Thursday, October 27, 2011

Book Review: Japanese Cabinetmaking (II)

 In last week's post I described some of the background to Carol A.B. Link's work from 1975, a doctoral thesis entitled Japanese Cabinetmaking: a Dynamic System of Decisions and Interactions in a Technical Context.  In this post I'd like to take a look the material which comprised the next portion of the text. This is a distillation of Link's experience living in the home of the Tsuzuki family, where a father and son carried on the family tradition of high class cabinetmaking.

'Cabinetmaking', as an English word, while it used to refer mostly to the work performed at the bench by joiners, now is applied it would seem to just about any woodworking activity in which storage boxes are made. If you asked most English speakers what a 'joiner' was, I'd wager 90% would not know, and of those who ventured a guess most would think it has something to do with someone who likes to join clubs or groups.  Or think it had something to do with a certain tool for slotting wood for the insertion of fiberboard/compressed wood 'biscuits'...

'Cabinetmaking' has, in these modern times, become almost as meaningless an expression as 'high quality' or 'craftsmanship' - just another piece of advertising hyperbole. Speaking of which, the latest word which seems to have lost all meaning must be 'artisan', now plastered on some 800 different industrially-produced products according to a data research group called Datamonitor. Someone's even started blogging about it. And further speaking of which, USA Today recently had an article on that very topic.

'Cabinetmaking', in the context of Link's work, is at best a rather loose translation of a certain class of woodwork done in Japan and may be entirely misleading unless the term is more closely defined. Link explains some of the nuances:

"In Japan joiners are placed in separate categories depending upon their specialty. The tansuya-san specializes in producing large tansu. The smaller and more varied products are made by a different specialist, the sashimono-shi. Although both tansuya-san and sashimono-shi are joiners, the sashimono-shi is regarded with deference by connoisseurs in general and the tansuya-san in particular. This is because sashimono-shi exercise their skills over an enormous range of products, have a very high degree of versatility and display great mastery of their craft. Sashimono-shi are now rare in Japan. One of the best, Mr. Yasuku Tsuzuki, lives in Kusakabe. He is a bijutsu-sashimono-shi. Bijutsu means "fine arts". The whole term can be translated as a joiner, whose level of skill is so perfected, that the cabinets produced are considered to be works of fine art just like paintings or sculpture. At the present time, there are only four or five bijutsu-sashimono-shi in the whole Kanto plain and they are all older men ranging in age from 68 to 96."

Link was fortunate to have an opportunity to spend a full year living with and observing the behavior and work patterns of a master craftsman, as they are rather thin on the ground, even more so today.

Link spends some time describing the Tsuzuki family structure and their members, along with their family tree. Yusuku, the master, began his apprenticeship at age 12, finishing that phase at age 21. She mentions that of his sons only Yukio, now 48, is carrying on the family's woodworking tradition. Yukio's daughter commutes to a job in Tōkyō for the Sumitomo company, son Tomoyuki is 19 and a college student specializing in electronics. Younger son Hideyuki is 13 and seems mostly interested in baseball.

The Tsuzuki shop is small and appended to the house, and shop business is the family's bread and butter supply - I mean rice and beans I guess! I felt some kinship with the Tsuzuki family, when Link notes that although they have plenty of orders and are always busy,

"Unfortunately  they do not really receive adequate compensation for their labors although their prices for their products seem very high to a purchaser. The simple fact of the matter is that ojiisan [Yususku] and Yukio work almost continuously in order to support themselves and their family. It is a sad situation but in present day Japan, there is no immediate solution for it."

All too familiar. When you hear that familiar refrain of, 'do what you love and the money will follow' - take it with a grain of salt. Sometimes money doesn't follow, or even appear with any regularity, but at least one can, hopefully, derive some satisfaction from the work itself. As Link notes later,

"Other major benefits are work satisfaction and ultimate justification for one's own life. As ojiisan and Yukio say, "you have a really good feeling (kimochi ga yoi) when you can and do make things yourself", and "there is nothing like the satisfaction you get when everything fits perfectly and is beautiful."

As Link subsequently remarks, and this has been amplified by many other writers, and in pretty much any account of the traditional crafts in Japan you might read in the past 30 years,

 "Evidently the Japanese youth do not seem to appreciate these sorts of benefits and, since the post war period, ojiisan has not had any live-in apprentices save for his son. They ultimately abandoned the hope of having new apprentices and razed half of their building seven years ago."

I'm not sure if it is entirely the case across Japan that such glamorous work as that of shashimono-shi suffers from a lack of apprentices, but certainly many of the other trades, especially what might be called the ancillary trades (makers of tools, sawyers, etc.) are experiencing a decline in numbers, a trend that has continued since the post war period. I dare say the same thing is occurring in the West - few young people choose a career in the trades, it is more likely that getting into a trade is as much a default or happenstance occurrence for those who couldn't get into college (or didn't want to go to college for whatever reason) and can afford to take out student loans to obtain a trade ticket. And given the nature of many trades jobs here, who can blame them? The work is generally dull, repetitive, occasionally hazardous, not esteemed by the society as a whole, and not tending to encourage artistry or virtuosity.

An interesting section of Link's work relates to the concept of the shoku-nin (職人), a term generally translated variously as workman, mechanic, or craftsman. Yusuku and his son Yukio see themselves as part of a select group of craftspeople, an 'in-group' which comprises only those who are joiners, lacquerers, fan makers and so forth. In their eyes, carpenters, mechanics and other tradespeople are not true shoku-nin. I find that interesting, and it reminds me of similar attitudes in certain trades in the West - those who would call themselves, say, a shipwright, or 'stair-builder' might have a very specific idea of what that work comprises and who qualifies. Like many who have spent years acquiring manual skills and a deep knowledge of their craft, the Tsuzukis are proud of what they do:

"By the Tsuzukis' standards, drawers must be perfectly flush with each other, must slide easily with no strain and they must not, under any circumstances, rattle. A rattling, loose drawer is anathema to ojiisan and Yukio. The first drawers were slipped into the chest with some trepidation, but their ultimate perfect fit brought an absolutely beatific smile of satisfaction to ojiisan's face.
    Those unacquainted with this work do not really appreciate this feature of drawers. The average person presumes only that a drawer should slide and the degree of perfection of sliding elicits a 'so what' reaction. Connoisseurs, cabinetmakers, their shokunin colleagues and dealers seek out this feature and have a regard for the care and dexterity that goes into perfect drawers that surpasses mere admiration. It is a sensitive awareness and esteem for the skill of the maker and the devotion that he has shown to his work to produce a superb product. This is based on the knowledge that one cut of the plane too many will ruin the job beyond repair."

