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

 

Grant O'Brien

 

A virginal by Marcus Siculus

          A very fine sixteenth-century Italian virginal signed:  "• MARCVS • SICVLVS • FACIEBAT • MDXXX •", with vinework arabesques at the ends of the signature[17], is to be found in the Benton Fletcher Collection of Early Keyboard Instruments housed in Fenton House, Hampstead in London.  At first glance, except for the keywell scrolls, the virginal by Marcus Siculus is superficially similar to many Venetian virginals (see a schematic representation of the keywell section in Figure 6).  However, it is clear from the measurements of its case and baseboard given in Table 3 that the Venetian oncia was not used in its design.  But if the instrument was not made in Venice how can we find the length of the oncia used by Siculus, and from this determine the centre where it was made and therefore where Siculus lived and worked?  Out of the continuum of possibilities for the value of the oncia used by Siculus, some method is needed first of all to make an educated guess at a rough value of the length of the oncia he used, and then to refine this further.

 

 

 

Figure 6 - A schematic representation of the keywell section, bridges and jackrail

Polygonal virginal by Marcus Siculus, 1540

Fenton House, Hampstead, London, Acc. Nº FEN/I/5

 

 

                                                                                                 Length:     1269

                                                                                                  Width:     332½

                                                                      Case left of the keywell:     242

                                                                                  Angled left side:     143

                                                                                 Angled left back:     752½

                                                                                                    Back:     275

                                                                                Angled right side:     396

                                                                    Case right of the keywell:     296

                                                                                               Keywell:     731

                                                                                 Keywell projects:     111

                        Left-hand corner:       54 parallel to the front;  130 perpendicular to the front. Corner angle = 67½°

                      Right-hand corner:       216 parallel to the front;  332½ perpendicular to the front  Corner angle = 57°

Table 3 - Measurements in mm of the baseboard without the case sides

Polygonal virginal by Marcus Siculus, 1540

Fenton House, Hampstead, London, Acc. Nº FEN/I/5

 

          The process of determining the unit of measurement used by Siculus begins by looking at the geometry of the near left-hand corner.  The tangent of the angle at this corner gives the ratio of the sides used to construct the corresponding angled side of the instrument. 

          For this virginal the angle at the near left-hand corner is 67½°.  Therefore:

 

          tan 67½° = 2.414

Also the lengths of the sides forming this angle (see Table 3) were measured and found to be 130mm and 54mm.  Thus  = 2.407, a value which, as expected, is close to the tangent of the angle there.

          A quick glance at a slide-rule[18] shows that 6/2.5 = 2.400 and suggests that the lengths of these two sides might have been designed to be 6 once and 2½ once.  This suggests that 130mm = 6 once so that there would be  = 21.67 mm/oncia and that 54mm = 2.5 once so that there would be  =  21.6 mm/oncia.  At the other corner of the instrument the measured angle is 57º and the tangent of this angle is therefore tan 57º = 1.540.  The sides making up this angle have measured lengths of  332½mm (the width of the baseboard) and 215mm so that their ratio is  which, again as expected, is close to the value of the tangent there.  A further glance at the slide rule shows that these are both close to  suggesting that the two sides were designed to be 15½ once (= 332½mm) and 10 once (= 210mm).  These all suggest a length for the oncia which can then be used for the other measurements of the instrument.  The calculation of the size of the oncia are shown in Table 4 below:

 

 

                                                                                         Measurement          Local                         Length of

                                                                                                     in mm          unit                             oncia

                  Component of left corner parallel to front:                       54    =    2½ once                   »   21.60

        Component of left corner perpendicular to front:                     130    =    6 once                     »   21.67

                                                             Length of front:                   1269    =    59 once                    »   21.508

                                                          Baseboard width:                  332½    =    15½ once                 »   21.451

                                                Case left of the keywell:                    242    =    11¼ once                 »   21.511

                                                                              Back:                     275    =    12¾ once                »   21.569

                                              Case right of the keywell:                     296    =    13¾ once                »   21.527

                                                                         Keywell:                     731    =    34 once                  »   21.500

                                                            Keywell projects:                    111    =    5once                   »   21.484

                                                            Back at the right:                    215    =    10 once                    »   21.500

