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Curtate cycloids revisited


catnip

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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

 

The rather neat thing about the cycloid is that it does not require any analytic geometry. As used for violins, even the arc length is can be figured out easily and that would be a nasty elliptic integral in general sense.  

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 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.

 

That would be very nice - thank you .

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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).  

 

I always appreciate the experiments you share, Don.

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As far as I understand it the Cremonese method would not think of the arch as a single shape. (The arch is created without a channel, the box is closed, the recurve is created and blended into the arching). What is the function of the channel and what criteria were applied to its finishing? Acoustic, structural, aesthetic?

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As far as I understand it the Cremonese method would not think of the arch as a single shape. (The arch is created without a channel, the box is closed, the recurve is created and blended into the arching). What is the function of the channel and what criteria were applied to its finishing? Acoustic, structural, aesthetic?

 

Aesthetic, in my ( incompetent ) opinion.

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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.

I think that would be great!

There's been quite a bit of interest shown during these two recent threads, as well as over the years.

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Curtate cycloide curves fits quite well to this instrument

http://www.thestradsound.com/ongoing/photosofthesoilstarted2014

 

No templates used. It is Roger Hargrave's, Michael Darnton's, Patrick Kreit's and Curious1's images and explenations that taught me how to make such arching and edge work. Some teachers are better than other because they actually teach :)

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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.

Kevin,

 

Can you point me to a source on how to draw ccyloids with compass and straightedge?

 

Thanks

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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.

 

If the back arching was inverted it certainly would be stronger, but it would also be resistant to being driven in any way by the post. I don't think this would be a desirable goal.

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If the back arching was inverted it certainly would be stronger, but it would also be resistant to being driven in any way by the post. I don't think this would be a desirable goal.

 

Hmmm... seems to me that flexibility in vibration is linear, and inverting the arching would have no effect on how it is driven by the post.

Strength would be higher only in that the loads from the post would be compression, rather than tension.

 

I will resist the temptation to try it.

 

edit:  upon further thought, some of the low-frequency body modes involving rib and block movement and rotation may be affected in odd ways if the back arching is reversed.  Pure plate modes shouldn't be affected.

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Steve, the consensus opinion here appears to be that such an undertaking would be impossible, irrelevant, and limit ones making options from infinite options to no freedom of choice at all, which has been defined by several people here as a Bad Thing.

Fortunately I am used to impossible environments, such as being subject to the whims of multiple government agencies, weather, incompetent contractors, incomprehensible regulations waived around by attorneys with the rural survival skills of a box of hammers, and my own willfully ignorant management.

 

I generally work with the hypothesis given:  "Old Cremonese instruments are designed/made/treated/etc with X."  If the evidence fits X, well, I can't eliminate X.  However, if there no evidence for X,or if the evidence clearly rebuts X, the it goes away.  Things neck down rather quickly in most fields, as I would expect to happen with violin design.  

 

For example, the universe of reasonable Renaissance arching design working principles is likely only moderately broad and of limited complexity.  I expect it sorts out when applied to the data from old Cremonese instruments rather quickly, and the work of Denis suggests that is the case.  A test would be to take a model for design based upon, for example, the radial system laid out in "Golden Arches" and to develop a test.  For example, his hypothesis is that a certain centrally located "beta" value of arching height is reflected at geometrically consistent points around the arch as an arch height at those points that is a harmonic? ratio of Beta (e.g., 4/5 or 1/2).  He adds that Beta may not be the high point of the arch, and that Beta may actually be a bit lower.  The constraints are substantially loosened by that kind of condition.  The test is easy.  Lay out points for various potential systems, figure out the arch height at those points on several instruments from one maker (or several makers, kept separate), and see whether those sets of points for each instrument are equal, within a certain tolerance.  If they are not equal for a given plan, that plan must be rejected.  If they are equal, within tolerance, then test against Beta for that instrument to see the relationship.  A spreadsheet assuming the the radially located points are 1/2, 2/3, 4/5, 3/4 etc of beta will give a range of possible betas.  Ratios that produce unreasonably high beta values must be discarded.  Ratios that produce beta values about like the height of the arch at the related Beta position are retained.  Then compare instruments.  If there's a good deal of noise and the fit isn't that good, and one violin looks to use 2/3 while another from the same maker in the same time period uses 4/5, sort of, and Beta requires a good deal of fudging, then that particular system is unlikely to have been used, or on the flip side, can't reliably be used to characterize the arching.  

