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. 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.

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Perhaps in the fourth and fifth movements Berio demonstrates that his musical thought can encompass such issues without the need of quotations in so far as the reappearance of previously quoted material may now be said to constitute merely cross-reference within Sinfonia.

With this allusion to the title of Sinfonia, the author rounds off an excellent guide to the work, which certainly achieves the objective he proposes. The RMA volume is a pleasure to the eye and does great credit to that organization.

By Kevin Coates. Clarendon Press, Oxford, ,? This exceptionally handsome book is intended to show the aesthetic influence of geometry and numerical proportion on the design of lutes, viols, guitars, violins, citterns etc. It has 31 large plates in the style of Fig. It is extremely well written, and it appears to have the virtue, too rare in musicology, of candour, since Dr.

Coates seems more concerned to show how he reached his conclusions than to cover his tracks. Then he explains his analytical procedure: Analysis was begun by first examining the overall measurements? Next, the body outline itself was broken down into its constituent single-radius arcs. The centres of these arcs were located by a simple device, made by engraving a series of concentric circles on a clear perspex sheet of suitable size, and drilling a small hole at their centre; this was laid against the contour in question and moved until the two curves coincided; the centre was then marked.

In this manner, any multi-centred curve, or pseudo-ellipse, can be simply resolved into its component arcs. These separate vectors would then be recorded, revealing any geometical design processes such as grids, planning arcs or circles, vesicas, etc, while their arithmetical values, upon generation, might disclose the presence of a proportional scheme. A general margin of error of 0.

His reconstructions are based on the mould rather than the exterior dimensions? No matter that, given enough circular arcs, any curve can be approximated to within a half millimetre or even less: Dr. The simpler alternative is more likely to have been used because it is easier to transmit and because, within reasonable limits, simplicity is and was aesthetically more touching.

For instance, the extremely complex scheme attributed on pages to the Tielke gamba shown in Fig. Perhaps more important than these are the simple elliptical curves for the middle bouts not to mention the elliptical rose. A far-off centre need not really imply the use of an immense surface for the final drawing, as a template might be used.

But it is always worth while to distinguish merely pragmatic geometrical elements from the aesthetically more in?

Some occasional mathematical over- simplifications, however, have caused Dr. Coates to miss the likelihood that certain designs involve a tempering, as it were, of d : Uh. Coates to miss the likelihood that certain designs involve a tempering, as it were, of two theoretically incompatible schemes. For example, on page he says that in Fig. V , which is nearly 7. For lengths over 12cm such a discrepancy would exceed a half millimetre.

I think he might have secured his main point? None of this is to call Dr. Some of the reconstructions are entirely convincing to me at least , and those to which someone may find a better alternative will, thanks to his candour about his method, always have the value of showing its pitfalls clearly.

The summary of analyses on pages may be premature, as he himself implies, but there is much else of interest. I particularly liked the clear distinction pp. Schneider, Tutzing, , DM. The exhibition, as well as numerous musical events in Stuttgart, was promoted by the Internationale Bachakademie, Stuttgart. As a complementary event the Gesellschaft fiir Musikforschung organized an international conference devoted to Bach, Handel, Domenico Scarlatti, Schutz and Berg.


Geometry, Proportion and the Art of Lutherie



Geometry, Proportion, and the Art of Lutherie


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