                                                              Back at the left:                    778    =    36¼ once                 »   21.462

                                         Maximum case sides height:                  171½    =    8 once                     »   21.438

                                                                                Total:                4605    =    214once   Average:  21.502mm

Table 4

The calculation of the local unit of measurement

Polygonal virginal by Marcus Siculus, 1540

Fenton House, Hampstead, London, Acc. Nº FEN/I/5

 

 

          This is very close to the value of the oncia for Sicily/Palermo[19] where one palmo had a length of 257.8mm giving an oncia of 21.483mm (the difference is only 0.09%) or, using other sources for Palermo in Sicily[20], the oncia had lengths which varied between the narrow limits of 21.483mm and 21.611mm.[21]  The measurements of the baseboard of the 1540 Siculus virginal are shown in Figure 7 in millimetres in the top part of the diagram and in units of the Sicilian oncia in the bottom part of the diagram. 

 

 

Figure 7

Measured angles in degrees and dimensions in mm (above), and

nominal angles and measurements in Sicilian once (below) of the baseboard

1 oncia = 21.502mm

Polygonal virginal by Marcus Siculus, 1540

Fenton House, Hampstead, London, Acc. Nº FEN/I/5

 

 

          Clearly the virginal was made in Sicily, probably in Palermo, using the Sicilian oncia.  But then the name SICVLVS means “from Sicily”, so that the region in which the maker was working was really staring us in the face the whole time!!

          The design of the instrument naturally did not stop with the baseboard and case height.  The measurements of the string scalings are shown in Table 5 below[22] and are plotted in the graph of Figure 8.  Here it is clear that the string lengths have a simple Pythagorean design based on f1 = 20 once from middle f1 to f3, and that the lengths of the f strings for the part of the compass below f1 were also designed by Siculus using simple whole numbers of Sicilian once.  The figure shows the basis of the string scaling design of this instrument in a particularly graphic way.

 

 

                                                                                  String Length

                                                                    Measured                 Nominal

                                                                         mm                  mm        once

                                                          f 3            107                107.5         5

                                                          c3            143                                  

                                                          f 2            215                215.0        10

                                                          c2            301                                  

                                                          f 1            431                430.0        20

                                                          c1            575                                  

                                                           f             794                795.6        37

                                                           c             969                                  

                                                        E/G#       1042                                 

                                                       D/G#       1070                                 

                                                          F            1077              1075.1       50

                                                        C/E         1100                                 

Table 5

The original string scalings after correction

Polygonal virginal by Marcus Siculus, 1540

Fenton House, Hampstead, London, Acc. Nº FEN/I/5

 

 

 These scalings are plotted in the graph shown in Figure 8 below:

 

Figure 8

The string scalings

The straight line indicates Pythagorean scalings based on f1 = 20 Sicilian once = 430.04mm

Polygonal virginal by Marcus Siculus, 1540

Fenton House, Hampstead, London, Acc. Nº FEN/I/5

 

          The analysis of the case geometry and dimensions, and of the strings scalings of the virginal by Marcus Siculus therefore provides a sort of internal consistency and proof of the validity of the method used to find the length of the unit of measurement of the maker and, in turn, of the centre in which the instrument was made.  It also shows the usefulness of the method to our understanding of how the string scalings (and other features such as the dimensions of the keyplank from which the keylevers were cut, the keyplank balance-pin line, the plucking points of the f notes, all not shown here) were designed.  But clearly it is possible with totally unsigned and anonymous instruments to carry out the same method to enable the determination of the unit of measurement and from the city or region in which the maker who designed the instrument lived and worked.

          For example, using this method the calculation of the unit of measurement used in the design of an anonymous polygonal virginal (MS-60) in the Händelhaus in Halle[23] resulted in the conclusion that it was also built using an oncia of 21.5mm.  This immediately suggested first, that the instrument was made in Sicily and second, that Siculus might also have been the maker of this instrument.  The instrument in Halle is larger and the string scalings suggest that it was probably designed to sound a tone lower than the Siculus virginal in Fenton House in London.  Comparison of the mouldings and the construction methods and materials showed that, although the unit of measurement used not only for the baseboard and case sides but also for the keyboard and string scalings was clearly the same, many of the other features were totally different.  The mouldings were different both in their details and also in their general style.  The handling of the case framing, the woods used and the jackrail support system are totally different in the two instruments, making it highly unlikely that they are actually by the same maker.  Nonetheless it is still important that the maker of Halle MS-60 can be said also to have lived and worked in Sicily where, although they occur in instruments by different makers, two pitches a tone apart must have coexisted in a way similar to that of most of the other major centres in Italy.

