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Roger Hill

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  1. I was planning that I would save this for a letter to the editor of Strad magazine for this fall when I would have more time and make it complete with fancy equations, etc. There seems to be a considerable amount of interest in the subject right now, so I will go ahead and cast this pearl. Let me tell you the history of what lies ahead (poets can tune out right here with no loss of vital information). As a young graduate student in physics I was a theoretician, and quite naturally took a number of graduate math courses. The only math course I took in which I topped the PhD math students was The Calculus of Variations. I topped that course because I was the only student to get one of the two problems on the final exam, which was to calculate the shape of a catenary of a particular inhomogeneous chain, a chain in which the mass /length of the chain increased linearly along its length rather than being homogeneous. IIRC (this was 42 years ago!), the professor gave us the physics, which I already knew, and asked us to set up and solve the equations as a minimization problem. I still have had a fondness for that curve, although I couldn’t come close to solving that problem today. When I started studying the violin, Torbjörn Zethelius was kind enough to send me his article on inside-first arching which I found very persuasive as to the method of construction. As I further studied arching, however, I became convinced that the crossed catenary approach leads to incorrect arch shapes. (Torbjörn, please do not take offense at what follows, I greatly admire your knowledge and I view what follows as an extension of your inside-first insight) Admittedly, I have never held a Strad, but the arching profiles resulting from the crossed catenaries just don’t look right to me. Imagine for a moment that one is in St. Louis, walking in a (very large) circle around the Gateway Arch. If you are looking in a direction perpendicular to the plane of the arch, what the arch appears to be is a catenary. As you walk around the circle, the arch you see no longer has a catenary shape, but appears as a more pointed curve, and that is the problem I have with the crossed-catenary approach. Looking at my Strad posters and the photos in the Johnson and Courtnall book, it is obvious that the top arch (generally) has a relatively flat section in the center. The crossed catenary approach leads to a more pointed top longitudinal arch profile than even that of the ordinary catenary, which also does not have the proper profile for the shape of the longitudinal top arch. The only thing I have found in any of my books as to the shape of the top arch is that Heron-Allen describes it as the arc of a circle having a radius of three times the length of the violin body. I have also seen it described as a cubic spline curve. It is neither. I have examined everything I can find online as to the proper curve to describe the longitudinal top arch and have found nothing. As I looked at the posters and photos, I recognized the curve. It took only a trip to the jewelry department of a craft store to confirm my intuition. If what I am about to describe for the top longitudinal arch has been written before, it is in something I cannot find or some $800 book which I am not about to buy. I therefore claim to have discovered this all by myself! The shape of the longitudinal top arch of the Cremonese violins (for which I have good pictures and curves) is that of a catenary of an inhomogeneous chain. The shape of longitudinal bottom arch for these same violins is an ordinary catenary, i.e. that of a chain having uniform mass/length. I am persuaded that the cross arches are the result of simple catenaries carved inside first, then transferred to the exterior. The edge flute carving leads to a curve that is for all reasonable purposes a curtate cycloid. The inhomogeneous chain used to create the longitudinal top arch is composed (generally) of two sections of heavy chain attached to either end of a section of much lighter chain having a length of 100 to 175 mm, or 4-7”. The lighter the center chain, the flatter the curve of the center section of the arch. Having one uniform chain and two different sectional chains I can match exactly the longitudinal arches for about ten violins for which I have good pictures. Further, all the cross arches on my Strad and Guarneri posters have a long section of excellent match between a catenary and the actual curve. The method of construction generally follows that laid out by Torbjörn. The arch shape is decided using the appropriate chain and a horizontal line on the wall the length of the distance between the end blocks. The high point is decided upon and that point marked on the chain (for most cases, this isn’t necessary for the back curve). The high point is located on the plate and drilled to a depth equal to the desired (exterior) height of the arch minus the maximum thickness of the finished (graduated) plate. The longitudinal arch is carved using the appropriate chain between the end-blocks as template. The interior cross arching is then carved using the plain chain as a template. The depth of the longitudinal arch at any point defines the cross arch catenary. Once the interior is carved, the arching is transferred to the exterior using the graduation punch set to the maximum desired thickness of the plate. The punch is set up with a support post having a rounded top. After the top shape has been carved and scraped down to the punch marks the plate will be of uniform thickness. The support post on the graduation punch is next replaced with one having a hollowed center to allow the convex top surface to fit securely and rigidly into the hollow as the punch forces the wood onto the post. The interior is then punched and scraped to the final graduation pattern. A couple of observations: the marks on the top of the cello in the picture given by MD are totally consistent with the above procedure, as are the inside punch marks on the Strad violin. The punch is used twice, first on the outside, then on the inside. Secondly, there is no need to use a drill with a special end-point to begin the carving of a plate. Guarneri may have used one simply to save time. Thirdly, it is much quicker to make a few chains than to make templates for every desired arching shape. Finally, there are some pathological violins that have an out of the ordinary shape. If you have the Hill book on the Guarneri family, examine the Andrea Guarneri violin of 1676, which has flat center sections for both top and bottom, only one chain required. Also, examine the Pietro Guarneri violins of 1708 and 1686 in which he places the high points of both top and bottom above the upper corners. You do this by having more of the heavy chain at the end of the violin where you want the high point to be located. For a truly flat center section, use the heaviest jewelry chain you can find with a center section of thread. You will find great entertainment in pondering arching profiles. For all of you pros who adopt this, my royalty fee is 10% payable immediately upon sale of any violin that uses the TJR copyrighted arching profiles. TJR is, of course, short for “Tony, Joe and Roger.” Have fun with this, I’m going fishing……….
