David Beard

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  1. Violin geometry references

    Hi Ben, I tend to think the off centeredness you're pointing to in the ornaments is the tip of large characteristic or old work. We tend to complete a design beforehand, and work to keep everything as true to that design as possible as we afterward work. I don't think we can successfully apply this same approach to older work. I believe the evidence suggests that the larger scale designs were more in the nature of a general road map or recipe for the work. And the many details were left less than completely defined until it came time to actually carry them out. There is also I think reason to see proportions and geometry used while carrying out work as merely practical, and sometimes differing from the proportions of the larger plan. Thus, on the large scale perhaps an area is divided in three. But in executing the work, perhaps for some reason there is cause to make the center portion actually a bit smaller, so the work might be executed as 5:4:5 for example, even though the general impression and larger idea is still 1:1:1. So a difference between a more or less predetermined 'guide plan', with geometry and ratios, and the actual executed geometry an ratios used to carry out the work. And, it seems from the evidence of their work, the workers in these old styles had more concern for relating every part to others be taking ratios from the actual work as it proceeds, rather than correcting back to any original planned size for various parts of a whole. And things like locations and centers were likely to be relative the current stage of work, and perhaps some related part, but not to any accurate calculation to a consistent center, or framework of location maintained from beginning to end of work in a modern way. An important related issue is that the proportions and geometry used in executing work seem to entirely about tradition and practicality. The notion of designing in certain preferred or meaningful ratios is absent in the actual work, though it might at times play a role in the larger 'guiding plan' or recipe. I think modern use of ratios confuses this point, and tends to drive toward using preferred ratios, or meaningful ratios. I can't see evidence of that in the actual works. It all seems entirely about tradition and practicality. Sorry this is rambling.
  2. Violin geometry references

    No. A sector is a tool for producing proportions with dividers. It apparently arose in the 1500s and faded out by the 1800s or so. Very hand in the workshop! By Hand and Eye website reviving the same sort of ideas we're discussing, but in the context of cabinetry and general woodworking practice historically.
  3. Violin geometry references

    Hi Francois, What a nice simple way to place an element proportionally between two other elements! Glad to hear this is a documented historical method. For my own work, I started off just walking distances with dividers, or using proportional dividers to get an initial size to walk out with the dividers. But recently, I've been making friends with 'sectors'. Again, this is apparently an historically common method of getting proportions with dividers. It has recently begun to be used again with some cabinet makers. Sectors.
  4. Violin geometry references

