Over the years I've given a number of presentations and workshops at international conferences, and I've also written many articles presenting the results of my research. As time allows, I am working through all my articles and lectures, correcting mistakes, and adding new information where needed. Eventually I plan to have all the texts available as PDF files, excepting those which are published elsewhere. This page will change from time to time, so check back occasionally.
Proportionality and Early Wire Gauge Systems
Delivered at the Facture Instrumentale en Bourgogne conference, Cluny, France, September 1999*
The interpretation of surviving wire gauge marks on fortepianos and harpsichords continues to present a challenge to modern builders and restorers. Some organologists, notably Alphons Huber, have proposed the existence of "systems" in a modern sense, a standard adhered to by manufacturers and makers of given regional or temporal groupings. However, at least two historical sources warn against making such an assumption, clearly stating that the gauge numbers used by the wire manufacturers are inconsistent and unreliable. Others organologists, such a Michael Latcham, point out that the evidence also does not support such a conclusion, but indicates individual solutions by individual makers. I propose a middle road, based upon a newspaper article of 1811 by the Viennese piano maker J. F. Bleyer. He describes "Nürnberg" string markings as a proportional system with 7 logarithmic steps between any two strings with a diameter proportion of 1:2. When the diameters from many different instruments thought to have original strings are "measured" using a "virtual" version of the traditional device for measuring piano wire, the slip gauge, we find that a large number of the diameters do indeed fall within the confines of such a system; occasional aberrations are quite likely examples of making-do with the materials at hand. Therefore, it is quite likely that original gauge markings should not be seen as representing specific diameters, but more so as defining the limits of broad zones of diameters with fixed proportional relationships. The use of precise modern analysis tools, such a regression analysis or log graphing, can produce the illusion of a chaotic situation, but when we duplicate historical wire sorting methods (as described by Bleyer and others), we uncover a probable tradition stretching from the late 18th century, and quite possibly earlier, to the introduction of modern industrial standards in the late 19th century.
Recommended Nürnberg Gauge Interpretations DOWNLOAD (PDF File 4k)
Published in: Matière et Musique. The Cluny Encounter (see link below)
For a synopsis of this article, go to Instruments/Strings
Steinway and the Invention of the Over-strung Grand Frame
Technical innovation or marketing success story?
Delivered at the Facture Instrumentale en Bourgogne conference, Cluny, France, September 1999
The invention of the over-strung frame is often heralded as the greatest "improvement" since the invention of the instrument itself. Its supposed advantages are twofold: (1) it allows longer bass strings, and (2) it brings the bridges closer to the center of the soundboard. By comparing straight and over-strung instruments from the latter half of the 19th century and through the analysis of string length, scale shape, soundboard design and modal characteristics, I demonstrate that neither of these assertions is true. The real reason may well have been that the over-strung frame is inherently stronger, and probably much easier to cast as a single piece. Thus Steinway was able to raise the string tension on his instruments more easily while simultaneous achieving higher levels of industrial efficiency and productivity. The concept of acoustic superiority is largely the creation of Steinway's aggressive marketing and pseudoscientific promotional materials.
Matière et Musique. The Cluny Encounter
Proceedings of the European Encounter on Instrument Making and Restoration
Jos van Immerseel, Claire Chevalier, Thomas Steiner. 392 pages
Order on-line from Alamire
Beyond Pythagorean: Ancient Techniques for Designing Musical Instrument Scales
Delivered at Rencontres Internationales de Lausanne, 3 - 6 April 2002
In describing the probable methods used by instrument makers of the past to design string scales, modern organology has offered no explanations beyond the use of whole units or simple fractions of the applicable measuring unit (inch, Zoll, duim, etc.). Scales are generally considered to be either "Just" - halving and doubling at the octaves - or modified-Just, that is, altering the Just lengths slightly using some sort of simple addition/subtraction system. However, neither of these approaches offers a convincing explanation for the scales found on a surprisingly large number of surviving instruments, scales which appear to be logarithmic though non-Pythagorean, exhibiting strings lengths and regular octave proportions which can only be described by irrational numbers. This paper demonstrates how simple geometric calculation templates, well known and used by craftsmen of all types since ancient times, could have been employed in harpsichord and piano workshops to easily and rapidly devise and apply such scales. An explanation is also given for why a builder may have chosen to use such a scale.
Keyboard Instruments - Flexibility of Sound and Expression
Proceedings of the harmoniques International Congress, Lausanne 2002
Bern, Berlin, Bruxelles, Frankfurt am Main, New York, Oxford, Wien, 2004.
