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
Limitations of the method and words of caution
The methods described above used to ascertain the unit of measurement are only one aspect of the determination of the centre of construction of a harpsichord or virginal, and only one aspect of establishing the maker of an anonymous instrument. In order to be certain of the authorship of an otherwise anonymous instrument it is necessary to compare such factors as the methods of workmanship, the materials, the case mouldings, the string scalings, and the unit of measurement used in the instrument’s design and construction. One of these features on its own is not enough.
The use of the unit of measurement in this analysis does of course rely upon the accuracy and reliability of the sources from which the lengths of the units of measurement have been taken. Many of the sources are derivative and simply repeat the measurements given by earlier authors. The original need for the publication of these tables of measurements arose chiefly as a result of meftrification imposed by law in the period between the Napoleonic invasion and the Unification of Italy, and the resulting need to relate the old units of measurement to the metre in the period in which modern Italy gradually took on a united nationhood. However by this time, and indeed during this period, legislation had changed the sizes of a number of the units of measurement somewhat from those used in the historical period of harpsichord building. For example in Tuscany, including Florence, the length of the braccio was altered as a result of legislation passed on 2 July, 1782. Also a law was passed on 6 April 1840 in Naples which increased the length of the palmo and the other local units of measurement by about 0.3338%, a small but significant amount. Some sources published after 1840, such as Ludovico Eusebio using the ‘decimalised’ palmo, and the anonymous author of the article ‘Misure’ in the Grande dizionario enciclopedico, give the later value of the length without taking into consideration the value before 1840. Most of the sources, however, even when published after 1840 give the pre 6 April 1840 value of the palmo and canna in Naples. It is therefore clear that great care has to be taken when using the published tables of measurements when making ascriptions based on them. This applies especially to the Southern area of Naples and Sicily which were sometimes separate and sometimes united in the “Regno delle due Sicilie” during the historical period. An instrument which apparently uses the Sicilian measurement may well have been made in Naples using the Neapolitan unit, and vice-versa.
Are we to trust the surprises thrown up as a result of the use of these tables? A good example of one such surprise is provided by a fine anonymous single-manual harpsichord, part of the collection of the Civici Musei Veneziani d’Arte e di Storia, in the Ca’ Rezzonico in Venice. This is a separate inner instrument in an outer case, and is extremely long having a spine measurement of 2505mm. The compass is G1,A1 to c3, and it has an elegant-looking keyboard with skunktail sharps and inlaid ivory decoration in the ebony-topped naturals. One of the most characteristic features of this harpsichord is the way in which all of the case and jackrail mouldings and the nut and bridge have been ebonized, thus accentuating the line and form of the instrument (see Figure 15). Unlike many Italian harpsichords which have one register fixed in position so that its jacks are always plucking its set of strings, both registers are movable and can be operated using a sophisticated hidden stop-lever mechanism. Incorporated into the design of the keyblocks on either side of the keylevers are small ebony buttons which operate iron rocker bars connected to the registers. Moving the ebony buttons from side to side engages and disengages the corresponding register. This system has been carefully worked into the design of the harpsichord and is also an individual and characteristic feature of this instrument.
Beginning with the angle of the tail of this harpsichord in the usual way described above it is clear from the baseboard and case-height measurements that the maker of this instrument was using an oncia with a length close to 29.37mm. Although close to the Venetian oncia of 28.98mm it is clear that the Venetian unit does not apply to this instrument. A number of the other measurements of the instrument such as the width and height of the internal core of the jackrail, the distance from the top of the soundboard liner to the top of the case sides, the height of the lower outside case moulding, the keyplank dimensions and the position of the balance pin line on the keyplank, etc. can also be shown to have been designed and measured out using this same oncia unit. The length of the piede with 12 once used by the maker of this instrument would therefore have been 12 x 29.37mm = 352.44mm.
The only important centre in Italy which used a unit of length near to this measurement during the period in which this instrument was built was Urbino. The piede in Urbino had a length near 353.5mm, making the oncia there 29.46mm only 0.3% different from the value obtained deriving the length of the unit of measurement from the instrument. This therefore suggests that Urbino may have been the centre in which this harpsichord was built. However, no stringed keyboard instrument maker is known to have worked in Urbino. Was the instrument therefore really made in Urbino? It has many individual and highly characteristic features such as the ebonized mouldings and bridges, the use of mother-of-pearl and ivory in the panelling of the nameboard, and the ingeniously-hidden stop-lever mechanism, all of which suggest that it came from a tradition with clearly-defined attributes not normally found in any other tradition. The possibility that this instrument is a unique example of harpsichord making in Urbino, perhaps characterised by these features, is at least a sufficient cause for instigating archival work in Urbino to see if there is any evidence for stringed keyboard instrument making there in the seventeenth century.