    Wish I'd had a little more free time these last few days, lots of interesting stuff coming out in this thread. I had some time today and yesterday, so took a look at Ben's example instrument. Now I'm just about out of time again, so will write up what I have, though not complete. First, note the instrument is rather asymmetric, and lacks a simple clear center line. Consider also how the lengths on the upper bass side are all longer than their counterparts on the treble side. It's possible that this instrument is not square to the camera. This is also suggested by the the pole for the tail gut appearing to by to one side of the center line. If the instrument's bass side is significantly closer to the camera, ratios between horizontal and vertical elements will not be well represented. But still, we can be certain from the photo the instrument is quite asymmetric. Also, from the photo alone, we can't be certain if the bass and treble side might be flipped around. When I analyze an instrument, I'm more interested in the geometry used to execute the actual work, rather than the ideal design concept that might stand behind that. So sort of reverse of Francois' approach. Since this is a new shape for my studies, a first step is to understand the geometry of the executed shape -- embracing the asymmetries. To help me find my way into this analysis, I've used the presumed concentricness of arcs for the outer edge and the double lines of purfling to help me locate the centers for the various arc segments. And I've used the lines between the joins and centers to help clarify the analysis as I worked. The geometry present in the executed shape: Note there is a stretch in upper shoulder of the upper bass side bout that is 'out of circle'. This section is 'smooth', but not circle geometry. This kind of thing appears only infrequently in old classical instruments. If the shapes were in fact based on bent splines, such things would happen frequently, indeed almost all the time. While you can easily bend splines to follow a shape that is already made from circle geometry, it isn't easy to produce circle geometry from nothing by bending splines. Bent splines won't automatically take circle geometry shapes unless you knowingly pushing them into it. That's child's play if you're tracing an existing shape, but difficult starting with a blank slate. And in the sound holes: The construction for the soundholes is simple compared to a violin's. The four eyes of the soundholes appear to be started with drilled or bored holes, like in violins. But all four are of equal size. Again in a feature common with violins, the first curves come from the eyes are double the radius of the eyes. The stems are then constructed from nearly concentric arcs. Once I have some sense of the geometry constructing the shape, I look to see what ratios might stand behind these shapes as the worker carried them out. In this case, the construction of the upper and lower bout shapes are several steps removed from a violin, but still there are parallels. There appear to be vesici behind these curves also: Here I've marked in the 3::1::3 vesici of the upper bout and the 2::1::2 vesici of the lower bout which appear as part of the shape. Note that drawing large circles through the upper and lower bouts gives some sort of sense about the bout shapes, but does not actually match the shapes as carried out. Still, this large circle might be part of the background concept for the shape? What further relationships are present? In the soundholes, we have some of the ratios Francois pointed out. Note that the lower eye horizontal position is calculation on the treble side, but by copying distance to the edge on the bass side. This appears occasionally in Cremona violin work, especially in the Amati family. And continuing to look at the body and outline: Here we see several further relationships. For one, the main curve for the center bout, and the curve up into the neck are both based on the vesici circles from the upper bout. And then the four corner circles are all pretty much equal to each other, and based on 1/3 the main cBout radius. We find the same 5 to 6 ratio that others saw between the upper and lower bouts. And identify a likely ratio of 3::2 between the outer edge width of the upper bout, and the inner purfling width of the center bout. With violins, a 2::3 ratio between the center bout and the upper bout was the most common choice through the first several generations of Cremona making. Ok. I'm out of time. More images from my analysis: Hard to know what body length is on this shape. What I've shown is just one candidate way to look. I'd need to see many similar instruments to gain confidence about what's actually going on here. The possibility shown is interesting because it possibly leads to positive ways to construction the shape from scratch. But this analysis from one instrument can only be very hypothetical. Lastly, I want to show the separation of ratios in some common ranges seen in violin work. I also added an image showing the Fibonacci compared to the golden ratio. I suggest, that for practical work the ratio 5::8 is almost always a fine approximation to give the visual effect of the golden ratio. And as a practical matter, workers who were continually using simple integer ratios for everything else are very likely to keep things simple and consistent by using 5::8 in the cases that to a modern eye look like phi.
  5. Violin geometry references

  6. Violin geometry references

    I tend to see the use of ratios in instruments and designs much more prosaically. I would have been happy to observe some sort of ideas behind the ratios, but after surveying ratio use in many classical instruments, it looks very practically and traditionally motivated (to me). So, the 2:1 ratio in the lute drawing I would be willing to see as simply convenient in the drawing. It doesn't necessarily need to have any more weighty meaning than that. Consider that today, some woodworkers like to use a measurement on everything. It can amount to a habit of working. Want to make up a design for a shelve from scratch. Ok. I need it to be about so big, well that's close to 18", I'll make it 18". Not exactly a process deeply loaded with meaning, just habit. In the same way, executing free designs with compass and rule and simple ratios for sizing need be seen as no more than habit, and tradition. The ratios framing the bodies of violin family instruments provide illustration. Traditionally, all such instruments from classical Cremona show ratios of 2::3, 3::5, 4::7, or 5::9. Now we could try to read meaning into these ratios. But the also fit a very simple rule of thumb: "double the width less a unit". In this sense we could see them as lengths the are just short of 1::2, or a musical octave. Meaningful, or just habit? Regardless, it's what they did.
  7. Violin geometry references

    Sadly, no. I'm limited to English, and what I can make out with painful use of google translate. So I always hesitate to quote Da Vinci, since my sources are generally dubious English translations, and collection of excerpts. I've read about is game in a book that proported to gather together Da Vinci's comments on learning art practices. In regard to his extensive references to simple integer ratios, I have checked these out in facsimiles of his notebooks. And I've struggled with google translate to confirm to my satisfaction that the gist of the English translations I've read is reliable. Wish I had a better answer.
  8. violin linings

    I don't know. Guess I'm chicken. I would only ever use willow or spruce, because those are the only ones I know great instruments have been built with. And there is no reason not to use these. For a violin maker, availability of spruce can't be an issue. I don't think it matters much between those two, but I've no idea how far you can stray without negative result, or at least at least a change of character. The woods chosen classically are at least four things: light, elastic, strong, soft. I would not use a hard or brittle wood, or a heavy one. Even with light woods I would want to make sure they are very elastic also.
  9. Violin geometry references