  2. Thank you, Ariane......I was hoping you might do that. I will try not to put you on the spot too often. Thanks, everyone else.
  3. I was reading some past threads and came across a post by Jeff Loen referring to this issue, and "Cremona's Lost Curve." I assume that the lost curve must be a catenary, curtate cycloid or some such. I would appreciate it very much if someone who has this issue could tell me the gist of what the article says so that I will know whether I need to research this further. TIA
  4. Humidity in Colorado Springs right now (Thursday, 6:30 pm) is 8%. Within the next 30 days we will have a few days where it is 80%. This fall we will have a lot of 5-15% days, while when the seasons are changing, we will have some cool, damp periods of 50-80%. We will have one heck of a lot more dry than damp days on an annual basis. Does this suggest that instruments built here for use here should have the inside sealed to slow the humidity swings? Thanks,
  5. at least some photos can be seen here: http://kevinleeluthier.com/stradivari_tool...variusTools.htm I don't know whether this is everything in the museum as far as tools are concerned
  6. Yes. It has been available on the internet for a long time. Unfortunately, this group is no longer actively posting research online.
  7. Thanks, Catnip. I would like to see that if someone has it. Mike: The body dimensions, F-Holes and scroll for the Cannone are given here: http://www.giordanoviolins.com/english/cannone02.html A nice summary of that data is here: http://www.paganini.comune.gen...neri_immagini_eng.htm The graduation map is given here: http://smitech.org/index.php?j...icle&op=viewFile&path[ Melvin has given the arch heights above and Luis has given us the rib heights. Should cover most of what you are interested in. It would be nice to have a better defined contour plot than can be deduced from Loen's color scheme, but we beggars don't have a lot of other options available.
  8. Melving: Thank you very much, those are exactly the numbers and comments I was hoping to see. I will be interested to see how much Guarneri changed his approach to the arching over the years. Selim: You did not hijack my thread, no apologies necessary. I am studying arching/graduation from the standpoint of developing my own approach to trying to get the vibration modes to be as close as possible to what I want and adjustable as required to create a desired sound. I expect to have the tops off of anything I create on a regular basis, as you are doing, so your comments are always appreciated. The only point I was trying to make after you noted that "Perfect Copies" may or may not, in fact probably will not, sound all that great is that violins do obey the laws of physics. The laws of physics for shell type bodies, in turn, are expressed in terms of their inertial and elastic properties of the materials they are made of. The weight of the Cannone certainly brings up the question of the inertial properties, which will particularly affect the high frequencies and the carrying power of its output.