That 'so what' reaction when demonstrating a nuance of a piece to a client or friend is, I'm sure, familiar to any artisan or detail freak. I think one of the weakest aspects, in terms of the business of being an artisan in this modern world, is clearly communicating the subtleties of the craft to the buying public. Most of us suck at that aspect of our work frankly. Take a look at the car or stereo industry, where they have managed somehow to make many of their customers acutely aware of the various technical and performance details which separate one brand from another. You'll hear people, product salespeople included, spouting such phrases as 'twin piston, vented rotors', 'multi-point injection', 'Corinthian leather', or '5 watt RMS power' without having the slightest idea in many cases what those terms really mean. If it sounds cool and is described in breathless excitement, or with the aid of T & A, then it generally seems to sell.

The Tsuzukis have a bit of an easier time with their marketing, partly on account of a buying public in Japan some ways more attuned to the virtues of handmade wooden products, and partly due to the way their products are distributed:

"One other way that the Tsuzukis receive a great deal of satisfaction and pride from their work is grounded in their marketing system. Their products are sold at two shops in Kusakabe, Saikiri and the Taikei Furniture shop, which carry only top quality merchandise. The other main retail outlet is the Mitsukoshi Department Store (a few other major department stores also sell their products sporadically). Mitsukoshi celebrated its 300th anniversary in 1973. Throughout these 300 years, Mitsukoshi has developed and maintained a reputation for carrying only the best products, especially folk art and craft items. In addition to commissioning works from the finest craftsmen, the people at Mitsukoshi usually inspect the merchandise they receive before accepting it. Ojiisan and Yukio are deservedly proud that their products are not inspected. They are assumed to be flawless and are taken from the loading dock to the sales floor without further ado.
     These features of self-evaluation by constant comparison of current efforts with past; critical appraisal of the work of others; unquestioning acceptance of products by all dealers serve to reinforce ojiisan's and Yukio's standards of workmanship. They also provide justification for their pride in status as shokinin."

I actually find it hard to imagine such a store here in the US, where Walmart rules the strip. Now, there are galleries dotted about here and there which showcase high end furniture, among other things, but in my experience and estimation those doing the selling often have little knowledge of the details and nuances which make for great furniture, and are left, like many salespeople, mouthing inaccuracies and generalities about the pieces. Fine furniture has always seemed to be considered on the fringe of the 'fine arts' in the West, for whatever reason, and thus it is more poorly understood, and less avidly promoted. Galleries selling antiques are sometimes an exception to this phenomenon. And maybe those generalities are enough sometimes, at least in terms of selling the odd piece, given that most of what a customer reacts to - by conditioning - are the surface and form qualities of a thing, but it is a definite shortcoming. The Tsuzukis are lucky to have the infrastructure, culturally and otherwise, in place which supports what they do to some extent. I gather though, that this is changing for the worse in Japan in recent years.

Interestingly, bound up in the Tsuzuki's self-identification as shokinin is a sense of superiority:

"They have a slightly disdainful attitude towards carpenters and the like, whom they consider to be engaged in relatively unskilled labor.
   Moreover they are rather contemptuous of salary men ['suits']. They feel the salary man is tightly bound to a corporate structure where he has no ability to enjoy any personal freedom and, more unfortunately, can obtain no gratification from his labors."

While their contempt and disdain for others is unfortunate in some ways, I wonder what they would think of the typical carpenter here, with, if I might paint a picture, his Ford F150, tool racks, boom box, travel mug, chop saw, Fat Max and nailer? I think I'll refrain from speculation.

I thought that Link's mention of the career path of the Tusuzuki's being more than just a day job, but a Way of life, a michi:

"Michi is a simple Japanese word for a very complex concept. This term has many translations, the most mundane of which is a road. It also means journey, a way of making a living, a means, a duty, a moral doctrine, and art, a specialty, a course, etc. In compound terms the range of meaning is even wider. The negative form michinaranu means illicit, immoral, improper, in other words directionless and without a goal.
    On a broad level michi means the path that a person takes through life. Each person has their own michi. some choose their own. Ojiisan had his chosen for him. The life and work of a sashimono-shi has become his michi. He not only works as a sashimono-shi, but he IS a sashimono-shi. He has gained knowledge of himself and harmony with the world in the same way a Zen monk gains knowledge and enlightenment by the Zen michi. He is a happy man. His son, Yukio, who had the sashimono-shi michi chosen for him by ojiisan, is also content in his michi. To understand this is to understand their way of life and work."

And that description of the Way, my friends, is the reason behind the name of this blog.

Link concludes the section with a quote from Carlos Casteneda's work A Separate Reality, a work I have fond memories of reading in my twenties:

"You should know by now that a man of knowledge lives by acting, not by thinking about acting, nor by thinking about what he will think about when he has finished acting. A man of knowledge chooses a path with heart and follows it; and then he looks and rejoices and laughs..."

If he's not starving to death that is. It's hard not to feel inspired though by those who have such clarity about their direction in life. I spent many years not knowing what my own direction was and certainly don't look back at those times with delight. I feel empathy for those who struggle to find purpose in their work, to find their 'calling', and can tell you that when one finds the right path for oneself, it is truly a blessing.

I guess I'll have more to say in the next part of this review. Thanks for coming by the Carpentry Way.

Monday, October 17, 2011

Book Review: Japanese Cabinetmaking

A few years ago a reader brought to my attention a clipping from an old Fine Woodworking magazine (Issue #57, March/April 1986, p. 106), featuring a review of a book on Japanese Cabinetmaking by John Willey in Maine. The author of the book in question is Carol A.B. Link, and the full title of her work is: Japanese Cabinetmaking: a Dynamic System of Decisions and Interactions in a Technical Context. Don't let the title put you off - it's an interesting and highly readable work. And a very hard bit of paperwork to obtain. You see, this 'book' is actually Link's PhD dissertation in cultural anthropology, undertaken at the University of Illinois in 1975. While the material is available on microfilm at the university, and I'm sure there is at least one bound copy in the stacks, in general, paper versions are somewhat hard to come by. I managed to make contact with Link's academic adviser, Dr. Keller,  who remembered Link and her thesis and said he would help out if my inquiries in other directions did not prove fruitful. In the end, I got nowhere with my attempts to pry a copy of the dissertation out of the University, and contacted Dr. Keller again. Then a stroke of good luck - his wife was clearing off some bookshelves and came across a single copy of the dissertation, which he then sent to me for free! So, that was lucky.

