Violin Forum/Message Board

[KenN]

This website has a way to draw a long arch: kcstrings.com/anton-krutz-geometry. In fact I've never seen that discussed anywhere. He uses the golden number (phi) and phi^2 (easy enough to get with a divider) and phi^5 (which is easier to get as 1/11 using the 5/11 ratio he used to get the mensure). I haven't checked out how he does the cross arches yet, I ws looking at the pages I printed out a work, but the long arch seem plausable.

[woodwiz]

Definitely worth checking out. The guy makes exceptional instruments.

[Andres Sender]

Hi woodwiz, you work with Mr. Krutz don't you?

Am I right that the arches are essentially ovoids constructed from three arcs?

[sdantonio]

Very interesting article. This is exactly the kind of aproach that I tried to get a discussion going here several months ago. But evidently people couldn't handle it here (interestingly enough there is another forum where people typically are violin makers with backgrounds in physics, mathematics or engineering and the same discussion went for several weeks before we exausted all the ideas).

Does anyone know if this outline is also applicable to other members of the violin family (violas, celli and basses)?

[woodwiz]

[sdantonio]

Hello Woodwiz,

The other forum was Left Brain Luthiers. Most of the people there seem to be trained engineers, physicists, chemists or mathematicians. The focus is more guitars with some violins thrown in. http://launch.groups.yahoo.com/group/leftbrainluthiers/

The founder was a retired professor of mechanical engineering. If you remember the old cast of characters from the Journal of the Catgut Acoustical Society it's kind of like that, but live and real time. The only thing missing is the ability to do much in the way of complex math in the forum. One of the current discussions is an analysis of brazilwood properties and alternative bow woods carried out at the Max Plank institute recently.

I read Antons web article very carefully today, I have a ton of questions. My notes are at work though and I'll have to post some of them tomorrow if I can pick you brain and see if you can fill in a few of the details he seems to have left out. People here will tell you that I have been kind of obsessed with developing a mathematical solution for the lengthwise arch, probably to the point of getting a bit anoying .

I put together a model of the long arch of the top from Antons description than compared it to digitised strad lengthwise arches I have on file and it overlays very very close. Antons seems to be a little fuller right under the fingerboard (about .75mm fuller), but otherwise they overlay to within about .1mm along the rest of the arch.

The back however, I have lots of questions on.

Steven

[sdantonio]

Hello Woodwiz,

I suppose the first questions that come to mind are:

1. on the back, is the highest point on the back arch at the mensur (as it is on the top), in the center of the instrument or approximately at the soundpost location (about 10mm further toward the heel from the mensur). I looking at a lot of pictures of old world instruments it appears that the highest point of the back long arch is approximately in line with the soundpost.

2. the beginning and end points of the back arch, are they calculated the same way as on the top?

3, the two secondary high points (the high points of the first 2 ovoid curves), are they (phi^2) * (distance from the high point to the curve end). In the diagram they appear symetrical and this would only happen if the highest point of the arch were in the instrument center.

Thanks
Steven

[Andres Sender]

I believe you're talking to Woodwiz.

[sdantonio]

Andres,

Sorry about that. First time I have had to use the edit function.

Steven

[woodwiz]

Highest point is at the menzur. It looks "off" on paper, but on the violin, because of the varying widths of the bouts, it looks just right.

I'll have to double check with Rick and Anton about the construction of the back centerline arch. I think I understand it, but I don't want to steer you wrong.

As for the cross arches, they are just 3 point arcs through the centerline arch and the arch line at the edge, then cut off at the golden proportion and faired into a recurve, more or less by eye. Not much recurve or channel on these violins. Shape and thicknesses at the edges apparently have a big effect on sound.

I have been playing around with curtate cycloids for cross arching, but I really like the shape of the long arch. Might try caternary cross arch, too. I know from experience how much difference the arching makes to the sound, but these curves are all very close, and the layout methods were widely understood in the 18th Century. Judging by the results, this arching is pretty good. Anton has stuck with the basic layout for years, now, making only small, incremental improvements in details such as recurve, graduation, ground, and varnish.

While most of my training is in engineering, I'm very leery of people who try to "engineer" a violin. It's great to systematically try out and evaluate different things, but I think you learn the most by making. I know I have learned a lot about voicing by taking old factory instruments, (re)graduating them, re-barring them, and observing how various graduation schemes interact with different styles of arching. Plain old hands-on trial and error have taught me more than I could ever learn from theory, especially since "everything affects everything," and it's really hard to isolate variables.

[KenN]

I've found that an elipse will make a nice long arch. On the back, using the five points you figured out, an elipse centered in the middle of the ribs (15-16mm down from the bottom of the plate) works pretty good. Since the mensure is not on center you need 2 different arches, the bottom one having a shorter long terminal point.
On the belly you need 3 elipses. I center them on the bottom of the back plate with one real long one going between the points on the bouts thru the mensure point, and the other two blending from there to the ends. Of course on both plate you have to decide how you want the recurve at the ends to be. Even within the given constraints there is a lot of room for bringing out your own style.
I also use the end points as the ends of the inside arch, which on the belly can use the same center an long end terminal points as the outside, but the back is a two arch composite. I actually drew a circle at the end point 2.5mm for the back and 3 for the belly and made the outside arch blend into the top of the circle instead of the middle. It works out quite well. And elipses would have been easy for someone to draw up in 1700.

[ed s]

Where do the luthiers on this forum locate the highest point on the longitudinal arch on the bottom plate on your past instruments? eg. centerpoint , at the mensure , at the soundpost , at the center of the graduation pattern , or do you just use the template from a poster or plan of a successful model and disregard location of highest point?

[sdantonio]

Ed,

most of the violin makers I have talked to personally locate the highest point of the back at the soundpost. But this may just be a New England thing. I'd like to hear from others on this too.

Woodwiz,

I think I figured out the arching for the back. I drew one up with Antons method, then I drew another using an older method I was experimenting with using 2 catenary curves spliced together and they overlapped to within a few hundreths on a mm. So close you could not possible control the wood to that accuracy.

Antons method gives a much better looking top curve though.

But if you ask him and confirm I am doing it correctly that would be great.

Steven

[ed s]

Thanks or the response Steven, the reason i asked the question is because over the past years on different forums all of the above locations were mentioned as the correct location for the highest point on the back plate arch. I have been locating the highest point at the bridge location. It would be interesting to hear from the experienced luthiers on this.

[ed s]

Based on the responses this must have been a very dumb question or the luthiers want to keep this proprietary. The development of the arch is very important as it relates to the sound of the instrument therefore I don't blame them for not sharing some of their knowledge.