  9. Magnus: I think that you and I are saying the same thing. I also think that you have greatly misinterpreted what I said. When I asked my original question, I wanted to see where the Cannone arches fit into the arching parameters as defined by Nigel Harris, and how they compared to the graduation map of the Cannone published by Jeffrey Loen. I hoped to study the comparison of the Cannone to the other del Gesu and Strad arches/graduation maps available. Regarding this effort, I see many attempts to duplicate the Cannone, including the arches and graduation. I think that it is futile to do that in the hope or expectation that one will come up with a great violin by doing so, regardless of how well one does about arching, setup, etc. Since the wood and varnish will be different, the elastic and inertial properties will be different and, hence, the sound will be different . My own belief is that the masters were trying to control a few major modes of vibration, as articulated by Jack Fry. If you go to Martin Schleske's site and examine the measured vibration amplitudes and graduation map of the 1712 Strad he presents the animations for, you quickly discover that the thinned areas of the top match areas of maximum amplitude for the breathing modes of the violin body. Big surprise. How much thinning Tony had to do there depends upon the arch in the areas where he wanted a large amplitude. The stiffness and density of the wood he worked with also affected those amplitudes, as did his varnish. What I tried to suggest was the futility of trying to duplicate a vibration mode by duplicating an arch/graduation model, when it is the elasticity/inertial properties (i.e., the spring constants) that would have to be duplicated if one wants to duplicate the violin's voice. I believe that this is what Schleske is attempting with his "Tonal Copies" of violins. He seems to be making progress in that endeavor but I can't think of much that is more difficult than trying to reproduce the sound of an instrument that has hundreds of identifiable resonances. I believe a more fruitful approach would be attempting to create violins with a satisfying breathing mode, a strong tweeter mode and a properly suppressed rocking mode as outlined by Fry. Each violin created in such a manner will be distinct, just as are all the Cremonese instruments. I haven't seen any well regarded luthiers taking such an approach. However, since the well regarded luthiers keep their techniques, recipes, etc. so secret, perhaps I am simply suffering from lack of knowledge as to what they are actually producing. Now, I freely admit that I am new here, I have no experience playing the violin, and am only working on my first violin. I have read virtually everything on the internet regarding violin acoustics and I am not a complete idiot, so please don't take that tone with me.
  10. Selim: ________________________________________________________________________________ ______________________________ I am talking about "Perfectly Exact Arching, Graduation, ..etc" that means exact copies of great originals. I have read and heard many times about the statistical reality; 10-15 percent fo the existing violins sound good. If it was possible to produce good sound (This is what I mean by decent sound), by exact copies, there would be millions of good sounds around. ________________________________________________________________________________ ____________________________ This brings me back to my hot button, namely spring constants and concomitant damping. These are determined by the wood/varnish composite properties, densities and thicknesses. Add the mass into the "simple" F=ma considerations and you conclude that since you don't have the same wood and same varnish, an exact copy of anything based upon only good wood, shape, graduations,etc is futile. it is the spring constants and inertia which must be duplicated. Mike and David: Don't let it out that we are not all geniuses, we have an important stake in maintaining our unquestioned authority on all matters great and small............. ;-)
  11. John: I am very familiar with Feynman's "Cargo Cult" analogy for bad science, but I would like to understand why you are so dismissive of Harris' work. He offers what are, to me, reasonable explanations of some of the behavior of the top plate of the violin, i.e. does it go up or down as string tension is increased. I have not seen this deconstruction of the forces on the top plate before. His statements that there is a preferred ratio (affecting tone quality) for the height of the top plate arch to the height of the bottom plate arch in the bouts I find intriguing and something that I have not seen others here comment on. Is there something obviously wrong with his explanation that I am missing? Please tell me more......... Selim: Here are my thoughts on arching. Please understand that I am working on my first violin and I do not play the violin. I have been studying these issues for only a few months. I apologize in advance to the non-scientists for getting a bit technical, but I don't have any other way to present this, as yet. Let 's take as an example a thin strip of wood carved into an arch and consider it to be made up of little pieces of wood (say 1/2" X 1/2") connected by springs which have the same stiffness properties as the wood. The stiffness of the springs depends upon how thick the wood is and the curvature of the arch. For a given thickness of a particular wood and length of arch, the higher the arch, the stiffer it is and the greater weight it will support. Hence the springs connecting the little elements of wood are each stiffer. Now, when we make the arch vibrate by forcing it at one point, the amplitude of the vibration of any little piece of wood is proportional to the following: driving force amplitude/(spring constant - (2*pi*freq)^2*mass)) For low frequencies, the spring constant (i.e. the stiffness) is the only term of importance. Now, if you study the deflections of beams, you discover that the spring constant is proportional to the CUBE of the thickness of the wood. As the thickness of the wood decreases the spring constant DECREASES dramatically and the amplitude of vibration INCREASES dramatically. Further, the radiated Sound Power Level (SPL if you are making loudspeakers) is proportional to the velocity of the surface which is being pushed against the air (like a speaker cone or portion of a violin plate). The velocity of the little piece of wood, in turn, is given by the amplitude of vibration times the frequency. For an element of wood in a higher (stiffer) arch to get the same amplitude of vibration, and consequently the same SPL (since the frequency stays the same), the spring constant must be reduced. A higher arch, which tends to be stiffer, must be made thinner because of the requirement that the spring constants be decreased in order to radiate the same SPL. These same considerations lead me to believe that asymmetric graduation coupled with arching is where the remaining mysteries of the violin are to be solved. (given a set of wood properties, varnish will modify the stiffness properties, but virtually any spring constant can be realized by adjusting the thickness) Does anyone else have a different take on why arches are so important? Perhaps a link I have missed and would benefit from? Thanks,
