Determination of the Centre of Construction, Anonymous Single-manual Harpsichord
Anonymous single-manual harpsichord, Naples, c.1620
Property of the Markiezenhof Museum, Bergen op Zoom, The Netherlands
The city or region of construction of
an anonymous instrument can be determined by analysing the size of the unit of
measurement used in its construction.
Until the time of the Napoleonic invasions of the Italian peninsula each
of the major centres in Italy used its own unit of measurement, and the size of
these units varied from place to place.
The braccio, piede, canna, palmo, etc. and
their subdivision into the oncia, soldo or pollice were therefore characteristic of each of the centres in
which instruments and virtually all other manufactured items were built. Therefore if the unit of measurement used in
the design and construction of an instrument can be determined, this can be
used in turn to establish the centre of its origin. This is a fundamental procedure, basic to the process of
establishing the region in which an instrument originated, and can be a great
help in establishing the maker of an otherwise anonymous instrument.
It
is quite clear that any maker of instruments - or any other object for that
matter - would have worked on a day-to-day basis using convenient numbers and
uncomplicated fractions of his local unit of measurement. For the plain reason that whole numbers or
simple fractions are easy to remember, an artisan would work in convenient
units of measurement when he is designing and executing the object he is
making. Because most of the
measurements used are, to a certain extent at least, arbitrary there is no need
to invoke complicated numbers in their design.
This is clear to anyone who has lived or worked anywhere in much of the
English-speaking world where the inch, a twelfth part of a foot, was until
recently still being used. Most of the
measurements used by hand-workers, artisans, artists, architects, designers and
all of those involved in industry and commerce were based on simple numbers of
inches, feet, and yards, or on their simple subdivision.
Only
where it is really necessary and where dictated by some rule or theoretical
concept would an instrument builder use a complicated or irrational division of
the local unit of measurement. This has
been shown clearly from the ground-breaking study made of many types of musical
instruments by Herbert Heyde[1]. Further work that I have done recently in
this field shows that the maker began his design by drawing out the baseboard
using dimensions which were simple integers or fractions of the local unit of
measurement, and the case sides that he then applied to the outer edges of the
baseboard were cut to a height also equal to a simple number of units (or units
plus simple fractions) of the local measurement unit. It is normally the height of the case without the top cap moulding in Italian instruments, and without
the added thickness of the baseboard in North-European instruments, that the
maker would measure in his local unit of measurement[2]. He would mark out a number of planks all in
convenient units and all of the same width, and then cut and apply these to the
outside edge of the baseboard.
Experience has shown that even here the case-wall heights are often
slightly less than expected in places where the top of the case has been planed
down to equalise the level of the top edges at the corners when these did not
match exactly after the case sides were assembled. It is therefore the maximum
case-wall height that corresponds to the makers design and not the average case-wall
height. Similarly the position and
measurements of all of the other design features of the instrument were made by
choosing simple units of the local unit of measurement. Clearly which measurements were chosen by a
maker in simple units would depend on his method of working and especially on
the order in which the various operations necessary to construct the instrument
were carried out.
The
problem faced by an investigator is to find the unit of measurement used to
design and construct any given instrument.
An instrument has many different measurements and it is not at all
obvious from looking at these expressed in millimetres what the local unit used
to arrive at them was. Even knowing
that the baseboard was constructed using simple units of the local measurement
is not, in itself, enough to divine the length of the unit used in its
design. This is further complicated by
the fact that, being hand made, none of the measurements of the baseboard or
the rest of the case, keyboards, string-length scalings, etc. is perfectly
exact. Any method used to find the unit
of measurement must therefore also be relatively insensitive to any
inaccuracies resulting from the working methods of the maker.
The
method used by these makers is based on the way in which they used a simple
geometrical construction to arrive at the tail angle of harpsichords[3].
Working in reverse, a study of
the measurement of the angle and of the orthogonal components of the tail side
enables a calculation of the unit of measurement. Establishing the unit of measurement used in the design of the
instrument can then be used to determine the centre in which it was built.
The
importance of such a method to the determination of the maker of an anonymous
instrument is obvious. The method
clearly does not pinpoint precisely who the maker was, but it does reduce the
number of possible makers from the vast breadth of builders active across the
whole of Italy. The following analysis
uses this method to determine where this otherwise anonymous harpsichord was
originally built.
In
order to determine the unit of measurement used to measure this instrument the
baseboard was measured (not including the case sides) and the position of
various lines scribed on the baseboard were also measured. These are shown in Table 1 below.
