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

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[42]
(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[43]
(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[44].
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 - f^{3}, four octaves without F^{T} and G^{T}, with 47 notes which
would have required 24 register blocks[45]. 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 f^{3} 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[46] to illustrate how its construction
is based on the Venetian *oncia*. In this case the keyboard was designed to be
25 *once* wide[47] so that the 50 keytails of the
50-note C/E to f^{3} 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*
[48].

**The boxslide register of the 1552 Marco Jadra polygonal virginal**

**in the
Pitt Rivers Museum, Oxford, No
1948.1****b1**

**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*[49]
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 f^{3}
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 f^{3}
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[50] 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[51]. 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*[52]
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 f^{3} 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[53]
that two of the instruments of Marco Jadra, a virginal of 1568 in the Victoria
and Albert Museum[54] and the
other a virginal of 1552 in the Pitt Rivers Museum, Oxford[55]
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 f^{2} 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[56]. The instrument was modified a number of
times before it was given its present state[57]. 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%)[58].

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:

_{} = 27.54mm

This compares with the value given by Colonel Cotty[59]
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.

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**Endnotes:**

[42] 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.

[43]
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.

[44]
For example, in many sixteenth- and early seventeenth-century Venetian
virginals, the width of the 50-note C/E to f^{3} keyboard plank was
designed to be 25 *once*. See footnote 47.

[45]
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 f^{3}
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.

[46]
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.

[47]
The width of the keyplank of this virginal is 724mm = = 24.98 *once*, obviously
meant to be 25 *once*.

[48]
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.

[49]
In Milan the subdivision of the *piede*
was called either the *oncia* or the *pollice* (the thumb).

[50]
*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.

[51]
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.

[52] See Howard Schott, in the reference given in footnote 50.

[53]
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.

[54]
*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

[55] See footnote 46.

[56]
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.

[57] These modifications are outlined in an unpublished restoration report by John Barnes held by the Royal College of Music.

[58] 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.

[59]
See Colonel Cotty, *Aide-Mémoire a l’usage
des officiers d’artillerie de France*, 2 (Paris, 1819) 896-7.