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 Franciscus
Patavinus dated 1552 in the
Museo Correr, Venice

As
explained above, in Venice and throughout the rest of the Italian peninsula,
the baseboard dimensions without the case sides were chosen in simple units or
fractions of the inch or *oncia*[7]
(plural *once*) that the maker was
using. Since the *oncia* was normally divided into twelve equal parts each called a
line or *linea* (plural *linee*) it is to be expected that
fractions involving twelfths, sixths, thirds, quarters and halves of the *oncia* would be involved in the design
and execution of the instruments[8]. The Venetian foot or *piede*[9] (plural *piedi*) had a length close to 347.76mm[10], and this was divided into 12 giving
an inch or *oncia* of 28.98mm.

The
Museo Correr on the Piazza San Marco in Venice holds a fine Italian virginal signed:
‘ **~ **FRANCISCI PATAVINI
DICTI HONGARO MDLII
**~** ’
[11].
The namebatten and the signature are definitely not original to the
instrument. The signature is written on
a piece of wood foreign to the rest of the instrument, and this wood appears to
be fir or spruce stained brown to match the appearance of the cypress used
elsewhere in the instrument. The fact
that the nameboard and signature are not original to the instrument does not,
however, mean that its maker is not Francesco Patavinus[12]. Indeed the mouldings on the instrument are
not even the same as those of the two other extant instruments thought to be by
Franciscus Patavinus[13]. However here, as with other makers I have
studied where there is a lack of correspondence of the mouldings, I do not see
any reason for doubting that any of these instruments are by Patavinus[14]. Although he seems consistently to have
signed himself ‘FRANCISCVS PATAVINVS DICTI [H]ONGARO’ so that he appears both
to have had Hungarian roots and to have come from Padova, he is almost
certainly to be identified with the ‘Francesco dalli arpicordi’ and the ‘Francesco dai manicordi’ who appears in the Venetian archives[15]
and who lived and worked there.

Figure 1
shows a schematic representation of the case mouldings, the keywell scrolls,
and the bridge section at the position of the c^{2} string of the 1552
polygonal virginal by Franciscus Patavinus in the Museo Correr, Venice. The application of the case sides to the
outer edge of the baseboard, and the additional height of the case sides
resulting from the extra depth added by the top cap moulding and ivory studs
are clearly indicated here.

Unfortunately the usual catalogue measurements of Italian and Venetian virginals (Table 1 and Figure 2) are taken of the outer case sides and, to my knowledge, never of the baseboard on its own. Hence the normal catalogue measurements do not normally enable one to make any sort of an analysis of the size of the baseboard from which the maker began the design and construction of the instrument. It is therefore necessary to measure the baseboard without the case sides and then to analyse these measurements.

**Schematic representation of the case mouldings, the keywell scrolls,
**

**
and the bridge section at the position of
the c ^{2} bridge pin.**

**Polygonal virginal by Franciscus Patavinus, 1552**

**Museo Correr, San Marco, Venice**

** **

Dimension Height* Thickness WoodFront: 1641 172-4 5.4-6.4 cypress

Case left of the keywell: 344 173½-4 6.4 cypress

Angled left side: 192 173 4.7 cypress

Angled left back: 864 172 5.0 cypress

Back: 313 173 5.1 cypress

Angled right side: 571 172-3 5.2 cypress

Case right of the keywell: 569 172-4 5.4 cypress

Outside of the keywell: 728 --- --- ---

Total width: 490 --- --- ---

Keywell scrolls: project 116 136 11 cypress

Baseboard: Italian style 12.4-12.8 fir**

Angle at the left-front corner: 72º

Angle at the right-front corner: 41º

* These heights do not include the top cap moulding which adds a further 5mm to each measurement.

** As there are no pitch pockets in this large piece of wood, it is almost certainly of fir and not of spruce.

**
Outside dimensions in mm including the case
sides, but not the outer mouldings**

**Polygonal virginal by Franciscus Patavinus, 1552**

**Museo Correr, San Marco, Venice**

**
Outer
dimensions in mm including the case sides, but not the outer mouldings**

**Polygonal virginal by Franciscus
Patavinus, 1552**

**Museo Correr, San Marco, Venice**

Table 2 and Figure 3 show
the baseboard measurements in millimetres of the 1552 Franciscus polygonal
virginal without the case sides. A
number of these are given in Table
2 in their nominal measurement in Venetian *once*. Many of these show a
close agreement between the measured length in millimetres and a simple nominal
number of Venetian *once*, and strongly
suggest that this was the unit of measurement used in the design of the
baseboard of this instrument. However
the measurements of the sloping edges at the left- and right-hand sides of the
case do not give measurements which can be expressed in whole numbers or simple
divisions of the Venetian *oncia*. This suggests that the measurements of these
sloping edges are not those that were used by the maker in the design of the
instrument. The angles at the extreme
ends of the virginal are also not simple numbers like 30º, 60º or 45º, or even
simple angles based on multiples of 5º or 10º.
These two facts must therefore somehow be related.