Schematic representation of the case mouldings, the jackrail section,
and the bridge section at the position of the c2 bridge pin.
The ebonized sections are indicated with shading.
Anonymous single-manual harpsichord, ?Urbino?, c.1630
Ca’ Rezzonico, Venice
The geometrical method of estimating the local unit of measurement from the tangent of the corner angle of a polygonal virginal or the tail angle of a harpsichord fails completely if the angle is 45º. In this case the tangent (tan 45º = 1) does not suggest two unique small simple numbers from which the local unit can be estimated: here any two numbers are possible, all of which have a ratio to one another of 1! This seems at first like a great failing of the method, but so far I have encountered this problem only once, and then only for the right-hand front corner angle of a polygonal virginal - the left-hand front corner was not 45º and enabled an estimate of the local unit to be made.
In all cases discussed so far it has been the tangent of the corner or tail angle that was used to estimate the local unit of measurement and indeed was that used in the design of the instruments being studied. However in the single-manual harpsichord by Onofrio Guarracino dated 1651 the tail angle is clearly 30º. The tangent of 30º is 0.57735…, an irrational number not composed of the ratio of two small simple numbers. However the sine of 30º is exactly 0.5000, suggesting that the two sides used by Guarracino to construct the tail angle were the side of the tail itself and the component of this side opposite the tail angle. Indeed this is found to be the case and the lengths of these two sides suggest an oncia = 21.61mm close to the oncia used in the other instruments by Guarracino. Clearly then it is not always the tangent of the angle that was used, and the reader must accept that the sine and perhaps the cosine were also used. Nonetheless the method of estimating the local unit of measurement remains the same.
Another potential limitation of this method is the inaccuracy of normal handworking methods. The method is relatively insensitive to this problem. With a large protractor it is possible to estimate the corner angles to within less than ½ of a degree. An error of ½º in an angle does not normally make enough difference to the value of the tangent for the usual tail or virginal corner angles in the range of 30º - 60º to lead to the wrong estimate of the initial value of the ratio of the lengths of the two orthogonal sides of the triangle making up the angle. Hence the initial estimate of the unit of measurement is unaffected by a small error in the maker’s construction, or the researcher’s measurement, of this angle. However if there is a large error in the angle resulting from the handworking methods, then a false estimation of the unit of measurement can result. An example of this problem occurred in the analysis of an apparently well-made anonymous polygonal virginal in the collection of Marlowe Sigal of Boston, Massachusetts. An analysis of the raw measurements of the lengths and corner angles of the baseboard of this virginal suggested initially that it was made in Florence. However the instrument is clearly of Venetian origin from the style and materials of its construction. But if it is assumed that the maker of this instrument removed 3mm too much from the left corner during the finishing of the baseboard, then the angle at this corner changes, the components of the angled side change, the overall length changes and the distance of the bass end of the keywell to the left corner of the instrument changes. If the missing 3mm are added to all of these, then the calculations of the local unit of measurement used to construct this virginal give a clear indication that Venice was indeed the centre in which it was built. This is a good example of the blind use of only one method to assign a centre of construction or maker from only one of the many features of an instrument which must be invoked during the process of authentication.
The rough estimate of the unit of measurement obtained by assuming a width for one register block of of an oncia in virginals does give a unit that applies to the other measured lengths in a number of instruments. However, not surprisingly, it does not apply to all instruments and all makers. As mentioned above it does not apply in regions where the unit is considerably smaller or larger than 30mm. Therefore this way of determining the unit of measurement for rectangular virginals is, as suggested previously, only one method of approach in the determination of the unit of measurement.
The method of using the geometry of a corner angle of a virginal or the tail angle of a harpsichord described here appears to fail completely for rectangular instruments such as rectangular virginals and clavichords where there are no obvious corner angles to be used. However, because the lengths of the sides of the baseboards of such instruments were usually measured out in whole numbers of the local unit, my limited experience with such instruments so far suggests that the ratio of the sides of the baseboard itself can be used. When measured out in millimetres and when used in conjunction with the tangent of the angle of either diagonal of the rectangular baseboard, an estimate of the size of the unit of measurement can be obtained in the usual way although the numbers involved are clearly much larger than those found for the corner angles of virginals or for the tail angle of a harpsichord. Also, usually there are angled components in these instruments (such as the wrestplank, for example) which can be used in addition to give and initial estimate of the unit of measurement.