Link studied cultural anthropology and the method she employed in tackling the subject matter was to go to Japan and live/work in a cabinetmaker's household (that of the Tsuzuki family), and write about her experience. That is to say, she chose to write about a lived experience rather than simply collate information from other written sources, a problem which, in my view, plagues many scholarly analyses of material culture and technology. If you don't use tools yourself, then the difference between an axe and an adze maybe obscured or considered irrelevant, however to a craftsperson who uses such tools, the differences are obvious and important.

Link spends the first two chapters of her work discussing the history of anthropological examinations of material culture and technology and finds them coming up short for the most part:

"Most people admit that technology is vital to man's survival. Some say that technology has made man what he it. It is currently fashionable to berate technology as the despoiler of all that is good, true and beautiful in human life. These admissions, concerns and criticisms indicate the importance of technology to man.

Despite this importance, one wonders why anthropologists are notable for a lack of interest in or cursory treatment of the subject."

I have found that to be true, and many academic treatises involving crafts and trades and their products make humorous errors at times in their descriptions of tools and their uses. Refer back to my review of Asian Furniture for but one example out of many.

Chapters 3 and 4 of Link's work take up the thorny issues of coming to satisfactory definition of what 'material culture' and technology' mean, and the establishment of a philosophical foundation for the study of technology as a system of behavior. Chapter 5 delves into the performance of technical behavior, a 'dynamic system of decisions and interactions':

"Technology, as a system of behavior, has features which allow it to be analyzed and understood almost as if it were communication. It is not precisely analogous to communication since it is an asymmetrical system. The difference hinges on who is communicating with whom or what. In everyday life people communicate with each other via language to convey information but in technical behavior, an actor communicates with materials via the body and implements (if any are used) in order to produce something. The actor does not receive a message encoded in language but he does receive feedback information (such as temperature) from the materials that he responds to in the same way one responds to sentences in a conversation. 

This is a dynamic process in that, at every moment in time, every feature of this system has been changed by, and is changing, every other feature in the system. In this way, technique is the knowledge that informs the activity of workmanship and vice-versa."

Link's discussion of workmanship is particularly interesting, given the ground-breaking done on this topic by David Pye, in his seminal 1968 work The Nature and Art of Workmanship. Link quotes Pye quite often, though not always in agreement with him. These are questions I continually mull over myself, puzzling the connections between culture and the material objects it produces, and the approach to workmanship bound up in the choices made. Why, for instance, is North American culture so preoccupied with producing mountains of crap, and almost nothing of lasting value for future generations to appreciate? Don't we care about our kids, and their kids? Why, despite the fabulous quantities and qualities of materials and products available here, is the quality of work done upon them often so abysmal, and how is it that cheap prices have come to trump almost every other concern in consumer's minds? Those questions are for another post, another time, but it is good that Link spends some effort in addressing ideas about workmanship and crafting of objects early on in her thesis. Her conclusion in regards to technique and knowledge in the crafting of material object is much as follows:

" can see that knowledge of techniques is much more than what can simply be written down. In view of this, it is time to radically alter our ideas about the nature of techniques. Pye came close to the mark when he stated that, "Technique is the knowledge which informs the activity of workmanship."(1968:22) and, as amended (p.28), the activity of workmanship informs the knowledge too. When approached this way, technique is not simply how-to or even the knowledge of how-to. It becomes a communications system wherein knowledge of techniques is expressed in physical activity and the results of the activity along with the activity itself inform the actor of what he is doing, how well he is doing it, and, most important of all, when to stop doing it. Thus, the exercise of a technique stimulates, indeed forces, the actor to decide what his next act will be. The next act, of course, is based on knowledge of techniques and so this becomes a continuous, dynamic process of technical behavior." (p.46)

Hence the sub-title of the work, Japanese Cabinetmaking: a Dynamic System of Decisions and Interactions in a Technical Context. While much of what she mentions above is fairly obvious to a craftsperson, though perhaps rarely stated so clearly, I think for those outside the work of those who make objects with their hands this is helpful clarification. Knowing where to stop - where the line of 'perfection' (or, as is more commonly expressed, 'good enough' - I term I personally detest) is and where it is crossed, often thereby producing a negative outcome in certain respects. That goes for both design and making of course. It's not simply a paint-by-numbers affair as some might assume who have not been engaged in a crafting process. Particularly with solid woodworking, where the medium can be almost capricious at times in moving with every saw cut or cracking, or splitting in unpredictable ways, or absorbing finished unevenly, or defying attempts to employ glue, etc. Like I've said before, this is a process akin to corralling sheep, where the best outcome is to get them all into the pen - you can pretty much forget about having them stand in precise rows. You have to shift on the fly and make continual course corrections and adjustments, being aware of your material and the end result and problem solving to an extent as you follow your plan. Baking bread can be like that too. Blacksmithing and many other crafts are likewise - an iterative process.

Later on in the fifth chapter, Link delves into the issue of standards of workmanship, taking cues again from Pye's work, where he mentions that what a craftsman wants to do is, "not to express the properties of materials [which are objective and measurable], but to express their qualities [which are subjective]." While I don't totally agree with this contention myself, it is a good starting point for discussion. Link notes,

"Standards of workmanship are embedded in a culture. Accordingly, they are part of the cultural context and personal knowledge of the actor since they are standards that he has assimilated into himself. Since they are culturally defined, they are shared to a greater or less degree by all members of that culture. For instance, everyone knows that plastered walls should be flat, smooth and perfectly square. But the plasterer's personal knowledge of standards is more elaborate than that of the layman. The plasterer's standards of 'flatness' may cause him to feel intensely irritated about a slight ripple in the surface of the plaster that would go unnoticed by the average person. Furthermore, the question arises as to whether or not any two plasterers would agree on the flatness of any given wall. It is unlikely, but why is this so?

...each person has their own set of standards that they have acquired by experiencing each performance. These have become their personal knowledge. since each person's experiences are intrinsically different, ultimately their knowledge is different. Consequently, discrepancies in judgment that occur between laymen, dilletantes (sic), and connoisseurs are a result of the amount and refinement of their own personal knowledge of a set of standards. The more refined these standards are, the more critical and demanding of the object and ultimately its maker the appraisals will be." (p. 53~4)

Ah, the good old days, the 1970's, when there were still standards of excellence to be observed and understood in the building arts. I do jest, but only a little I'm afraid.  A lot of what I've observed, especially in recent years, is that not only do clients have little to no idea of what constitutes good workmanship, but the people doing the work, whether it be framing walls, applying sheetrock, plaster, casing stairwells, hanging acoustical ceiling etc., seem to have little or no internalized standard of what is good work and what is not. Or if they do have such a standard, many would appear to not give a damn about such things, that they know even if the work is poor they still get paid and the client doesn't notice so.... The problem here is that many workers in the trades do not seem to have assimilated into themselves, as Link put it, high standards of work. Possibly because, in North America at least, examples of high standards of workmanship are seldom encountered in daily life except in certain mass-produced items, like Apple Computers, or BMW sedans, say, or food in certain restaurants where the chef is highly trained and passionate about what they do.

