The use of simple geometry and the local unit of measurement in the design of Italian stringed keyboard instruments:
an aid to attribution and to organological analysis
A knowledge of the unit of measurement has been shown here to provide one of the most important and potent methods for the analysis of the construction method and design used by makers of stringed keyboard instruments in the historical period. The determination of the size of the unit and the centre in which the unit of measurement was used can be invoked to suggest or confirm the maker of an instrument. Establishing the centre in which an instrument was constructed using this analysis can greatly narrow the field of possible makers from the large number with which one would otherwise be faced. The method can also be used, as with the Marcus Siculus and Ignazio Mucciardi instruments, to suggest the centre in which these makers, about whom no biographical information is otherwise available, lived and worked. The method can also suggest, as with the anonymous single-manual harpsichord in the Ca’ Rezzonico in Venice, that harpsichords may have been built in centres such as Urbino, not previously recognised as locations in which stringed keyboard instruments were made.
It is of course important that, using the methods described here, the same result should be obtainable by any investigator. As with any scientific process the method for determining the unit of measurement used in the design and construction of Italian stringed keyboard instruments during the historical period described here is impartial and unbiased, being based on some of the simple geometrical methods and construction principles used by their makers. To that extent it does not involve any preconceptions or bias on the part of the investigator. And to that extent it is not dependent on who the investigator is or what his or her preconceptions or biases might be.
As suggested at the beginning of this paper a knowledge of the centre in which an instrument was made is basic to the understanding of musical practice in that centre. Although it has been recognised for some time that Italian instruments are only superficially similar there is still a strong tendency, based on the inability in the past to be able to distinguish regional styles in Italian stringed instrument keyboard construction, to consider a single tradition for the Italian peninsula as a whole. In fact, however, there are many regional traditions, each with their own design principles, construction methods, decorative styles, pitch standards, etc. These traditions changed and evolved over the 300-year historical period of harpsichord and virginal building in Italy, and the way that this happened is complicated by the alteration and re-use of older, out-of-date instruments (see footnote 73). Nonetheless it is clear that the time is now ripe for a study of the stringed keyboard instruments made on the peninsula based on a distinction and division according to these regional variations.
Any attempt to understand the stringing and pitch of Italian stringed keyboard instruments, for example, is doomed to failure unless the instruments studied are correctly grouped according to the region in which they were built. The fact that an instrument built in Florence and one built in Naples have the same scalings does not necessarily mean that they were designed to sound at the same pitch. Regional variations in pitch standards and stringing materials could strongly affect the pitch at which the two instruments were meant to sound even though their scalings are the same. Similarly two instruments from different centres with string scalings in the ration of 9 to 8 does not in itself mean that they were designed to sound at pitches a tone apart for similar reasons. Hence any study of Italian pitch and stringing practice is premature unless the centres of construction are known with certainty. Indeed because more than half of the surviving Italian stringed keyboard instruments are anonymous any such study would be inaccurate unless the additional information provided by the anonymous instruments, assigning their centre of origin correctly, is incorporated. The procedure outlined here provides a method for doing this and is fundamental to any such study, whether of pitch and stringing or of any other aspect of the design of such instruments.
Although the method outlined here is useful for all of the reasons indicated above, there is one further way in which its application is important. I want to show in a subsequent paper which will be published next year in this Journal that a knowledge of the size of the unit of measurement can be used as a powerful tool in the analysis and determination of the original state of an instrument that has been radically altered. In this case the analysis shows that the use of the unit of measurement, because it entered into the designer’s mind in all aspects of the construction and design of the instrument, is essential to the determination of the original case length, the original scalings, the original dimensions and compass of the keyboard, the layout of the wrestplank and nut, and the position and angle of the lower belly rail. Without a knowledge of the unit of measurement used by the maker of this instrument the determination of the original state would have otherwise been impossible.
The implications of the use of the unit of measurement in instrument design are far-reaching. An extremely exciting prospect still requiring investigation is that the unit of measurement was the fundamental factor responsible for the regional variation in pitch found throughout the Italian peninsula. One of the most commonly-heard sounds during the historical period of harpsichord and virginal building would have been, not that of a plucked string, but that of a pipe in a pipe organ. The influence that church and chamber organs had on establishing the local pitch must have been extremely important. Since these organs were, like all other objects, made using the local unit of measurement, the size of the unit must have influenced the pitch of the organ. An 8' pipe in one centre would be a different length from an 8' pipe in another because of the difference in the local unit of measurement. To what extent this factor really affected local pitch is at least very interesting and certainly requires further investigation.
Perhaps the most interesting aspect of the method, however, is that it begins to give an idea of how the makers of these artefacts thought and how they worked. It enables us to enter into the minds of the instrument makers, and shows that they worked in a very pragmatic practical way. I have found no evidence whatsoever in the work that I have done so far in this field that the makers were in any way concerned with the use of the Golden Ratio or of the numbers that make up the Golden Series. It is when one discovers that the blocks in the boxslide register of a virginal are each 5 linee in thickness, that the spacing of the jacks in a harpsichord register is exactly ˝ oncia, that the keylevers comprising the 50 notes of the C/E to f3 compass in Venetian instruments have a width of 25 once so that each keytail is exactly 6 lines in width and each natural is 10 lines in width (and that the width of the sharps and the spacing of the tails of the naturals are also based on a simple number of linee), that the tone separation in pitch of many Venetian instruments is based on the use of f2 scalings of 9 once and 8 once, etc. that one really starts to understand how makers thought. It is only then that that one begins to realise how simply and elegantly their instruments are designed.
7 November, 1998
 See John Barnes, ‘The specious uniformity of Italian harpsichords’, Keyboard Instruments, Edwin M. Ripin editor, (Edinburgh University Press, Edinburgh, 1971; reprint, Dover Publications, New York, 1977) 1-10.
 This is contrary to the evidence collected by Hubert Henkel, in the catalogue of the keyboard instruments from the Musikinstrumentensammlung of the Deutsches Museum in Munich (Besaitete Tasteninstrumente. Fachbuchreihe das Musikinstrument, Vol. 57 (Verlag Erwin Bochinsky, Frankfurt-am-Main, 1994). The evidence presented, incorrectly in my view, by Henkel is not based on the measurements of the instruments as designed by the makers: Henkel, in the Italian instruments, uses the outside case measurements and not the measurements of the baseboard without the case sides and, in the North-European instruments, the total height of the case adding the baseboard thickness to the height of the case side planks, etc. and then he seems, to me at least, to indulge in number crunching in order to make these numbers fit the numbers from the Golden Series.
 The ratio of the frequencies, or the inverse ratio of the lengths, of two notes a Pythagorean tone (major second) apart is 9/8.
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