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Review: Geometry, Proportion, and the Art of Lutherie

Review: Geometry, Proportion, and the Art of Lutherie

Kevin Coates

Oxford at the Clarendon Press, 1985

Out of print (1999)

Originally published in American Lutherie #4, 1985 and Big Red Book of American Lutherie Volume One, 2000



I have avoided reviewing books on the subject of lutherie in the past since most of them didn’t really merit reviewing. Books of the how-to type on the subject seem to find their market in spite of poor writing and illustration, lack of scholarship, and/or incompetence on the part of their authors. This book by Kevin Coates deserves mention for its total lack of any of the above shortcomings and really sits in a class by itself in terms of scholarship in lutherie in the English language.

The book is a study of the application of geometry and proportion as understood by the makers of the Renaissance and Baroque Eras to their instruments. While this seems at face value to be a rather elementary endeavor, in fact it requires more than a superficial understanding of the principles of Euclidian geometry and the historical background of their application in the West, especially as they relate to lutherie. Consequently, one is very hard pressed to encounter ideas and writing on the subject in English from other sources, aside from a few articles on lutes and related instruments in the Galpin Society Journal by Friedman Hellwig and perhaps a handful of others.

At casual glance, one might be tempted to think the title redundant since geometry is a manifestation of proportions, but Mr. Coates’ concise explanations of the mathematical nature of the former and the aesthetic nature of the latter make abundantly clear the irrevocable marriage of the two, and more importantly, how the prevailing aesthetics of the times influenced the manipulation of the mathematics to produce the desired aesthetic of beautiful proportions. Anyone who doubts my dictum that successful instrument makers are merely reflecting the prevailing notions of taste and beauty should certainly study this book very carefully.

The book is organized into a brief mathematical refresher for those of us who had trouble remembering the basics of geometry, a short history of geometry, a discussion of proportion, including the famous golden section and Fibonacci numbers, the ionic volute, a section on the thirty-three various instruments analyzed, followed by summaries, observations, conclusions, and abundant appendices, bibliography, and index. It is without doubt the most intense 178 pages of treatise on the art of lutherie I have had the privilege to read.

Contained within Mr. Coates’ well-crafted treatise are the essential facts necessary for the modern luthier to not only plausibly recreate the mind set of the 17th-century maker, and his notion of beauty, but also the elements of inspiration necessary to suggest a direction of design proportion in the 20th century, by applying the principles of geometry and proportion to prevailing aesthetics.

I must admit that my reason for originally purchasing the book, which I first saw at the Boston Early Music Exhibition, was greed. It contains the most exquisite and perfectly hand-drawn plates of thirty-three examples of historical instruments including six instruments of the lute family and three different guitars. The reason that they are meticulously hand drawn rather than photographed is for the sake of maintaining proportional fidelity on flat paper of a three-dimensional object. The lens of a camera even under the best of circumstances would tend to introduce some small degree of distortion. Since in nearly every case, Mr. Coates decreed a margin of error of no more than .5MM from the actual in order to establish proportional layouts, this precluded the use of photographs. Consequently each plan view of the various instruments, with their carefully placed scales to allow for expansion and contraction of the paper, is in essence a finely drawn plan capable of being converted into working drawings for the astute luthier who might wish to copy one of the instruments. Few, if any of us, are capable of producing such accurate drawings, so carefully measured, assuming we had access to the instruments, and the cost in time would be prohibitive. So from this standpoint alone, the book is an incredible bargain. Of particular interest to lute makers is the drawing of the 7-course Heiber lute in the Brussels collection. I have seen many contemporary copies of this lute which all have duplicated the peculiar flattening around the clasp area of the outline which is unique to the lute in its current condition. I had always felt that this was a distortion due to age and/or bad repairs and not intrinsic to the original design, but of course I had no proof other than my opinion and sense of proportion. It is very informative to see the proportional analysis by Mr. Coates of this instrument and learn that not only was this flattening not original, but also that the original scale had been shortened to its current 59CM from an original length of 60.1CM. This alteration suggests an adherence to proportion even in the face of questionable repairs, and as such gives some clue as to when the alteration was made.

