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
Further ways in which the unit of measurement was used in the design of a virginal or harpsichord
It is not surprising that the local unit was used in the design and execution of virtually every aspect of the construction of an instrument, so that its use can be recognised in many aspects other than the baseboard and case height measurements. Some of these can, in turn, be used to extract the unit of measurement used in the design of the instrument when this is otherwise unknown.
The unit of measurement must also apply to the width and sides of the keyplank (ie. of the outer measurements of the jointed board from which the keys were cut), the balance line marked on the keyplank (ie. the distance of the balance line at the outside edges of the keyplank ignoring the added natural touchplates and the arcades), the angling of the strings, the scalings of either the c or of the f notes, etc. It is usually not at all clear what the unit of measurement is that will give simple numbers for the measurements of all of these different aspects of the construction of the instrument, and it is a stab-in-the-dark procedure to try to determine the unit for all of these different measurements in any situation, such as with a rectangular virginal or with a clavichord, where it is not possible to rely on the geometrical methods outlined above. Another hint is necessary in order to arrive at a rough value of the oncia, soldo or pollice that can then be refined as was done with the geometrical method described above.
During my analysis of a number of instruments I have noticed, at least with many of the virginals built in Venice and in centres where the oncia had a length of about 30mm, that the width of the blocks used to make the boxslide have a width of of an oncia, or of 5 linee, regardless of what the absolute size of the local oncia might be (see Figure 12). In the Italian tradition the boxslide is made up of a number of flat blocks of wood, each with two shallow recesses in them inside which the jacks move. The blocks are glued together so that the lateral spacing of the pairs of recesses corresponds to the lateral spacing of the ends of the keylevers, which is often also a simple division of the local unit of measurement. Care seems to have been taken in Venice and the other Italian centres using an oncia with a size of about 30mm to make the thickness of each of these blocks exactly 5 linee. Thus 24 such blocks would have a thickness of 24 x = 10 once. The choice of a total width of 10 once for 24 register blocks may be a throwback to an earlier period when keyboard compasses were often F,G,A - f3, four octaves without FT and GT, with 47 notes which would have required 24 register blocks. For simplicity in the design this was given a width of 10 once. Because the strings are normally parallel to the jackslots in the slightly-angled boxslide, the width of 24 register blocks can be measured simply by measuring the width of 24 complete pairs of strings (omitting one string at one end of the string band or the other for the usual C/E to f3 instruments) in a direction perpendicular to the strings. Hence measuring the width of the string band may be enough to determine the unit of measurement in the small number of instruments where this width was designed by the maker to be 10 once.
Figure 12 shows a drawing of the bass end of the boxslide register of the 1552 Marco Jadra virginal to illustrate how its construction is based on the Venetian oncia. In this case the keyboard was designed to be 25 once wide so that the 50 keytails of the 50-note C/E to f3 compass were each exactly ½ oncia wide, and so that the successive blocks containing two jackslots had a lateral spacing of precisely 1 oncia, and a thickness of of an oncia .
The boxslide register of the 1552 Marco Jadra polygonal virginal
in the Pitt Rivers Museum, Oxford, No 1948.1b1
1 Venetian oncia = 28.98mm
Needless to say the geometry of the virginal boxslide registers is not always as simple as that found in the Venetian instruments. Clearly when the local unit of measurement is markedly different from about 30mm the maker is forced to design the width of his string band and registers with other dimensions in order to avoid either an unnecessarily narrow or unnecessarily wide string band. Gianfrancesco Antegnati, working in Brescia (where 1 oncia = 39.62mm), made the total width of 24 pairs of jackslots equal to 7½ Brescian once ( per jackslot). Also Annibale de’ Rossi, working in Milan (where one oncia or pollice = 36.265mm), gave the width of 48 strings (24 jackslots) a width of 8 pollici so that each boxslide block had a thickness of = of a pollice (12.09mm). The latter measurement for the register-block width when expressed in mm is fortuitously almost exactly the same for Milan as that resulting from the use of of a Venetian oncia found above.
Staying with the 1552 virginal by Marco Jadra in the Pitt Rivers Museum, Oxford, it is clear that the Venetian oncia was used in the design of a number of the other aspects of the keyboard. Here the 50 notes of the C/E to f3 compass have a width of 25 once (see also footnotes 44 and 47). Hence the lateral spacing of the keylever tails is just ½ oncia per key. The 30 natural notes also have a width of 25 once so that each natural is of an oncia wide, or each natural is 10 linee wide, and one octave with 7 natural keys is 70 linee in width. The sharps, the c, e, f, g, a, and b keytails, and the d keytails can be shown then to have widths of 6 linee, 5½ linee and 7 linee respectively (see Figure 13 below). One octave is therefore composed of the width of the sharps = 5 x 6 linee, plus the width of the c, e, f, g, a, and b keytails = 6 x 5½ linee, plus the width of the d keytail = 7 linee, giving a total width of 70 linee, the same as that calculated using the natural fronts (see Figure 13 below).
