different arch shapes that play very well.

 

I don't think that they are necessary to making a good violin, but are very useful as a reference. Having said that, I can easily imagine a time when I'll go back to using them, especially if I have an assistant who does more than the most basic roughing out.

 

For me,  curtate cycloid templates are easy to make and can be useful if you're struggling to come up with a template for some Cremonese-looking cross arches, and the discussion about what the Cremonese makers actually used can be saved for some other time (over a beer, maybe). 

 

There is no "math" involved in making cycloid templates, only a little arithmetic.  You have to know the width of the arch (low point to low point) and divide by 6.28 (2 x pi), and you have to know the arch height (low point to high point) and divide by two. That's it. Some thin stock, dividers, a saw and a coarse file are all you need. 

 

They are actually kind of fun to make and play around with. If anyone is interested in actually trying to make some and see for themselves (you can compare them to arching drawings in the Strad posters, for example) then I'd be happy to put together a little demo on making them in order to encourage it. I would be interested in the direction this discussion takes if a few people try it and then comment again.

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
  • Recently Browsing   0 members

    • No registered users viewing this page.



×
×
  • Create New...