The last job I was working on for another contractor was a place to hear the usual comments of, 'oh, from 20' away nobody will notice that', etc.. The last time, upon hearing it in a conversation with a co-worker, I turned to him and said, "I don't care what someone else may or may not notice. How would you do the work if this was your own house? Would it matter to you then?" My coworker had nothing further to say, curiously enough, but I am left wondering where/how the internal guidance system, the morality, dare I say it, of doing the right thing, doing a solid careful job, even though no one else may notice or care, became disconnected for many who who pick up a hammer and tool apron -or other tools for that matter.

Link sums up her look at standards of workmanship with the following contention:

"In regard to technical behavior, there is always a difference in excellence judged to be skilled or unskilled workmanship. As far as the connoisseur goes, skill is judged on the basis of the output of the project. As far as judgment of artisans by their peers goes, each is judged as a member of a class. As far as the judgment of artisans by themselves goes, each is skillful to the degree which they achieve their self-imposed standards. Here the actor, the artisan, is his own critic. Consequently, actors who have very refined standards have become connoisseurs, and as long as they are physically able to carry on their behavior in conformance with these standards, they are good, skilled artisans; experts and masters of their trade."

In the end, the only really qualified judge of an artisan's work is the artisan himself, or one with equivalent technical mastery and understanding of the medium. Others may like or dislike the work for various reasons, aesthetic or philosophical, but ultimately the buck stops with the maker. If that person does not hold out high standards for themselves or becomes content with where they are in terms of the quality of what they make, then their continued ascension in skill and workmanship is stopped. To progress, the idea must always be, not yet, not yet.

In the next part of this review, I will turn to Link's experiences and observations during her time living and working with the Tsuzuki family of sashimono-shi, in Kusakabe City. I hope you'll stay tuned and thanks for dropping by today.

Wednesday, October 12, 2011

Following Mazerolle: Pavillion Carré Rampant Établi

Another in a series looking at French carpentry drawing from the 19th century masterwork by Louis Mazerolle, Traité Théorique Et Pratique De Charpente. Having crawled my way through the dormers in the book, I decided to take up where I left off at the end of the series on three-legged joiner's benches (<--link) or trépied établi. The word établi means workbench, and a établi de menuisier is a woodworker's bench. In the case we have here, is is a square pavilion (pavillion carré) on a sloping wall plate, which seems to be thought of as a bench, or rampant établi

Here's a perspective view of this sort of structure from the text:

It's meant to go on a stone wall structure.

Mazerolle shows another building on the same page which has the situation of a different sort of descending wall plate - a pair of hipped roofs atop a gable:

A most curious looking structure.

As you can see clearly from the first example, the wall plate slopes on all sides, and hence the overall plane of the slope travels on a diagonal, from non-adjacent corners. This is not the only case where one might have to deal with a wall having a titled plate line - another 19th century layout text by Delataille shows a couple of examples, the first with a tilt along just one orthogonal axis:

Like Mazerolle, Delataille shows these tilted plate buildings following on in terms of the lesson track, from odd 'joiner's benches' - like this one with 4 legs, Saint Andre's crosses out the wazoo, and a pronounced tilt:

Last, Delataille also shows an example with a plate tilted on a diagonal in relation to the plan, with a dormer tossed in for extra fun:

 Delataille's text has very abbreviated developed drawing of the pieces illustrated in perspective, however these are nearly indecipherable. To say they are cryptic would be a compliment. At least, they do not tend to encourage this writer to delve into them at this point in time.

In terms of other students of French carpentry over the years and what they have chosen to tackle, it isn't hard to find examples of this sloped plate problem within larger assemblies meant to demonstrate a certain school's technical repertoire - as this photo shows, if you look to the upper left side of the shot:

 That example shows a hipped roof with a ridge and the common rafters oriented square to the descending plate - and a Saint Andre's cross on another roof face for good measure.

Of course, a hipped roof with a tilted plate is but one step along the course of study - one could also have, say, conical roofs with curvilinear Saint Andre's Cross bracing, on tilted plates, like this example:

But, one thing at a time. I continue to work away at Mazerolle's drawings, which have their share of issues, as I've mentioned more than once in past postings. At the outset of the pavillion carré rampant établi exercise, Mazerolle makes the following remark:

"En pratique, les pavillions rampantes ne s'exécutent que rarement, c'est plutôt une étude de trait de charpente,..."

Rarement, indeed. So, this étude is all about studying what happens in a framed structure when the plate is tilted, another example serving to deepen a student's understanding of L'Art Du Trait (developed geometrical drawing for carpentry). I will say that while structures with tilted plates are pretty uncommon, I think if I were to see one, I would find it an utter delight, the kind of thing that would brighten up the landscape and bring a smile to my face. Those are the sorts of structures I wish I saw more of in the built environment - we've got quite enough big box stores and cookie-cutter McMansions already, don't you think? It would need to be done with sufficient tilt that it looked deliberate, if you know what I mean.

There is more than meets the eye upon initial inspection of this roof form though: in this example not only is the entire wall plate is tilted, but the interior purlins in the roof are also tilted just the same. Of course, those tilted purlins are sandwiched between principal rafters and common rafters, and are attached to diagonal truss struts on their back sides. The commons and principal rafters are aligned, in plan, more or less orthogonally to the descending wall plates.

At the outset, when considering the problem, I could see that some parts were going to have to be parallelogram-shaped sections, however I also know from past experience working problems in the text that the French carpentry preference seems to be the employment of square section timbers - to rotate a square section timber into a given roof plane and then make connecting parts fit it by cutting curious birdsmouth-like connections on their ends. There was plenty of that in the crazy Mazerolle sawhorse project from a year or so back. The French, at least as far as what Mazerolle (and As it have noticed in other works from that time) does, the upper surfaces of a hip rafter are backed in many cases, but otherwise the plan is to get square-cornered timbers to do the job everywhere, even if it makes for ungainly and ill-aligned constructions. But hey, beauty is in the eye of the beholder as they say.

