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

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[60]. 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[61]. Some sources published after 1840, such as
Ludovico Eusebio[62] using the
‘decimalised’ palmo, and the anonymous author of the article ‘Misure’[63]
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[64].
This is a separate inner instrument in an outer case, and is extremely
long having a spine measurement of 2505mm.
The compass is G_{1},A_{1} to c^{3}, 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[65],
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 c ^{2} 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[66], 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[67]
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[68]. 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[69] 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[70]. 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[71], or because they are in a simple proportion to one another[72]. 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.

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**Endnotes:**

[60]
See Angelo Martini,
*Manuale di metrologia*, (E. Loescher, Turin, 1883; reprint Editrice Edizioni
Romane d’Arte, Rome, 1976) 206.

[61]
See Giovanni Gandolfo, *Tavole di ragguaglio ovvero prontuario di compiuti
fatti di pesi, misure e monete legali italiane*, (Naples, 1860) 12-17.

[62]
*Compendio di Metrologia Universale e Vocabolario Metrologico*, (Unione Tipografico Editrice Torinese,
Turin, 1899; reprint by Forni Editore, Bologna, 1967).

[63]
Anonymous author, *Grande dizionario enciclopedico*, 12 (Unione Tipografico-Editrice Torinese,
Turin, 1970) 626.

[64]
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*.*

[65]
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.

[66]
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.

[67]
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.

[68] 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.

[69]
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.

[70] I would like to express my thanks to Marlowe Sigal for his help in measuring this instrument prior to its analysis by me.

[71]
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.

[72] 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.