In addition a word of caution has to be added to allow for an occasional inability to distinguish two or more centres because their local units of measurement are either very similar or the same, or because they are in a simple proportion to one another. Again additional features must be examined in order to establish the centre of origin of the instrument. Fortunately, however, the sizes of the units of measurement in the Italian Peninsula are quite widely spaced and spread over the range of about 18 to 58mm so that the determination of the unit of measurement leads to a clear conclusion about the region in which the instrument was built.
 See Angelo Martini, Manuale di metrologia, (E. Loescher, Turin, 1883; reprint Editrice Edizioni Romane d’Arte, Rome, 1976) 206.
 See Giovanni Gandolfo, Tavole di ragguaglio ovvero prontuario di compiuti fatti di pesi, misure e monete legali italiane, (Naples, 1860) 12-17.
 Compendio di Metrologia Universale e Vocabolario Metrologico, (Unione Tipografico Editrice Torinese, Turin, 1899; reprint by Forni Editore, Bologna, 1967).
 Anonymous author, Grande dizionario enciclopedico, 12 (Unione Tipografico-Editrice Torinese, Turin, 1970) 626.
 A study of this harpsichord was made as part of the same project for the Civici Musei Veneziani d’Arte e di Storia as noted in footnote 11. The Museo Correr holds an unpublished report entitled Cembalo italiano anonimo ad una tastiera dalla Ca’ Rezzonico by me on this instrument.
 Giovanni Croci, Dizionario universale dei pesi e delle misure in uso presso gli antichi e moderni con ragguaglio ai pesi e misure del sistema metrico, (The Author, Milan, 1860), the anonymous author of the Tavole di ragguaglio fra le nuove e le antiche misure….della Repubblica Italiana pubblicate per ordine del Governo, 2 (Milan, 1809), L. Malvasi, La metrologia italiana ne' suoi scambievoli rapporti desunti dal confronto col sistema metrico-decimale, (Fratelli Malvasi, Modena, 1842-44) and Luigi Pancaldi, Raccolta ridotta a dizionario di varie misure antiche e moderne coi loro rapporti alle misure metriche…, (Sassi, Bologna, 1847) give values of the piede in Urbino between the narrow limits of 353.37mm to 353.793mm, so that the oncia had a value close to 29.46mm.
 This occurs in the 1568 polygonal virginal by Marco Jadra in the Victoria and Albert Museum, London. See: Howard Schott, Catalogue of Musical Instruments. Volume 1 - Keyboard Instruments. Victoria and Albert Museum, (Victoria and Albert Museum, London, 1985) Museum No. 155-1869, pp. 24-5. This instrument is discussed in detail in my article ‘Marco Jadra. A Venetian harpsichord and virginal builder?’, Gedenkschrift für Kurt Wittmayer, to be published in 2004 and edited by Silke Berdux, and referred to already in footnote 9.
 This instrument is in private possession in Rome. The date of the instrument is not entirely clear: it is either 1651 or 1657. My thanks to Andrea di Maio for bringing this instrument to my attention and for supplying me with information about it. This instrument is not listed along with the other instruments signed by Guarracino in Donald H Boalch, Makers of the Harpsichord and Clavichord, 1440-1840, (Third edition, edited by Charles Mould, Clarendon Press, Oxford, 1995) pp. 343-6.
 The study of this instrument and a number of other harpsichords that can be shown to be by Guarracino will form the subject of a paper currently in preparation.
 This study, like many others involving an examination of the fruits of human endeavour, is scattered with pitfalls. The polygonal virginal in the Victoria and Albert Museum, London by Gianfrancesco Antegnati (Inv. No. 490-1899) has a measured angle of 60º at its front right-hand corner, suggesting that Antegnati may have been using the cosine of 60º = 0.5000 to construct the right-hand sloping side. However, comparison with other instruments by Antegnati from which the size of the oncia that he was using can be calculated shows that the perpendicular and parallel components of the angled right-hand side have lengths of 9 and 5¼ once. Here it is fortuitous that tan 59.75º = = 1.714. In other words, the fact that the measured angle was 60º (actually 59.75º) does not, in this case, mean that the sides involved in the cosine of 60º were being used in its design. It is still the orthogonal components of the sloping side and therefore the tangent being used in the usual way.
 I would like to express my thanks to Marlowe Sigal for his help in measuring this instrument prior to its analysis by me.
 Both the piede manuale and the piede liprando with an once = 42.81mm were used, because of the political affiliations in the period of the Savoy, in both Genoa (Liguria) and Turin (Piemonte). Also there is an coincidental similarity in the oncia of the Genoese piede and the oncia of the Roman palmo mercantile both of which are close to 20.75mm.
 Reference has already been made in footnote 6 to a situation in which the centre of construction of an instrument is made uncertain because the units of measurement used in two cities are in the simple ratio of 3 to 4.
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