  12. Well, let's stipulate that Harris has more than his share of human failings. He also is the only possessor, that I have encountered, of a PhD in physical sciences with a thesis topic of violin arches. Does anybody have any experience with his arching parameters, particularly the desirable top-to-back arch height ratios in the upper and lower bouts? Cannone he mentions as one violin having desirable arching parameters, hence my original question. Thanks,
  13. Luis: I will get the poster/CD/etc. but it takes a few weeks. A del Gesu calendar took a few months! I am looking at the calculation of the EAR ratios that Harris discusses right now and hoped that the heights vs. location would be readily available from the cognoscenti. Melving: Nigel Harris is an old guy, ie about my age (67) who finished a PhD based upon violin physics research and has done several articles explaining the physics of the violin. I conclude based upon reading of his articles that he knows what he is talking about. His website is here: http://www.violin.uk.com/frame.htm, see "Research" plus his articles can also be found here http://www.oberlinacoustics.ne...location=articlesMain. thanks for your help,
  14. Nigel Harris uses the del Gesu Cannone as a desirable example violin in his discussion of arching ratios, particularly the ratios of the front to back arch heights in the upper and lower bouts. I do not have the Cannone poster, but would like to compare the Cannone ratios to those of the del Gesu violins for which I do have posters, the Kreisler and Kochanski. If someone could post the arch heights and longitudinal positions for the various templates of the Cannone arching from the poster I would appreciate that very much. Also, any thoughts on the actual longitudinal arch shapes/curves, their effect on tone and Harris' studies would be helpful. I Know that Michael Darnton thinks that arching shape is of paramount importance to tone. (I have spent hours reading everything that a search of this forum yields) Thanks for your thoughts.
  15. Did those who regraduated the old del Gesu's redo the tap tones? Does varnish have a noticeable effect on them? Curtin seems more skeptical of tap-tuning in a passage in Courtnall and Johnson. Did he become more of a believer? Thanks,
  16. another picture from the museum is here: http://kevinleeluthier.com/str...radivarius_Planes.jpg If someone knows how to post, please do so.
  17. Hi Jacob: Try this on for size, guaranteed to not get you bogged down in engineering jargon. Here is a simple example of a resonant vibration. Take a child to the park and let him play on a swing. Give him one push to start swinging. He will swing pack and forth a a particular frequency that is determined by the length of the swing. Now, stand behind him and give him a push each time he comes to a stop on the back swing. What happens? the amplitude of his swinging increases but the frequency does not. (he goes higher and higher and starts to whoop it up!) You are pushing on him at his resonant frequency. Now, quit pushing and what happens? He swings for a number of additional cycles as the amplitude of swinging decreases, finally coming to a stop. Why? because of friction in the hinges at the top of the swing. That friction is the damping force on the vibrations, oscillations or whatever we call his periodic motion . The quantity called "Q" or "Q-Factor" is proportional to the number of cycles required for the swing to come "approximately" to a stop. Now, varnish on the violin may provide damping or it may reduce damping. We are dealing with a composite and the experience of the maker with a given varnish is about all we can rely on. Further, when we use a particular wood/varnish composite, all of its mechanical properties (stiffness, damping, etc.) can be altered by different wood properties, different varnish properties and different amounts of each. You can create identical vibration properties with an untold number of different specifications for the individual components of the composite. Roger Hill
  18. The opinion of an informed violin maker is given here: http://rappasviolins.com/1272....*key*=*session*id*val*
  19. Darren: Great article. Thanks, should solve most of my problems with f holes. Catnip: I'm using a 1/2" mold so should be able to apply one set of linings before removing from mold. Jacob: I have great respect for your experience, but am still of the opinion that graduation is where the action is. Here is why I think that: If I take two strips of spruce, one 2 mm thick and the other 2.3 mm thick, clamp each end of each and apply the same force at the same point on each, the thinner one will deflect 50% more than the thick one. The deflection varies as the inverse cube of the thickness of the beam. (1.15)^3 is about 1.5. The radiated sound power level produced is proportional to the amplitude of vibration times the frequency. At a given frequency, the thicker strip will produce only 2/3 the sound power level of the thin one. That is a huge difference. I have seen comments that the asymmetric graduations of the masters are simply the result of their not being able to control differences of .3 mm in graduation. I doubt they could either, but I believe they could do simple tuning adjustments to an initial graduation to produce a sound they were satisfied with. My conjecture is that they started with a graduation map they liked, built and finished the violin and then put something on the violin surfaces (tea leaves, linseed oil, or whatever) and played single notes to disturb the indicating medium, whatever it may have been. If they didn't have the surface vibration patterns they wanted, they reached through the f holes with specially designed scrapers to reduce thicknesses (very slightly) in a well understood manner until they got the disturbance patterns they wanted. This is what Jack Fry did in the demonstrations of improving violin tones he has given. I think this is as plausible an explanation of the asymmetric graduations of the Cremonese makers as any I have seen. Given that tiny differences in thickness make large differences in radiated SPL, I am looking forward to my own experiments along these lines, beginning with the graduation maps that Fry suggests as a starting point. If it turns out that my conjecture leads nowhere, I'll admit it. Thanks for your willingness to help me.