To understand this relationship and how the front corner angles were constructed it is necessary to examine their geometry. The tangent[16] of the angle at the left-hand corner, for example, is:

tan
72° = 3.07 ≈ 3 = _{}

This suggests that the sloping
surface at the left-hand side of the instrument was made up by drawing the
hypotenuse of a triangle with orthogonal sides that are in the ratio of 3 *once*:1 *oncia*, 6 *once*:2 *once*, 9 *once*:3 *once*, etc. The actual measurement of the sloping side
of just over 6 *once* immediately
suggests that the two orthogonal sides of this triangle were designed by
Patavinus to be 6 *once* and 2 *once*.
Similarly at the right-hand corner the tangent of the angle there gives

tan
41° = 0.869 = _{} ≈ _{}

and suggests that the angle formed at this corner resulted
when Patavinus drew the hypotenuse of a right-angle triangle with sides 12½
(the width of the instrument) and 14½ *once*.

Figure 4 shows
the dimension in millimetres of the baseboard in directions perpendicular and
parallel to the front of the instrument, and indicates the close agreement
between the measurements at the front of the case with simple units of the
Venetian *oncia*. Figure
5 shows the lengths of each of the sides of the baseboard of the
Franciscus Patavinus virginal as it must have been designed by Franciscus, with
the calculated angles at the front corners which would result from their construction
using triangles with sides measured in simple numbers of Venetian *once*.
The agreement between the measured values of both the lengths and of the
front corner angles makes clear the design of the baseboard of this instrument
by Franciscus in units of the Venetian *oncia*.

Other
dimensions such as the maximum case height of 174mm (6.004 *once*) also give simple units of the subdivision of the Venetian *piede*.
In fact the Franciscus Patavinus virginal shows the use of the local
unit of measurement in many other aspects of its design which have not been
shown here. But the dimensions and
balance point of the keyplank (ie. of the jointed board from which the keys
were cut), the string scalings, the angling of the strings, the dimensions of
the blocks from which the boxslide was made, etc. were all based on the use by
Patavinus of the Venetian *oncia*. The dimensions of the Patavinus virginal
show the use of simple units of the Venetian *oncia* in a manner that is particularly simple and clear. The dimensions of other instruments
sometimes involve slightly more complicated numbers, and may involve
subdivisions of the *oncia*, *soldo* or *pollice* into thirds, sixths and twelfths, as well as the more usual
halves and quarters. Some of these are
illustrated in the examples discussed below.

**
** **Measured Nominal dimension**

**
dimension in Venetian once**

**
mm mm once**

Length: 1622 1622.9 56

Width: 359* 362.3 12½

Case left of the keywell: 348 347.8 12

Angled left side: 183 --- (6.31)

Angled left back: 862 --- (29.74)

Back: 304 304.3 10½

Angled right side: 555 --- (19.15)

Case right of the keywell: 565 565.1 19½

Keywell: 709 710.0 24½

Keywell projects: 116 115.9 4

Maximum case height: 174 173.9 6

* The more-or-less unaltered length of the keywell braces indicates that the wood of the baseboard has shrunk and that this measurement was probably originally about 362mm.

**
Dimensions of
baseboard without the case sides and mouldings**

**Polygonal virginal by Franciscus Patavinus, 1552**

**Museo Correr, Venice**

**Measured dimensions in mm of the baseboard without the case sides**

**
and measured angles at the front corners**

**Polygonal virginal by Franciscus Patavinus, 1552**

**
Museo Correr, San Marco, Venice**

tan 72° = 3.07
≈ 3 = _{} tan 41° = 0.869 = _{} ≈ _{}

**Measured dimensions in mm of the
baseboard without the case sides**

**
and
measured angles at the front corners**

**Polygonal virginal by Franciscus
Patavinus, 1552**

**
Museo
Correr, San Marco, Venice**

At the front left-hand corner: At the back:

174mm = 6.004 *once *420mm
= 14.49 *once*

58mm = 2.001 *once *898mm
= 30.99 *
once*

304mm
= 10.49 *once*

**Baseboard dimensions without the case sides measured in the Venetian oncia = 28.98mm**

**
showing the front corner angles calculated
from these.**

**Polygonal virginal by Franciscus Patavinus, 1552**

**
Museo Correr, San Marco, Venice**

tan
71.6°
= 3 = _{} arctan
_{} = 71.6°

tan
40.8º = 0.862 = _{} arctan _{} = 40.8º

The virginal
by Franciscus Patavinus was clearly designed using the Venetian *oncia* of length 28.98mm. The baseboard measurements make this
particularly obvious, and also show that the various angles were drawn, not by
using a protractor, but by drawing the diagonal of a rectangle with sides which
were a simple number of Venetian *once*
in length. The position and length of
the long diagonal side at the rear left-hand side of the instrument was drawn
by joining the end of the near left-hand sloping side and a point on the rear
of the baseboard which was 31 *once* in
from the left end. Hence the irregular
pentagonal shape of the baseboard arises from a series of orthogonal measurements,
perhaps drawn out on a jointed plank that was originally 56 *once* (4½ Venetian *piedi*)* *long by 12½ *once* wide. The close agreement between the measured angles at the front
corners of the baseboard and the angles calculated theoretically from the
orthogonal components of the sides used to construct them is a further
confirmation of the method used by Franciscus to construct the baseboard.