          Another example of the use of this method involves the instruments of Ignazio Mucciardi, about whom there is also no biographical information.  A similar analysis of the unit of measurement used in the design and construction of the instrument in private possession in Salerno about 40 km. Southeast of Naples[24] and attributed by me to Mucciardi[25], and of the single-manual harpsichord in the Museo Nazionale di Strumenti Musicali in Rome among others[26], shows that these instruments were built using the Neapolitan oncia.  This strongly implies that Mucciardi must have lived and worked in or near Naples, in the area where the Neapolitan oncia was being used.  The fact that the Salerno harpsichord was once owned by Sant’Alfonso, who founded the order of the Padri Redentoristi and who died in 1780 (the year in which the harpsichord in Rome was built) suggests that Mucciardi must indeed be from Naples, or possibly from Salerno.  Mucciardi is a very common Neapolitan surname, and an archival search for biographical details of Mucciardi would, based on the information I have found from an analysis of the unit of measurement used in these instruments, have to begin in Naples or the surrounding area.  A recent article published by Francesco Nocerino on harpsichord building in Naples[27] identifies a Pasquale Mucciardi who was active in Naples in September of 1780.  It seems highly likely therefore that Ignazio and Pasquale Mucciardi were both active in Naples in the same period and that they were probably related.  The signature on the Rome instrument which reads “Ignazio Mucciardi nipote del ? ‑ ‑ ? fecit 12 Giugno  1780” suggests further that the illegible part of the signature might read “Pasquale”[28], and that Ignazio was the grandson or, more likely, the nephew[29] of Pasquale Mucciardi.  Clearly without the determination of the unit of measurement used in these instruments it would be impossible to know where to begin a search for information about Ignazio Mucciardi, and indeed it would not have resulted in the knowledge that there was a harpsichord-building tradition in the Mucciardi family in Naples.

 

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Endnotes:

[17] Raymond Russell, Catalogue of the Benton Fletcher Collection of Early Keyboard Instruments at Fenton House, Hampstead, (Faber and Faber, London, 1957; revised London, 1969) 11.  Russell casts doubt on the reliability of the signature on this instrument, but I can see no reason to question it.  The instrument bears the accession number FEN/I/5.  I would like to thank Mimi Waitzman, of the Benton Fletcher Collection for her permission to examine and measure this instrument, and for her help in carrying out my examination.

[18] The ratio here is fairly simple and the size of the components in local units used to make it up are fairly obvious.  But when the ratios are more complicated, as they are at the right-hand corner of this instrument for example, then I know of no other better method of determining the two numbers that give rise to the ratio involved than using a slide rule.  In fact the initial use of a slide rule to determine the ratio of the lengths of the component sides of the triangle making up the corner is essential to the analytical process of determining the unit of measurement used to design and construct the instrument.  By setting the slide rule to the value of the ratio determined either from the tangent or directly from the measured lengths of the components used to make up the diagonal side, and then looking for the simplest numbers that make up this ratio, it soon becomes clear what these component lengths are in the local unit of measurement.  A circular slide rule is particularly convenient for carrying out this procedure.

[19] L. Malvasi, La metrologia italiana ne' suoi scambievoli rapporti desunti dal confronto col sistema metrico-decimale, (Fratelli Malvasi, Modena, 1842-44).

[20]See Appendix 2 at the end of this paper.

[21] An oncia of length near 20.17mm based on a palmo = 242mm seems also to have been used in Sicily (see Appendix 2 at the end of this paper).

[22] These have all been corrected for a modern re-pinning of the bridges to compensate for a sideways movement of the strings caused by case distortion resulting from the string tension.