I started drawing, and after oh, a day's work, things were not quite lining up as they were supposed to. That led to some erroneous conclusions on my part, and further steps down the wrong path, to the point of having the entire roof nearly complete. Then it became more obvious something was wrong. At one point it appeared that one of the fundamental aspects of the drawing, the diagonal tilting plane for the wall, and how it relates to heights along the walls themselves, was, uh, out of kilter. I communicated with my collaborator Tim Moore in France, who took a look and did a brief mock-up of the tilted plate, only to find that it did match the conditions indicated in the text.

I was baffled for a while, not knowing where things were going awry for me. I checked and double-checked my drawing, and while I could find nothing apparently wrong, the numbers still weren't adding up as they were supposed to. Then I decided to go back to a blank slate, as it were, and redraw the tilt of the plate from the beginning. When done, it conformed to the text's version! Upon further reflection, I realized that the way I had approached the titled plane at the outset of the drawing process, using a 3D rotate tool in SketchUp, had caused the discrepancies. Assumptions can be a killer sometimes! Nothing to do with SketchUp, just the logic of how I went about the drawing work, and the penalty paid for the wrong turn. Oh well, only 8 hours of drawing lost....

Practice, practice... I worked the redraw though for several hours and caught back up. Here's how that looked:

Another view:

The usual spaghetti nest. I hope is is clear how the purlins, colored brown and orbiting around the roof at about mid-height in the above picture, are tilted just like the wall/floor.

A closer in view reveals the interior bracing structure, tilted in plane with the floor and purlin ring, tying together all the principal rafters with king piece, an assembly which the French term an enrayure:

I was satisfied with my drawing result at that point. In order to achieve completion to that point, I had varied my approach from Mazerolle. He wanted, it appeared, all the parts to be square-cornered sections of wood. In some email with Tim Moore, he suggested that maybe it would be okay to use square rafters and principals, something I had more or less ruled out at an early stage. I wasn't even sure they could be configured to work, such that a purlin could be sandwiched between them. I did some exploration in that direction, and found that square-cornered rafters, both common and principals, could in fact be used. Trouble was, as I had surmised earlier, there would be downstream effects as a result.

Here's one of those downstream effects - note the fit of the principal rafter against the king piece:

The fact that is is skewed is not the end of the world, and there is enough of a broad surface on the face of the king piece. Okay, well, you might sat it is not all that noticeable, so perhaps it could be lived with.

Worse though is the fit between the truss struts, what the French call contre-fiche, and the underside of the principal rafters:

You can see that the end of the contre-fiche is not centered on the principal. The problem with off-centered pieces in truss structures, of which this is a very simple type, is that they distort the load path, which might tend over time to induce a certain amount of twisting to the principal rafter or other places. Maybe not so bad in this case, and the contre-fiche could be re-angled to be centered on the skewed-over principal, but there is that matter of load paths again. It's not an ideal arrangement as far as I'm concerned.

However if you take a look at how the horizontal member of the enrayure abuts the principal, one can see an even bigger disparity of fit:

Again, while the horizontal strut from the enrayure could be kicked over, and it appears in Mazerolle's drawing that this is intended, there is the load path issue. Multiply that by four principals, and I wasn't liking the way things sat. While the principals could be made square and the commons left as they were, I elected to erase all those changes and went back to the arrangement that had made sense to me in the beginning - virtually all the parts in the roof are parallelogram-shaped to conform to the various intersecting planes involved.

One exception are the purlins, which are quite clearly intended to be square sections, more or less, in the text's illustration. It's actually not possible, given other constraints in the drawing, to make them dimensionally-perfect squares in section, though they end up being pretty close. One area though where the insistence in using square-cornered material is leading to a slightly unattractive outcome though is at the underside of the hip rafters, where the purlins meet one another. Here's one such meeting:

And here's another:

All four are staggered from one another in regards to their top surface heights, though it is only apparent when you can compare them at the meeting points under the hips. The stagger between pieces is remediable, however it would mean that the top surfaces of the purlins would have to be decidedly non-square. I initially drew them that way and liked the look, and if I were to actually build a roof or structure like this I would opt for the purlins to have a more seamless fit by making their upper surfaces non-square to their sides, and they would fit much more nicely to one another under the hips.

The enrayure in my version of the drawing is composed entirely of parallelogram-shaped pieces, and I think the result is quite tidy:

All the pieces have co-planer surfaces and are centered upon the faces of all connecting members. If square-cornered pieces had been used, as the text shows, the result would have been, well, to choose a phrase, higgledy-piggledy. That is a word, isn't it?

The adjusted shapes of the principal rafters back to parallelogram-sections means that the contre-fiche pieces, themselves parallelograms in section, fit in a centered manner and the load path is directed as I think it should be:

Some final pictures of this tilt-o-whirl roof placed on a framed wall structure. Obviously, it needs the rafters extended to form eaves, and there are a few parts missing from the roof, but it conveys the idea and was as far as I decided to take it for the time-being:

An elevation:

Another elevation:

The drawing conveys certain lessons, some obvious and some hidden, and I think the main one related to establishing the tilted roof surface outline on the ground plan, and having a way of relating different locations on the roof in any elevation view of the two trusses. I'm not going to get into those particulars here today, but it was worth the walk down the path to see what Mazerolle was trying to show. I'm sure there may well have been a lesson I missed there, by choosing to construct something a bit different that what was shown, but I imagine I will be presented with that lesson sooner or later by way of another drawing exploration. I've got a long way to go yet.

The reason I focus such energy on studying drawing, is that if I can draw it, I can build it. I may never get a chance to build such a structure, however you never know what comes along in project-land, and sometimes a lesson learned in one application has unexpected uses elsewhere. Understanding this oddity may unlock the keys to other puzzles later on.

By studying these drawings, which believe me take a huge time and energy commitment, I am able in certain respect to get into the head of Mazerolle, understand more deeply the tradition of which he is renowned master, and hopefully come to understand the uniquely French approaches to timber carpentry, even if I don't always agree with what they are doing - or appear to be doing!

After all, traditional carpentry, as someone once remarked, boils down to just two things really:
  • putting lines on the wood
  • cutting where the lines are 
While I cannot claim mastery of either area, it is the putting of the lines on the wood which proves to be the far more difficult task of the two, and the route to gaining a deeper knowledge of that aspect of the work is one requiring thousands of hours of study, no way around it. It's an enjoyable trip so far, despite the frustrations and wrong turns which plague much of my experience.

Thanks for coming by the Carpentry Way.

Thursday, October 6, 2011

Penrose: 500 Years Late?