The 25 once width of the keyboard gives rise to a 3-octave span (the width of 21 naturals) of 25 x = 17½ once. Since the Venetian oncia = 28.98mm (see footnote 10), this gives rise to a 3-octave span of 17½ x 28.98= 507mm, exactly equal to the measured 3-octave span, and a value near to that found on many other Venetian stringed keyboard instruments which are clearly using this measurement and division of the keyboard.
x = 5½ linee, y = 6 linee and z = 7 linee
A typical division of one octave in the keyboard of a sixteenth-century Venetian harpsichord or virginal when the total width of the 50-note C/E to f3 compass = 25 once
One Venetian piede = 347.76mm; one oncia = piede = 28.98mm
and one linea = oncia = 2.415mm
On the other hand there is also a number of Venetian instruments such as the Franciscus Patavinus virginal and the 1568 virginal also by Marco Jadra in the Victoria and Albert Museum, London which have a keyplank that was designed to be 24½ once in width instead of the 25 once as above. This gives rise to a three-octave span of 24½ x x 28.98mm = 497mm, a value also found to be close to the measured values for these instruments. Marco Jadra is not alone in occasionally using different measurements for the keyplank width of his instruments, giving rise to different consequent measurements of the 3-octave span. Clearly the three-octave span of an instrument is not a characteristic of a maker since the same maker sometimes used different values for this measurement. The use of the words Stichmaß and standard measure for this width is clearly inappropriate since the width of the octave, of 3-octaves or the total width of the keyplank cannot in any way be considered standard or characteristic of a maker. Rather, the different sixteenth-century Venetian makers using the common 50-note C/E to f3 compass, for example, practically all begin the design of their instruments by making the total keyplank width either 24½ or 25 once. Therefore the measured 3-octave spans of 479mm and 507mm resulting from these keyplank widths are characteristic of Venice and not of the individual makers working there.
Clearly the string scalings themselves were designed using simple values of the local unit of measurement, and a number of examples of this have already been seen incidentally in the consideration of some of the instruments discussed above. These string measurements were often designed using whole integers of the unit of measurement and not integers plus complicated fractions. This suggests that the makers were using simple, easy-to-remember numbers, and were not necessarily concerned with the subtleties of taking the strings as close as possible to their breaking point by choosing complicated fractional numbers in the design of their string scalings. In Venice, for example, the instruments of Ioannes Celestini, Dominicus Pisaurensis, Benedetto Floriani, etc. use either integral or half-integral numbers of the Venetian oncia as the basis of their string-scaling design. I have been able to show that two of the instruments of Marco Jadra, a virginal of 1568 in the Victoria and Albert Museum and the other a virginal of 1552 in the Pitt Rivers Museum, Oxford were separated in pitch by a tone (major second) or, using my usual convention, by R + 2. In this case the design of the instruments separated in pitch by this amount is particularly elegant and simple since the f2 scalings were based by Jadra on 9 once and on 8 once, the Pythagorean ratio between the string lengths of two notes a tone apart being simply !
Another aspect of the use of the unit of measurement in the investigation of the history of an instrument can be illustrated from the analysis of the design and construction of the anonymous single-manual Italian harpsichord in the Royal College of Music in London, Catalogue Nº RCM 175. Calculation of the unit of measurement used in its construction in a way similar to that used for the Yale University Bolcioni harpsichord makes clear that the instrument was designed and built using the Neapolitan oncia = 21.736mm. The instrument was modified a number of times before it was given its present state. Many features, such as the moulding on the top of the present nut, the use of separate upper and lower guides instead of boxslides, the shape of the moulding on the outside edges of the upper guide, the construction and guiding system used for the keyboard, etc. are typical of those found on instruments by the Florentine makers Bartolomeo Cristofori and his pupil Giovanni Ferrini. But is there evidence that the Florentine soldo was used in the construction of any of the components of the present state of this instrument which would help to link it to Florence and a Florentine workshop?
The present two registers have a moulding on their outside edges which is characteristic of the work of Cristofori and Ferrini, and seems to be from their workshop. Hence, as these two both worked in Florence, the registers should have been constructed using the Florentine soldo. To check this the spacing of the jackslots along the register was measured.
Figure 14 shows a graph of the jackslot spacing of the front register of RCM 175. Here the distance from the spine of the instrument to the edge of each jackslot is plotted against the note sounded by the jack whose jackslot is being measured. The more-or-less uniform spacing of the jackslots gives rise to a straight-line plot whose mathematical characteristics can be calculated using normal statistical analysis.
Spacing of the jackslots using the Florentine soldo
Anonymous Italian single-manual harpsichord, Naples, c.1650
Royal College of Music, London, Cat. No. 175
The usual linear regression analysis by the method of least squares gives a correlation coefficient for this data of r = 0.9999936 indicating a very good fit of the measured data to a straight line. The calculated slope of the line is m = 13.7675mm/jackslot with a standard deviation error of only 0.0101 (0.07%).