Working in reverse in those instruments where the centre in which they were built is not known it is possible to use the angles at the front corners to guess what the measurements used to construct them was, and from this to make an initial guess at the length of the unit of measurement. This will be illustrated in the examples below. In harpsichords the tail angle was normally constructed in a similar way, and using this angle to guess at the orthogonal components of the angle used to construct it can enable one to make an initial guess at the length of the unit of measurement used in the design and construction of all of the rest of the instrument.

Click here to go to the next section

Click here to return to to main page of the section on Italian Geometry

**
Endnotes:**

[7]
The words inch, ounce and *oncia* all
derive from the Latin word *uncia*
meaning ‘a twelfth part’. Therefore an
inch is a twelfth part of a foot and a troy ounce is a twelfth part of a troy
pound. However there are a number of
cases, such as the normal English pound weight, where the division was into 16
ounces and not into 12. In Rome the *piede* was divided into 16 *once* and existed alongside the Roman *palmo* which had 12 *once* (hence 1 *piede* = 1*palmi*).
Other divisions are also possible as in Florence, for example. Here the *braccio*
was divided into 2 *palmi* each of
length 10 *soldi* (*soldo* in the singular).
Therefore the *braccio* had a
length of 20 *soldi*.

[8]
This is not always true, however, and sometimes the *piede* and *palmo* were
divided into 10 units, and sometimes the subdivisions were also in 10
units. In Rome, for example, the *oncia*, a twelfth part of the *palmo*, was divided into 5 *minuti* and 10 *decimi*.

[9]
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 for a discussion of a number of instruments built using
the Venetian foot or *piede*.

[10]
*See*:
Colonel Cotty, *Aide-mémoire a
l’usage des officiers d’artillerie de France*, 2 (Magime, Anselin &
Pochard, Paris, 5/1819) p. 899 (here 1 Venetian *piede* = 347.7588mm so that the *oncia*
= 28.9799mm). The Venetian *piede* is among the best-documented units
of measurement and various sources give values from 347.398mm to 347.759mm (see
Appendix 2
at the end of this paper).

[11]
I have examined this instrument in some detail during the course of a study
project organised by the Museo Correr and by Il Laboratorio of Milan and indeed
it was during the study of this virginal for the Museo Correr that I discovered
the simple geometry used to design the baseboard. An unpublished report entitled *Spinetta poligonale Franciscus Patavinus, 1552* written by me for
this project is held by the Museo Correr in Venice

[12] The new namebatten may have been made for the instrument when the old, original namebatten went missing or was damaged for whatever reason. In fact this seems highly likely since it is improbable that the appellation “DICTI HONGARO” would have been used by someone attributing the instrument to Franciscus unless he was sure of the original form of the signature.

[13]
Donald H Boalch,* Makers of the Harpsichord
and Clavichord, 1440-1840*, (Third edition, edited by Charles Mould,
Clarendon Press, Oxford, 1995) pp. 319-320 lists altogether 4 instruments by
Patavinus. The second of these is
listed only in the catalogues by Franciolini (*see*: Edwin M. Ripin, ‘The
instrument catalogues of Leopoldo Franciolini’, *Music Indexes and Bibliographies*, Vol. 9 (New Jersey, 1974) 3A-14,
p. 14) as an instrument signed “IONNES[sic] PATAVINI[sic] DECTI[sic]
HONGARI[sic] MDXXXX”. In addition there
is a polygonal virginal in the Brussels Museum of Musical Instruments (No. 272)
listed in Boalch/3 under Antonius (p. 222) with a signature “ANTONI PATAVINI
OPVS MDXXXXX[sic]” on a namebatten that does not belong to the instrument.

[14]
Besides numerous similar construction methods used, the bass ends of the
boxslide registers of both of the virginals have the inscription “ba_{ò}i”
= *bassi* written on one side, an
indication to the maker while he was assembling the instrument which end of the
boxslide was for the bass and which for the treble. The Florentine makers Francesco Poggio and Stefano Bolcioni also
both use the word “*bassi*” on the bass
end of their virginal registers to indicate its orientation during the
construction of the instrument. But I
know of no other maker who used the form “ba_{ò}i” with a long
_{
ò =
}‘ss’,
and no Venetian maker at all who left this indication on the bass end of the
boxslide register.

[15]
*See*: Stefano Toffolo, *Antichi Strumenti Veneziani. 1500-1800:
Quattro secoli di liuteria e cembalaria*, (Arsenale Editrice, Venice,
1987) pp. 161-2. The Italian word
‘arpicordo’ seems to have been used for what we now define as a virginal, or in
modern Italian a ‘spinetta’ or, more properly, a ‘spinetta traversa’. A ‘manicordo’ was the word used for
clavichord.

[16] See Appendix 1 at the end of this paper for a brief and simple review of geometrical definitions.