[23] See:  Konrad Sasse, Katalog zu den Sammlungen des Händel-Hauses in Halle.  5.  Musikinstrumentensammlung - Besaitete Tasteninstrumente, (Händel-Haus, Halle an der Saale, 1966) 28-9.  I would like to express my thanks to Christiane Rieche who allowed me to examine this instrument, and to Stephan Ehricht who gave assistance in many ways including taking the moulding shapes of this instrument for me.

[24] A detailed report on this single-manual harpsichord prepared by me in 1997 is held by the Padri Redentoristi, Convento di Pagano, Salerno.  The instrument is believed to have belonged to St Alfonso, founder of the Padri Redentoristi.  It was bought by him and was in his possession at the time of his death in 1780.

[25] This attribution is based on the similarity in the construction methods, such as the use of diagonally-placed soundboard wood, the use of wedge-shaped pieces of bone in the ebony inlay of the sharps, the use of a panelled nameboard with inlaid decoration, the size of the bridge-, hitch- and tuning-pins, and upon the similarity in the shape of the decorative mouldings and the natural key arcades.  I have no doubt that Mucciardi made the Salerno harpsichord.  Only one harpsichord, in the Museo Nazionale degli Strumenti Musicali in Rome, is signed by Mucciardi and is referred to in footnote 26.  At least three other instruments can be attributed to Ignazio Mucciardi on a similar basis.  The other instruments are also all single-manual instruments and are all built in the same style.  The instrument in the collection of Dr Rodger Mirrey, Paddington, London, England has a compass of G1,A1 to f3, and has a keyboard with boxwood naturals and with black and white sharps decorated in the same manner as the Salerno and the Rome instruments.  The key arcades have not survived on this instrument.  It also has a soundboard constructed with a sloping grain, and with a similar internal construction.  It uses the same unit of measurement as the Rome and Salerno harpsichords (the owner holds a copy of a report by me analysing the unit of measurement used in the design of this instrument).  Another harpsichord attributed by me to Mucciardi is in the Museum of Cultural History in the Smithsonian Institution, Washington, D.C. (Inv. No. 326,903).  This instrument bears the false signature “Johannes[sic] Antonius Baffo Venetus F MDLXXXI”).  It also has a compass of G1,A1 to f3 and similar construction characteristics.  Another instrument by Mucciardi is a single-manual bentside spinet in the Musikinstrumenten Museum in Berlin (See Dagmar Droysen-Reber and Horst Rase, ‘Historische Kielklaviewre bis 1800.  Beschreibung der Instrumente, Teil I’, Kielklaviere.  Cembali, Spinette, Virginale, General editor Dagmar Droysen-Reber, (Staatliches Institut für Musikforschung Preußischer Kulturbesitz, Berlin, 1991) Cat. No.  2216, p. 171-4).  This instrument also has a compass of G1,A1 to f3.  The Berlin spinet is not ascribed to Mucciardi in the new Berlin catalogue, but many features of its construction and decoration are clearly the same as those usual on the other Mucciardi instruments, such as the white wedge-shaped inlay in the top of the sharps, the panelled nameboard inlaid with black and white decoration, etc.  From the information available in the Berlin catalogue it is also clear that the same size of oncia was used in its construction as in the Salerno, Rome and Mirrey harpsichords.

[26] This instrument is not listed in Maria Luisa Cervelli, ‘Per un catalogo degli strumenti a tastiera del Museo degli Antichi Strumenti Musicali’, Accademie e Biblioteche d’Italia, 44, Nº 4-5 (1976) 305-43, but see Maria Luisa Cervelli, La Galleria Armonica, (Istituto Poligrafico e Zecca dello Stato, Rome, 1994) 279.  This instrument was restored by me in 1980, exactly 200 years after it was built and signed “Ignazio Mucciardi nipote del ? ‑ ‑ ? fecit 12 Giugno  1780”.

[27] Francesco Nocerino, ‘Arte cembalaria a Napoli.  Documenti e notizie su costruttori e strumenti napoletani’, Ricerche sul ’600 napoletano.  Saggi e documenti 1996-1997, (Electa Napoli, Naples, 1998) 85-109.

[28] See footnote 26 above.  The word “Pasquale” would fit perfectly into the amount of space occupied by the illegible part of the signature with the spacing of the handwriting of the rest of the inscription.

[29] In Italian the word nipote can mean either grandchild or nephew/niece.

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