The master builder tradition was based on pattern, not fads. Pattern was largely associated to geometry and that geometry was also used to develop building proportions, down in some cases to the smallest of details. In this blog I've spent lots of time looking at such things as the Golden Ratio, the number 1.6180339887..., along with a classic medieval drawing method for producing various figures and patterns, the vesica piscis (here and here).

A related aspect to patterning involves tiling. It's not uncommon for carpenters (who, unofficially at least, seem to also wear the hats of tile-setter, brick-layer, plasterer, etc.) to be engaged in placing floor and bathroom tiles, and parquet flooring, though now somewhat of a rarity, is an area allowing for much creative variation. The French in particular developed that area in depth. Laying bricks and cinder blocks, paving stones, acoustical ceiling tiles and so on are also examples of tiling. So, general carpentry practice often involves tiling in one form or another. In Japan, I might note, it is considered a disaster if a room is tiled so that tiles have to be cut to fit at the edges - they like to plan ahead and get a sublime result. Yep, that's right, choose the tiles before you decide on the exact size of the room.

Tiles that fit together to one another without leaving gaps as they cover a given surface are said to 'tessellate' - the root of that word being tessella, which is Latin for a small cubical piece of clay, glass or stone (used to make mosaics). Tessellations may be composed of regular or semi-regular elements. 'Regular' means that the tiling elements are congruent regular polygons, and there are only three of those - equilateral triangles, squares, and hexagons. A bee hive's honeycomb arrangement is a classic example of a natural tessellation using hexagons. Semi-regular tiling also involves polygons, however more than one type is mixed in, like octagons with equilateral triangles, or hexagons mixed with squares and equilateral triangles, like this:

That's called a 'rhombitrihexagonal' tiling. Not a word you would typically bring out at the dinner table in polite conversation. For a fairly in-depth look at the possibilities of polygonal tessellation, take a look at Brian Galebach's page (<-- link) cataloging hundreds of variations.

Other irregular and curvilinear shapes can tessellate and Maurits C. Escher, a world-famous artist, produced quite a lot of work employing tessellations and morphing shapes, like this classic from the 1940's, Reptiles:

I've found this matter of tessellation an interesting topic for a long time, and of course with the continual drawing, design and study I do, geometry and pattern are never far from my thoughts.

One of the curiosities of tessellation relates back to the above-mentioned golden ratio and the fact that the polygon which associates closely to that ratio, the pentagon, does not tessellate. Kepler noted this in his 1619 work Harmonices Mundi (meaning: The Harmony of the World), where he proposed a way of tiling which made use of pentagonal symmetry, a drawing he called 'Aa':

So, looking closely at this figure we can see that regular pentagons are mixed in with pentagrams, regular decagons, and a curious sort of fused-together pair of decagons. An excellent page discussing pentagon tilings can be found here.

So, the problem with pentagons and their apparent intractability as far as tessellation is concerned stymied mathematicians for many years. Until the 1970's in fact, when British mathematician Roger Penrose discovered a pair of tiles, the 'kite' and 'dart', each having pentagonal geometry (i.e., 36˚ and 72˚ angles), would tessellate. He wrote about this discovery in a 1978 article entitled 'Pentaplexity' (<-- link).

Here are those two tiles, the 'dart' on the left and the 'kite' on the right:

With these two tile shapes, a surface can be covered leaving no gaps, and a pentagonal symmetry manifests. Here's an example - note the floor Professor Penrose is standing upon, at Texas A&M University:

Possibly the kite and darts aren't so obvious in the above photo? That's because the shapes have been 'welded' together, as it were, and the abutment lines erased. Perhaps this example will be clearer:

Compare the two pictures to see how the form of the tiles can be made plain or obscured, as desired.

Yesterday I was looking at the news and saw that the Nobel Prize for Chemistry had been awarded to an Israeli scientist, Dan Shechtman, who discovered what are called 'quasi-crystals'. Schectman, who made his discovery on April 8, 1982 while working in the US, "fundamentally altered how chemists conceive of solid matter" - this, the academy said in its citation for the 10 million kronor ($1.5 million US) award. In fact, Schectman's discovery, like a lot of paradigm-breaking discoveries in Science, was met by reflexive skepticism and mockery by his peers, even prompting his expulsion from his research team, before it later won widespread acceptance as a fundamental breakthrough. First they ignore you, then they laugh at you, then they fight you, then you win, as Gandhi wrote. I like stories like that, and you have to admit, these icosahedral quasi-crystals of metal are pretty cool looking:

 I started doing more digging and reading about these unique forms, and that lead me to Peter Lu's site. He's a whiz-kid at Harvard, a physicist who has interests in ancient Chinese technology and Islamic art - tilings that is. If you have a spare 70 minutes and feel like geeking out, I strongly recommend taking in a  video on his site, a film of a lecture he gave entitled "Decagonal and Quasicrystalline Tilings in Medieval Islamic Architecture" (<-- link). I found the talk so enthralling I watched it twice, but then I do have an obsessive side.  Anyway, if you check out the video, you will come to see why I chose the title for this post. I hope you enjoy it!

Thanks for coming by the Carpentry Way. Happy tiling.

Tuesday, October 4, 2011

Lucarne Et Nolet Sur Arêtier (II)

Bit of a non-blog today, but what the heck.

In my previous post on the hip-mounted dormer, I mentioned some issues I had with the interface between the lower end of the noulet, the top of the dormer wall plate, and the adjoining sloped brace and tie which carry the load of the hip. Following the drawing, I initially obtained a hole in the roof, and this led to a solution where I kicked the bottom of the valley piece over to the side a bit more at its lower end. This got rid of the hole, and seemed all in all a tidy solution. I finished off my description of that issue with the following:

"That's my solution and I'm sticking to it until someone can show me some way that the text's proposed version can work cleanly."

 Well, I have in fact come to see the issue a bit differently, and have come to consider another way to solve that problem, though, like the solution I had already come up with, not in a way in which the text proposes or indicates. I had some emailing with Tim Moore, a computer graphics guy with a blog on stereotomy (see the link in sidebar to the right of the page), and he suggested a move involving changing the shape of the horizontal tie of the hip support bracing. I looked at his idea in some detail, and after an initial sketch of the changes i felt that while it presented a workable solution, it seemed to wander ever farther from what was shown in the text.

However, further reflection upon my solution ensued. I noticed that while my solution was nice and tidy, it did in fact appear to create a problem in terms of the intersection of the dormer roof planes with the main roof planes. So, I decided to explore in the direction Tim was proposing. After a bit of fiddling, and a cascade of downstream effects which occur from moving a piece here and there, I was able to produce an intersection between parts which kept the lower end of the valley piece aligned to the outer edge of the hip bracing diagonal member.