  20. Well, let me tell you the whole sordid tale. I was trained in physics and my sole interest is in how did the masters get the tones we all know and love. I got interested in making a violin after my wife bought me the book about Sam Zygmuntowicz for my 66th birthday. One of the books referred to extensively in that book is the Heron-Allen book so I bought and read it. Thought "I can do this" and decided that I would build the 1734 del Gesu presented in it. The Heron-Allen book comes with "full size" plans for a 1716 Strad and a 1734 del Gesu, with the del Gesu instructions presented for an inside mold, while the Strad instructions are for an outside mold which seemed to me to be a real pain in the rear way of doing things. As I examined the "full size" plans more carefully I discovered that they would produce a body length of about 13 3/4" for the del Gesu and 13 5/8" for the Strad. Knowing that I had a reprint of the Heron-Allen book I figured that the reprinted plans were simply not done accurately. I then bought posters for the Strad Kruse (if it is good enough for Isaac Stern......), The del Gesu Kreisler and the Strad 1716 and del Gesu 1734 plans from International Luthiers and the Ray Doerr del Gesu King Joseph plans. Now, the IL plans show body lengths of 14 +/- inches. I figured that H. E. Brown had merely copied the Heron-Allen plans since the copyright on the book would have been expired when he made the drawings in 1975. These seemed more or less correct so I started the del Gesu. Now, as I continue studying the plans I discover that the f holes of the IL plans do not match those of the Heron-Allen plans, even adjusting for size and more interestingly that the longitudinal top arch from the 1716 Strad and 1734 del Gesu are identical! The transverse arch shapes are identical if you adjust for width variations between the Strad and del Gesu body outlines. Further to the point, the Ray Doerr plans for the King Joseph state that the outline and f holes are "typical Guarnerius", whatever that is. So, I am convinced that whatever I am making, it is based on drawings that came from somewhere, maybe a buddy of a friend gave them to Heron-Allen or Brown or whomever. I think that all I can end up with is a franken del Gesu but if I use more or less correctly sized f holes that won't matter too much to me. My principal interest lies in the plate graduation to achieve good tone, but whatever I do I don't want to screw it up with a bad varnish application. I have some ideas about grounds I want to try and ideas that the top graduations are where tone quality is achieved. Thus, if I have appropriately sized and placed f holes, I have a good test subject to play with. If I produce a perfectly awful violin that is ok. I will have been entertained and will have learned what not to do. If I produce good ones, I will give them to deserving students. Your suggestions and advice are greatly appreciated. Thanks
  21. Happily at work on my first violin. I am using plans drawn by H. E. Brown in 1975, simply labeled "Joseph Guarnerius model (1734c.)" and published by International Luthiers. The Cozio site lists about a half-dozen 1734 violins by Guarneri del Gesu. Anyone know if this one is among them? I also bought the plastic del Gesu ff hole template from International Luthiers; naturally it doesn't match the plans, nor does it match the ff hole design given for the del Gesu in the Heron-Allen book, nor the FF hole design for the King Joseph drawings by Ray Doerr, nor those of The Strad Kreisler poster. It differs from all of these in that it is about 1/4" shorter than and narrower than any of them. Further, all four violins listed have different ff holes sizes. Any opinions as to actual length and width of del Gesu style ff holes most appropriate for this violin? As an added complication, the International Luthier plans plans do not give rib heights. I chose 31.5 mm tapering to 29.5 mm at the front. Forsee any problems with these heights? Thanks,
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