This slope = 13.7675mm/jackslot is equivalent to 0.50005 soldi/jackslot, based on the Florentine soldo of 27.532mm found in reference tables. This therefore appears to be a spacing of exactly 50 jackslots in 25 soldi:
Using this to calculate the soldo gives:
This compares with the value given by Colonel Cotty for the braccio divided into 20 soldi of 550.64mm, of 1 soldo = = 27.532mm. This is only 0.01% different from that estimated here and strongly suggests that the register slots were indeed cut out by designing them to be exactly ½ of a Florentine soldo apart.
It would be an incredible coincidence, therefore, if the instrument was not altered in Florence. The use of the Florentine soldo and braccio in the design of the registers, and the similarity of the construction features of the added and altered parts to those normally found on the instruments of Cristofori and Ferrini gives additional strength to the argument that the instrument was indeed given its present final state by one of these two builders who both worked very much in the same tradition. This is then further confirmed when the Florentine soldo is applied to the dimensions of the keyplank from which the keyboard was cut (also made in the style of Cristofori and Ferrini), to the altered string scaling design, etc. all of which were clearly designed in simple units of the Florentine soldo. This, in addition to the many other characteristics, make it almost a certainty that one of these two makers had a hand in the re-working of this instrument.
Needless to say the size of the soldo found for this instrument re-worked in Florence by Cristofori or Ferrini is the same as the soldo found for the two Bolcioni instruments built entirely in Florence and discussed earlier in this paper.
 The angling of both the balance line and the rear of the keyplank of a virginal effectively provides two further angles and measurements and, from them, possible estimates of the unit of measurement for the instrument being studied. This aspect is not elaborated here but provides yet another example of how an initial estimate of the unit of measurement could be obtained.
 In most of the North-Italian centres the unit of measurement is usually around 27 to 32mm. However in Rome, Naples and Sicily, and in such northern centres as Genoa and Mantua, for example, where the oncia was only 18 to 21mm, the blocks of the boxslide would have to be more than of an oncia thick, otherwise the strings would be placed uncomfortably close to one another and to the jacks. See Appendix 2 at the end of this paper. The use of the oncia in the design of the blocks of the boxslide registers in Brescia and Milan where the size of the unit of measurement was greater than 32mm is elaborated briefly below.
 For example, in many sixteenth- and early seventeenth-century Venetian virginals, the width of the 50-note C/E to f3 keyboard plank was designed to be 25 once. See footnote 47.
 In fact almost all of the surviving virginals of Gianfrancesco Antegnati working in Brescia in about 1550 have or originally had this F,G,A to f3 compass. Antegnati uses 24 register blocks each with 2 slots in them, and leaves the second jackslot between the ends of the F and G keylevers unused.
 Illustrated in Francis W Galpin, Old Instruments of Music, (Methuen, London, 1910) p. 124, plate XXIII. My thanks to Hélène La Rue for her co-operation and help in allowing me to examine this instrument.
 The width of the keyplank of this virginal is 724mm = = 24.98 once, obviously meant to be 25 once.
 See further my article, ‘Marco Jadra. A Venetian harpsichord and virginal builder?’, Gedenkschrift für Kurt Wittmayer, to be published in 1999 and edited by Silke Berdux referred to already in footnote 9.
 In Milan the subdivision of the piede was called either the oncia or the pollice (the thumb).
 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. My thanks to James Yorke, Assistant Curator of Furniture and Woodwork at the Victoria and Albert Museum for his co-operation and assistance in allowing me access to this instrument.
 The keyboard based on a keyplank width of 24½ Venetian once would not have keyfronts and keytails and octaves divided in a simple way like that of the 25 once keyboards. However it would be a simple matter of using a geometrical project of the 25 once design to give a keyboard with a width of 24½ once and with all of its other width dimensions in proportion both at the keyfronts and at the keytails.
 See Howard Schott, in the reference given in footnote 50.
 See my article, ‘Marco Jadra. A Venetian harpsichord and virginal builder?’, Gedenkschrift für Kurt Wittmayer, to be published in 1999 and edited by Silke Berdux already referred to in footnote 9.
 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
 See footnote 46.
 According to a number of different sources in Appendix 2 at the end of this paper the oncia in Naples had a length close to 21.81mm.
 These modifications are outlined in an unpublished restoration report by John Barnes held by the Royal College of Music.
 My thanks to Orestis Papasouliotis of the STATLAB Statistics Laboratory at the University of Edinburgh for his help in the determination of the accuracy of these results. Here, to calculate the standard deviation error, it was assumed that the error of measurement was 0.1mm, that the error in marking out and cutting the register slots by the re-builder was 0.1mm so that the total error in the position of each slot was 0.2mm.
 See Colonel Cotty, Aide-Mémoire a l’usage des officiers d’artillerie de France, 2 (Paris, 1819) 896-7.
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