My only reservations about the book revolve around two points. One, that the instruments selected for study, while undoubtedly old, have not been clearly and unquestionably established as actually being what they are purported to be. For instance: Example 1, a viol attributed to Zanetto, now no longer has its original label, and Example 2, a viol attributed to Giovanni Maria da Brescia ca. 1575 was considered by David Boyden in his book, The Hill Collection, to have been made around 1520–1525. This type of attribution of authorship is vital to know for certain, in order to put into proper perspective the continuum of craft practiced by the luthiers of old. For instance, the bass viol by Battista Ciciliano ca. 1590 (Example 3), whose measurements and proportions indicate a basic unit of measurement related to Brunswick inches, was supposed to have been made by the son of the Venician luthier, Antonio Ciciliano in a city where the prevailing unit of measurement at that time was unrelated to Brunswick inches. Does this mean that it was made by some other maker who used Brunswick inches, or was the tradition passed to Antonio Ciciliano and consequently his son, originally from outside the Venice area, from a tradition originally established in Brunswick inches? Answers to these questions rely on the crucial information of the actual authorship and date of an instrument. Unfortunately, in many cases this is not absolutely possible to establish, and consequently, we must accept a consensus for a given example. If the attribution of authorship of most old instruments in the world today had to hold up to the same rigorous standards of veracity as the rules of evidence in a criminal trial, most old instruments would have to be assigned Anon. as their maker. While scientific examination of the most careful kind can often tell whether a given item could be by a given maker of a certain date, it cannot tell that it is for certain. Unfortunately, in the case of these examples and many others equally worthy in the world, even the most rudimentary scientific analysis has not yet been performed to at least determine if they indeed could have been made by the attributed authors.

In the case of the central theme of the Coates book, this particular precision of information is not that critical, for the thesis is that old makers did indeed know, and use the knowledge of geometry to produce their designs. The proof of this usage is so eloquent in the provided examples as to make the question of actual authorship not that important. It is vital only to the researcher who may wish to make use of the actual geometric layouts to prove some other point, for instance, origin of a certain tradition, relationships of master and pupil, and so on.

My second objection is one of quantity. With the exception of three instruments attributed to Stradivari, the other makers are only represented by one example each, and as such, give no clue as to a temporal development of a given maker of the methods of layout and how they might have changed as he moved away from the master’s influence over the years. In this respect, the book only provides a tantalizing taste of what may yet be discovered in the proportions of these old instruments. I note that the book is merely a book form of what was originally a doctoral dissertation by Mr. Coates, and I suspect the greater breadth I yearn for is to be found in the complete dissertation. Corrolary to the second objection is the lack of information relevant to other details of the instruments, such as brace placements and positions, plate thicknesses, body depths, and other essential information relevant to the acoustical design of an instrument. If I may answer this objection, I suspect that it is because some of this information was simply not readily available by external examination of the instruments, and since the majority were museum examples, permission may not have been forthcoming to obtain it by modern methods where possible. Certainly, the amount of time spent by Mr. Coates in just accomplishing the presented material was enormous, and to wish for more would really be unfair. After all, it was not the stated intention of his book to provide every minute measurement of a given instrument, only to show the usage of geometry and proportion in their creation.

Without question this is a book which belongs in the library of any serious luthier, or anyone interested in the organology of Western musical instruments. It is a treatise whose knowledge will stand for many moons unchallenged. As works of this lofty quality are wont to do, I would not wait until my local bookstore has them in stock to purchase a copy, for it may go out of print by then. I bought my copy from Tony Bingham, 11 Pond St., London, NW3 2PN, England for $60. I suggest you pick it up post haste.

— R.E. Bruné (1985)

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