 

That type of testing of possible parameters is not difficult, and is fun.  

 

If you set your laser system up again, run videos with the laser highlighting various diagonal angles.  See what shows up.  

 

Thank you for your patience.  I have sort of started a file on this type of thing, apparently violin processing goes on in the background while I ponder abuse of process and the effect of misconduct in quasi-criminal hearings.  I don't blame it; violin thinking is much more interesting!

 

Be well.

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Curtate cycloide curves fits quite well to this instrument

http://www.thestradsound.com/ongoing/photosofthesoilstarted2014

 

 

Nice looking instrument, but I can't believe that curdate cycloids fit in the area around the f holes.  The contouring of the lower wings is not following where the cc curve would be.  Backs are different.  Backs can have cycloids the entire length.  Bellies can too, but the f holes have to be carefully placed, and they will still probably look like they don't really belong there, that they were just added as an after thought.  The center area between the f's may follow a catenary, or a cutate cycloid, but outside the f holes doesn't.  

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Kevin,

 

Can you point me to a source on how to draw ccyloids with compass and straightedge?

 

Thanks

you may be able to do this, somehow - but masonite circles worked much better for me - the primitive sort that I am.

Programs can out put just about anything that you'd like.

But the act of making these curves by hand entices me also.

But a compass and straightedge? 

no. Or, good luck.

you're going to need to make and use some circles or some round blanks 

then figure out your height for that width and drill a small hole.

 

I'll look for a video to show here about how simple and easily made any curtate you'd like to make is. That is, if I understand you correctly and you want to MAKE them.

 

Right?

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Kevin,

 

Can you point me to a source on how to draw ccyloids with compass and straightedge?

 

Thanks

Interesting question. We have strong evidence for the use of a compass, from surviving markings, and no evidence for the application of curtate cycloids, except that they can be fashioned to be a decent fit in some situations.

 

Not that I am in any way opposed to their use. But I think it might be a bit much to light a bunch of candles, and bow down at the CC altar as if it was the only true path to salvation.

 

Heavy incorporation of a compass in an arching scheme would make it more interesting.

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If the back arching was inverted it certainly would be stronger, but it would also be resistant to being driven in any way by the post. I don't think this would be a desirable goal.

Oh, I'm not suggesting that the back should be inverted, just that the way it functions "pushing on the weak" is part of what makes "it" do what "it" does...and that the top and the bottom serve perhaps opposite roles, in a way, and that should be "known" when discussing arches and their role in "it" all...

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Ok, I should have kept my mouth shut. I made a quick template this morning, and then spent even more time than that trying to get the stuff on MN. All the photos I took came out sideways and in the wrong order, and I found it hard to explain myself.  I eventually gave up and used a more familiar method. 

 

You can see the result here:

 

https://www.youtube.com/watch?v=BbXixyOvJJw

 

I will not leave it up long, but it shows the steps involved in making a template using dividers. Please forgive the poor production...

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Oh, I'm not suggesting that the back should be inverted, just that the way it functions "pushing on the weak" is part of what makes "it" do what "it" does...and that the top and the bottom serve perhaps opposite roles, in a way, and that should be "known" when discussing arches and their role in "it" all...

I wouldn't suggest that either. The point I was trying to make is if the back is too rigid (inflexible), the post won't be able to drive the back effectively, and the lower frequency response of the instrument will suffer.

 

Edit: A post fit too tight should approximate this situation.

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