    Lets not get lost in conflicts over word usage. Words are often reappropriated for particular purpose, and often have distinct usage in different languages. I'm using geometry, construction, ratio, and proportion in ways that I believe are clear enough to be understood. For me, that's enough. Even though both ratio and proportion historically have been given more specific meanings, I'm using both interchangeably to refer loosely to comparing things by simple integer counts of a shared unit. Please allow this casual usage. The word geometry has been used in so many ways. It doesn't just mean 'earth measurement' anymore. My particular usage --to refer to line and compass constructions, with or without specific ratios or measures -- is close to the usage in Euclid. So, if you will, please be lenient and just roll with it? Yes, for the artist especially, portions often reference surfaces. Or more completely, they reference 2-demensional projects of a surface in 3 dimensions onto a plane which is normal to the viewer. Artists, and builders and designers more generally, tend to favor using proportions on based on these flat projects, without referencing the complications involved. Indeed, most of the 'proportions' or ratios mentioned by the likes of Vetruvius and Da Vinci don't if you measure lengths along the 3 dimensional surfaces instead of along the flat projections of those surfaces. For violin making, some features fully involve these complications, and others don't so much. The curves of the soundholes lie on a surface which is curved in 3 dimensions. So discussion of proportions will tend to be about the project of these shapes. However, there are ambiguities because work might be done directly on the curved surface, or on a flat surface and then transferred. Neither of these will exactly correspond to the projection onto a flat plane. The curves of the volute and head present less complication. Even though the widths of the head change in complex ways, the arc shapes of curves correspond to cylinders that are square to the projected version of the shape, so there is no distortion in the design shape in this case. And this is were the casual use of the word 'outline' is handy. Even though the volute is a complicated 3 dimensional shape, it is very substantially governed by the projected outer boundaries of its shape. And this is what a mean using the convenient word 'outline'. The plates present yet another specific case. Of course, the most interesting thing is the arching. Again, we have a 3 dimensional surface. But the plates are also bound by an outer edge, or 'outline'. The outline lies essentially in one plane, which makes it exactly equivalent to its normal projection. 'Geometry' gives a simple word to refer to the pattern of connecting arcs that give the right kind of shape. Ratio or proportion gives easy reference to the numeric ratios behind the geometry construction that give the exact shapes seen in particular instruments. The arching is indeed more complicated. And it's one of the few spots were freehand and smoothing (read bent splines) plays a significant role. Nevertheless, you can see that a few bounds or controls to free work run through classical arching. First, the channeling has a boundary in relation to the out edge. The width of the channel boundaries are generally set from simple ratios at the widest part of the upper and lower bouts, and the narrowest of the center bout. At these locations, the channel width is generally a simple ratio of the width from edge to center, for example 1/4, 1/6, 1/8. This width is then carried at a constant width through the bout, but free hand joined through the corners. So instruments, of cellos for example, present a different width at the top or bottom block which smoothly transitions to the main channel width for the bout. The execution of the channels within these boundaries are relatively varied in classical work. In earlier generations, the channel bottom tends to occur midway through the channel, with something approaching symmetrical curvature on either side. But in later generations we see a tendency for the channel bottom to push toward the outer edge. Since the channel shape must smoothly connect to the central arching, this forces a flatter curvature coming from the channel bottom toward the central arching. So we have three important boundary curves that help govern the arching. First is the plate outline, whose design is well determined by geometry and proportion. Second we have the channel boundary that is partially determined by ratio, and strongly relates to the outline. And last we have the channel bottom which might have been set by rule for some makers, but seems to have been set in a free relation to outline and channel boundary in later work. The last boundary governing the plate surface shape is the long arch running along the plates center line. This long arch is significantly different for the back and top plates, with the top plate's long arch having a long nearly flat portion running above and below the bridge toward the corner lines. The back in contrast tends to have only a very short near flat portion directly above the bridge line. Perhaps there are rules behind the long arc shape that I just haven't found. But it seems that this very important shape may have been essentially a production of smooth freehand and tradition. I find using the boat builder's technique of setting a few of the elevations along a division of the length of the arch to be helpful. For me, a divide the length of the plate into ninths and decide where along this the flat portions will end, and where the height will fall half way in its path to the channel boundary. But working a plate's long arch remains substantially freehand. Once the long arch is set, we have now four boundaries to govern the plate arching: the outline, the channel boundary, the channel bottom, and the long center line arch of the plate. This in itself would not be enough to well govern the plate arching, except that we can see that we can observe the central portion of classical plate arching conform to a simple workshop friendly rule. This only applies to the cross arching of the central arching (convex viewed from outside) around the center line. We can note that in the cross arching, from the center line to the edge of the channel boundary the plate falls a certain distance. The plate falls from its maximum of any particular cross arch at the center line, down to the channel boundary (which is the height of the work edge as you make the plate). The simple rule is that 1/2 of this fall is reached 2/3 the way from the center line to the channel boundary. This rule is actually recursive, and completely determines the cross arching from the center line, out 2/3 the way to the channel boundary. The recursive version of the rule is that for any on the cross arch between channel boundary and the maximum of the cross arch at the center line, there is a distance from the point to the center line which we will call the 'run', and there is a height difference between the cross arch height at that point and its maximum, which we will call the fall, and: 1/2 the fall occurs in 2/3 the run. This easy to apply workshop rule completely determines the curve of the cross arching from the center line to 2/3 the way out to the channel boundary. But you are still free to place the channel bottom and carve the curve from channel bottom to edge however you will. And we see most of the differences in classical makers arching styles arising from this liberty. But after carving the channel curve from channel bottom to edge, and after carving the convex center 2/3 of the cross arch by rule, the channel boundary and the need for a smooth curve leave you almost no liberty in completing the cross arching. So we see that in classical arching there is some liberty in establishing the channel, and the long center line arch of a plate, but after that the process is well determined.
  10. Violin geometry references