Here's how that solution looks, and no, it doesn't look a whole lot different than what i came up with previously:

The lower end of the valley is aligned to the outside face of the sloping hip brace, and there are no holes.

With a few parts removed, the slight change effected in the horizontal portion of the hip support assembly is clearer to see  -see how it is raised above the dormer wall plate?:

And one more, with all the parts back in place:

So with all that done, I seemed to have found a solution which, though at variance with what was shown in the book in terms of how the central horizontal portion of the hip support truss (some would call it a 'tie' however that term is misleading in this case) was configured.

I then decided to compare the roof surfaces after placing some temporary roof planes on the dormer and immediate surrounding area on the main roof. I then learned that my apprehensions about there being an issue with how the intersection of roof planes would look in regards to my original solution were unfounded.

Here's one solution:

And here's the other:

Not much to pick apart is there? The one with the red plane on the main roof is the revised framing solution described in today's post, while the one with the orange main roof plane is the one I wrote about previously.

So, there is more than one way to solve it, and I'm not sure in the end which is to be preferred. One thing is true, and that is a faithful duplication of the text will result in a hole in the roof. The solutions involve either modifying the central horizontal member of the hip support truss, or swinging the lower end of the valley piece over further. Six of one, and half a dozen of the other I guess.

Thanks for coming by the Carpentry Way. Here's a taste of what I'm currently working on, drawing- and study-wise:

Saturday, October 1, 2011

Lucarne Et Nolet Sur Un Comble Moins Élevé

The titles keep getting longer it seems, as does the length of the post. Today's piece is about the final dormer drawing shown, in detail, in Louis Mazerolle's work Traité Théorique Et Pratique De Chapente. This dormer differs from the preceding dormers - lucarnes - I have written about in several respects. This is the first dormer to have a form of king piece truss, and the first dormer to have the rafters overhang the eave. Thus there is no molding to worry about. The most significant difference however is that the main roof in this case is lower - moins levé - than the dormer roof. Thus, a portion of the back side of the main roof has to climb up to meet the peak of the dormer, creating a situation where there are 'hip' pieces resting atop valley pieces at the intersection of the two roof planes. So, like the other dormers to be studied in this text, the main problem to solve is that of the shapes and dimensions of the valley/hip pieces which enable the roofs to connect seamlessly.

It occurred to me that for those readers not especially familiar with the geometrical issues which come up in roofs with hips and valleys, namely the places on a roof where differing roof planes come together, a few pictures might help to better explain the situation, particularly in respect to this dormer.

Here's the basic set-up: we have a dormer at right angles to the main roof, and a simplified truss on the dormer which (for this example) I have made to look just like a capital 'A':

 Next, I have placed a couple of planes on top of the dormer so the intersection of the dormer's roof planes with the main roof plane can be more obvious:

Note the horizontal traces associated to both truss and roof planes (one at the ridge, and another line each tied to the tips of the rafters) which extend from the dormer roof on back and through the main roof. On the main roof I've connected these upper and lower traces to match the tipi-like shape of the dormer roof meeting the main roof.

So, at the spot where the dormer roof meets the main roof it would be jolly nice to have some sticks of wood in there to connect things together. In the next drawing I have taken the 'A'-shaped roof truss and moved a copy over and laid it on angle to rest against the main roof plane:

Slight problem here Houston, as it is obvious that the roof truss, when laid over to slope of the main roof, is not tall enough to meet the ridgeline from the vertically-oriented truss on the dormer. While the width of the dormer, as measured at the bottom end of the truss rafters, remains the same at the main roof, we have a longer distance to climb up that roof plane - the truss needs to be put in a medieval torture device and stretched some. In the following picture, I have worked some magic and s-t-r-e-t-c-h-ed the truss laying against the main roof so that it meets the dormer's theoretical ridge height:

Can we sit back and bask in glory, another tricky problem solved? Well, not quite yet. You see, while the stretched truss portion does now reach all the guidelines established by the traces at ridge and rafter tips, if we put the roof planes back in place we can see another issue cropping up:

It would appear that the laid-over truss bits, which are square in section sticks just like the vertical truss, poke out from the roof plane. Here's a view from the other side:

If we left those sticks protruding like that the finished roof surface wouldn't look too good.
There are two solutions for this - the, uh, cheesy one, called in some parts of North America a 'California' valley, would be to move those sticks of wood on the main roof in and down so that  they touch the dormer roof plane along just an arris - the upper outside arris on the sticks. Then over goes your sheathing, and wham-bam with a bunch of nail-gunning fun and it is all tick-tacked together. As the song goes,  Little boxes, little boxes, on the hillside...

A better solution, except in terms of getting it done as fast as possible, would be to re-shape the sticks of wood laying against the main roof so that they met the planes from the dormer perfectly. This is the French solution, although they also employ what we might more usually call a 'valley' rafter; that is, a stick of wood cut so that it has a vee-shaped trench running down its top surface, one half of which is in plane with the dormer and one half of which is in plane with the main roof. Those are a lot of work to make, and not the sort of solution we are looking at today.

These re-shaped valley pieces used in these dormer examples from Mazerolle's book take a while to learn how to draw but are tidy, strong, and efficient solutions to connecting the dormer roof planes to the main roof. Here's a look at how that original 'A'-shaped truss would be re-shaped to conform to the width, height, and surface planes of both dormer and main roof:

I next apply the roof planes again so you can see clearly that the valley pieces, laying flat against the main roof also fit flush to the dormer's roof planes:

And a look from the other side showing how the folded-back upper portion of the 'A' conforms to the reverse side of the main roof:

Now, to produce these pieces requires a bit of developed drawing work - all the dormers in Mazzy's book are showing applications of the same method to produce these curiously-shaped valley pieces. The developed drawing work is presented for you in the book:

This drawing is deceptive however for several reasons. For one thing, only a small portion of the actual lines required to do the 2D drawing, to completion, are shown. For another, and as regular readers of this blog will have heard from me in the past, one can expect to find 'mistakes', 'misdraws', omitted labels and other such vexations. I now expect to find these problems in the book, with every single drawing, so it does not put me off like it used to. I'm now battle-hardened. Ah, the good old days, when I had a naive belief that an illustration in a layout book would be accurate....

In terms of the text associated to this particular lucarne drawing, in the final paragraph Mazerolle remarks (my best translation at least):

"...but in order to not unnecessarily complicate the text a lot of operations are described only once so readers should pay close attention to the explanations and refer to them as needed."