ISBN 978-3-03910-244-0 / US-ISBN 978-0-8204-7025-2
Order on-line from Peter Lang
Temperament and intonation in ensemble music of the late eighteenth century: performance problems then and now
The music of the eighteenth century presents a particularly complex problem to those performers today who wish to employ historically appropriate temperaments. Musical forms and instruments were developing rapidly, placing new demands on instrument makers and players alike. The situation was further complicated by the collision of four different commonly used pitch levels, each separated by a semitone from the next, requiring the ability to transpose either the keyboard or instrumental parts upwards or downwards by a semitone, a whole step, or a minor third. The obvious solution would have been equal temperament, and in fact, it was often suggested by writers of the time; however, it was just as often rejected, and a myriad of alternatives exist. This article serves as a basic examination of the issues involved, explaining not only the temperaments available to a musician of the times, but also touching on the differences between the rigid intonation of the tempered keyboard and the use of intonation among melodic instruments. The purpose is more to present the practicing musician with an overview of the complexity of the topic rather than to provide any definitive solutions.
Music of the past - instruments and imagination
Proceedings of the Harmoniques International Congress, Lausanne 2004
Bern, Berlin, Bruxelles, Frankfurt am Main, New York, Oxford, Wien, 2006. 302 p.
ISBN 978-3-03910-993-7 / US-ISBN 978-0-8204-8370-2
Order on-line from Peter Lang
Non-Pythagorean proportions and the Diapason in the design of Iberian Harpsichord scales
One of the tenets of modern organology is that the strings of keyboard instruments have generally been designed according to the theory that length is inversely proportional to pitch, resulting in a progression of string lengths known as a Pythagorean Scale. Recent research has begun to focus on surviving Iberian instruments, heretofore largely neglected. While few have survived, it would appear that a significant number of their builders had a tendency to employ non-Pythagorean scales. One recent study suggests that these instruments represent a curious collective adherence to archaic methods used in the design of Medieval instruments. The present article offers an alternative viewpoint, showing how such scales could easily have been constructed using a traditional organ builder's design tool, called a Diapason. For the first time in modern organolgical literature, the geometric logic by which the earliest and most common form of the Diapason returns a series of values which describe a non-Pythagorean scale is clearly explained, and the various types of possible progressions which can result from different types of Diapasons are enumerated. The scales of several Iberian instruments are then examined in light of these alternative methods, arriving at the conclusion that their makers, rather than exhibiting an archaic conservatism, may well have formed part of growing 18th century movement towards the use of extended non-Pythagorean scales as are now ubiquitously found in the modern piano.
No 64 (2009):137-168
Late Medieval Strung Keyboard Instruments: New Reflections and Attempts at Reconstruction
coauthored with David Catalunya
Ample iconographic evidence exists to demonstrate that small strung keyboard instruments were quite common in medieval times. A number of surviving texts either state or imply that one manner of exciting the strings was by striking them with some kind of hammer mechanism. Chief among these sources is Arnaut de Zwolle's well-known manuscript, which describes a number of different instrument layouts as well three different plucking actions and a simplistic hammered action. Arnaut's text has provided a great source of inspiration for modern makers wishing to recreate such instruments, due to its relatively high degree of detail. However, precisely because it is the only such source, his solitary vision has also acted as a conceptual straightjacket, essentially discouraging any serious consideration of credible alternatives. The purpose of this study is to explore the territory beyond Arnaut, with the ultimate aim of imagining a new design for a hammered keyboard instrument not based on any one extant source, but nonetheless within the confines of medieval musical instrument making. The primary aspects of such an instrument - the stringing, the action, and the structure - are considered from two different angles: first, in the light of what hints the scant extant information provides about what probably was done; and second, in terms of what would have been possible considering what is known about general medieval mechanical and structural technology and metallurgy. This dual-pronged approach opens up the field to a broader range of possibilities, from among which one particular set of solutions has been chosen for a hypothetical reconstruction.
Scale Analysis - purpose and methodology
Delivered at the Accademia Bartolmeo Cristofori conference, Florence, Italy, December 1997
The analysis of string lengths, diameters, pitch, tension, tensile strength "pick-up" and inharmonicity can be greatly facilitated when all factors are expressed proportionally, using a common logarithmic "Pythagorean" unit of measure, similar to the use of cents instead of Hertz in discussing temperament. One Pythagorean unit is a proportional difference of 1/12th root of two, 1:1.059463, or the same proportion as one equal-tempered semitone. When all factors are expressed using this unit, the complicated interrelationships of scaling and stringing factors can be understood easily, without the use of slide rules, computers, logarithmic graphing paper or scientific calculators. Furthermore, I demonstrate how the often-employed "c2-equivalent" approach distorts the data, and how the citation of c2 length alone is often a gross simplification which can lead to dangerous oversights about scale aberrations. Examples of mistakes and misconceptions from the organological literature are cited, and I show how they could have been avoided by the use of proportional thinking. I propose a possible ancient methodology for scale design, using simple workshop tools and techniques based upon Pythagorean theory.