    Yes!! And Da Vinci even recommends that artist apprenticed kids should choose games that cultivate seeing ratios for their off hours amusement!
  11. violin linings

    Other than in some electric guitars, I'm not aware of paulownia being favored for acoustic properties? Light is not the only concern in acoustic wood choice, so is the return of energy -- elasticity. Is it a talkative wood when you run your finger nails on it?? Anyway, linings don't seem to be a super sensitive choice. Obviously both willow and spruce have been used in very successful instruments. For myself, I make my blocks and linings of red willow -- just to follow the main Cremona tradition. But I don't think of it's necessarily very important.
  12. Downforce Experiment

    You play a lot Martin. For me, the strongest effect I've noticed as a player is that if the back of the bridge isn't basically perpendicular to the plate I'll sometimes note a reduction of power in tone and directness of articulation. In that sense, a straight up an down back of bridge seems best to me. As you suggest Martin, setup traditions embrace a vast amount of collective learning, that in most cases is like to represent a more complete picture of playing needs than a narrow line of scientific reasoning is likely to embrace.
  13. Beady eyes... extreme version of fisheye

    I haven't experimented with it, but isn't ox gall a traditional wetting agent for artists? Don't know if there might be some way use it in your case.
  14. Violin geometry references

    Hi Ben, I keep puzzling on how this historical method might have contributed to the success of classical making. It isn't obvious how it might have contributed, other than as a basic aesthetic idea. The main thing I keep coming back to kind of connects to that very unpopular MIT study that says their is an aspect of a kind of 'evolution' running through classical making. In a way, I can see this classical method of design by choosing proportions and constructions within limited ranges of traditional options as a mechanism that might have help violin makers learn what worked and what didn't. The set of design choices made in a particular instrument can be seen acting like it's DNA. It's a recipe that substantially, but not entirely determines the final outcome. And it's a recipe that can be repeated entirely, or with fine grain variations. I suspect that this was a powerful benefit to classical making. Something that more or less accidentally boosted their communal learning. It's a thought?
  15. Violin geometry references

    So you're suggesting that maybe midway through his career, Strad didn't have to keep doing what worked for the first decades of his work? Some of them never made 500 instruments. Yet they all show a freedom in making design variations without loosing the integrity or character of classical work, even at the beginnings of their careers. Yes. I agree that people can be amazingly skilled. But even if some of them at times work freehand, still we find the shapes they made fall into a special and very limited kind of shape (which is meaningful considering the vastly greater number of shapes you can make freehand that don't fit this special group). All these classical shapes can be very closely replicated by using only one line or arc per every change of curvature (or direction) of the design shape. This makes the classical instrument shapes very special within the range of all possible shapes. And, whether carried out directly with compass construction, or drawn with a smoothing assist tool like a bent spline, or even drawn by a talented freehand, it means that the idea behind the shapes is simple compass and rule geometry. Similarly, the fit to simple proportions in these constructions and shapes implies that proportions were the idea, regardless the method of execution. Though, for all but the most talented, the easiest methods to achieve these are either to directly put the proportions into your work with drawing tools (dividers), or to copy your work from someone else who did this work for you. So sure, a Da Vinci or a Strad wouldn't always need tools to produce the result, but their works still show these ideas behind the shapes.