Yes, my friends, pay close attention. This reminds me of of a certain tradition you will see in the martial arts world, where the master will walk out onto the floor and, without so much as a "how do ya do?", will throw a few people around for a while then make an exit, stage left. No explanation was offered for how the techniques shown are to be done or were done, or why those ones were done and not others. The keen student who experiences this just once will realize, hopefully, that the next time the master shows up he/she had better keep their eyes pinned like laser beams upon the moves of the master to have any hope of gleaning some useful information. In the West, this approach doesn't tend to sell so well, as students are habituated, it would seem, to not paying close attention when the moves are done and expect to be able to ask many detailed questions afterward, "why...?", "how come...?", "what if...?", and, "could you do that again, slowly?". The real answer to all those questions, in that context, is simply this: train more.

Mazerolle is a bit like that, except a terse explanation is offered, and then the moves shown sometimes are entirely misleading. And, it must be said, a certain intellectual apprehension of the material is most helpful. It's a special kind of challenge, and since he's long dead I have no opportunity to question anybody about the hows and whys. You have to take it as it comes and be prepared for some struggle. At least I do - struggle, that is. There are undoubtedly more gifted and insightful individuals out there who would see the solutions and grasp the essential points far more quickly than I. But then this is hardly a race, and the tortoise did do rather well in the end against that rabbit, no?

So, back to the 2D part where all the secrets may be revealed, if you know where to look. Here's what the drawing looks like when most of the lines are in place:

The method being shown is the same method I have run through several times already with this text, and involves figuring out footprints of sticks and the planes which associate to them.

Here's a bit more focused view of the portion of the drawing in which the valley pieces are worked out:

I'm not going to delve into a detailed look at the how and why aspect here, but in the following drawing (with some layers stripped away for clarity), with another zoom-in, you can see the white footprints that are produced by way of the developed drawing technique shown:

Notice how all the footprints are rhomboids. The two at the left side are for the 'hips' which climb up above the main roof, while the footprints at the right are for the valleys laying against the main roof.

I was surprised by the shapes obtained since in all previous drawings the sections of noulet (valley rafters) were trapezoids, not rhomboids. Still, with every new drawing in the book, something new and different is shown, something to which I must pay close attention, so I tend to accept at face value what is shown  - until later. 'Later' is the point where I construct in 3D parts from the 2D floor sketch. And then new things come to light....

First off, the book shows both a footprint for the 'hip' pieces which climb up above the main roof, along with a side elevation view which shows the shape of those hip pieces and where their lines are located. Following this faithfully, I produced the following 'hips':

Notice how they only meet the main roof's surface along an arris? It's like a 'California' version, with all due apologies to the fine people of that state.

Here's another sketch where I have placed a semi-transparent plane in there on top of the hip pieces, a plane aligned perfectly to the back side of the main roof:

This solution is not workmanlike, in my humble opinion. Those small white triangles at the bottom are, in effect, the footprint  of the missing bits of these hip rafters - if the hip pieces had these bits fleshed in, the result would be as follows:

The hips are now shaped so as to fit the backside of the main roof flush. Looks/works better, no?

And the valley pieces had a similar problem. Refer back to the drawing above showing the plan of the footprints and you will see that the valleys on the right side of the drawing also have rhombus-shaped footprints. If we make the valleys in a shape which conforms to that rhomboidal footprint, we obtain the following result:

You can see clearly that the horizontal slice in white at the top of the valley produces that desired rhombus print, however the problem is that a portion of the valley piece is now occluding into the body of the main roof. That won't fly. The solution is the reverse of what I did for the hip pieces - instead of adding material, with the valleys I must subtract a bit so that the back surface of the noulet is flat against the main roof.

Once those shape adjustments have been accomplished, the footprint plan looks like this:

You can see that the footprints are not rhomboids, but trapezoids, as they should be.

In regards to the footprints though, there was an even more significant problem with the drawing in the book. If you examine the foregoing drawing carefully (click to enlarge), you will see that the lines which govern the footprints are labeled 'D.P.', which stands for devers de pas. The D.P. lines for the valley footprints are developed in a similar manner as to those for the hip section footprints to the left of the drawing, however the points they connect to, and the places that they originate from in other sections of the drawing, are of course different from one another. Trouble is, if you follow the drawing in the book exactly, you will produce footprints which are not angled quite correctly. I was able to prove this by way of constructing 3D pieces from the 2D. This 3D also enabled me to solve the problem - I re-configured the 3D parts so they were shaped correctly, and then took horizontal slices (ie., 'footprints') of those sections and placed them back down in the plan view. From there, I projected traces off of those footprints to see where they led. A bit of reverse-engineering that would make modern China proud.

What I discovered by the reverse-engineering was that the text had swapped the connection points for the foot development D.P. lines with one another. That was a first for Mazerolle, as the 'foot-printing method', as such, is, I do believe, his special and unique technique. His claim to fame as it were. The how and why of this particular error cropped up in the text is unknown to me, but I was glad to have the 3D for solving such a problem.

The result is a valley and hip piece combo that serve to tie all the colliding roof planes together - with what must be said to be a bit of an ungainly arrangement where the hip and valley pieces connect to one another:

You can see that the hip and valley pieces do not meet each other with their inside faces. Now, they could be made to meet on their inside faces, however another stick of wood governs the desired outcome here, a stick I have colored blue in the next sketch:

The French love to have everything aligned in a particular way, and with the pieces colored blue, the desired outcome is that the cuts on each end of that blue stick are done with a simple bevel cut, not a compound bevel cut. So, if one reshaped the hip and valley pieces so that their inside faces met seamlessly, then the cuts on the end of the blue-colored pieces would have to have compound cuts to fit correctly. In this case, that (the compound cut) is something I would choose to do, as I really don't care much for the 'stock' arrangement here (excuse the pun).

One of the aspects to the love of alignment I just mentioned relates to the decorative rafter tails - the valley pieces have their tails cut so that they are perfectly co-planer to the other dormer rafters:

In that case, alignment, as a desired outcome, is all good.

A few final pics showing the placement of the new dormer in with the other ones I have studied thus far:

I haven't fully integrated this dormer framing in with the other parts of the conglomerate - not quite sure yet where the whole drawing is going. A view from inside:

'Standing at street level' and looking up:

A front elevation:

 Quite a motley collection of lucarnes, each a scarring and traumatic memory (just kidding, sorta...):

All for today. There's more Mazerolle drawing stuff to come down the pike, though at this point I'm not entirely sure which drawing I will tackle next. I'll probably take a break for a short while to recharge.