Length: |
1989 |
Width: | 747 at front; 742 at the bellyrail |
Cheek: | 478 |
Tail: | 196½ |
Component of the tail parallel to the spine: | 67 |
Component of the tail perpendicular to the spine: | 186 |
Tail angle: | 70½º |
Depth of keywell: | 125 |
Width of wrestplank in the treble: |
148 |
Width of wrestplank in the bass: | 188 |
Width of gap: | 44 |
Width of belly rail: | 26 |
Width of upper belly rail: | 17½ |
Table 1 - Original dimensions measured out on the baseboard.
Anonymous single-manual harpsichord, Naples, c.1620
Property of the Markiezenhof Museum, Bergen op Zoom, The Netherlands
The
procedure of determining the unit of measurement used to construct this
harpsichord begins most easily with the measurement of the angle of the
tail. The tangent of this angle is . This suggests that
the two sides of the triangle that form the tail angle are 8½ once and 3 once. The measured lengths
of these two sides in mm divided in turn by these numbers gives an approximate
estimate of the size of the oncia which
can then be applied to the other measurements of the baseboard, keyboard,
wrestplank, string scalings, and all of the other parts and design features of
the instrument. These sides have
lengths of 186mm and 67mm and their ratio gives:
This, in turn, suggests that the
length of the unit of measurement used in the construction of this instrument
is about mm or mm, and these can be used to give an initial estimate of the
unit of measurement in order to calculate the other dimensions in the same
units.
A
summary of the measurements of the baseboard, the scribed lines on it, and the
case height millimetres and in once
are given in Table
2 below.
Measurement |
Local |
Length
of |
|||
in mm | unit | oncia | |||
Component of tail perpendicular to spine: | 186 | = | 8½ once | gives | 21.88mm |
Component of tail parallel to spine: | 67 | = | 3 once | gives | 22.33mm |
Long side: | 1989 | = | 90½ once | gives | 21.98mm |
Baseboard width: | 747 | = | 34 once | gives | 21.97mm |
Baseboard cheek (short side): | 478 | = | 21¾ once | gives | 21.98mm |
Width of wrestplank in bass: | 188 | = | 8½ once | gives | 22.12mm |
Width of wrestplank in treble: | 148 | = | 6¾ once | gives | 21.93mm |
Depth of keywell: | 125 | = | 5.7 once | gives | 21.93mm |
Width of gap: | 44 | = | 2 once | gives | 22.00mm |
Thickness of bellyrail: | 26 | = | 1.2 once | gives | 21.67mm |
Thickness of upper bellyrail: | 17½ | = | 0.8 once | gives | 21.88mm |
Case sides height: | 190 | = | 8½ once | gives | 22.35mm |
Totals | 4205½ | = | 191.2 once | Average: | 21.995mm |
Table 2 - Calculation of the unit of measured used to design and construct this instrument.
Anonymous single-manual harpsichord, Naples, c.1620
Property of the Markiezenhof Museum, Bergen op Zoom, The Netherlands
This length, 21.995mm, can be compared
with a number of similar units of measurement used in the Italian peninsula in Table 3
below (see also
A list of Italian units of measurement arranged according to the length of the
unit). Clearly the centre which used a
unit closest to that found here is Naples where, in addition to the oncia of 21.835mm, an oncia of length 21.973mm was used. This must correspond to the unit that was
used in the construction of this instrument[4]. The instrument has many features of other
instruments made in Naples as discussed below.
Although Genoa also used a unit near to that found here the fact that no
seventeenth-century harpsichord makers are known to have worked there and the
similarity of the instrument to those made in the Neapolitan tradition excludes
Genoa as the centre in which this instrument was made. No other centre had a unit of measurement as
close in value to that found for this instrument. The error between the value found here and the value given in the
tables of metrology is only 0.1%!
This therefore suggests that Naples is the centre in which this harpsichord was built.
Large Length Sub- Length Reference
Location Unit in mm Division unit in
mm source*
Genoa Palmo 248.08 12 oncia 20.674 Ca,Did,GDE,Mal,Mar,Kr,Cha
Rome Palmo
mercantile 248.99 12 oncia 20.749 Eu,Mar,Mal,Dou,Pa,Co
Sicily/Palermo Palmo 257.80 12 oncia 21.483 Mal,Eu,Mar
Naples Braccio 698.00 32 oncia 21.813 Ca
Naples Canna 2096.10 96 oncia 21.834 Ca,Dou,Pa,Or,Cha
Naples Palmo 262.01 12 oncia 21.835 Dou,Cr
Naples Canna 2109.36 96 oncia 21.973 Ga,Mal,Mar
Naples Palmo 263.67 12 oncia 21.973 Did,Ga,Mal,Mar
Genoa Piede 263.93 12 oncia 21.994 Did
Savoia Braccio 270.70 12 oncia 22.558 Kr
Verona Piede 270.90 12 oncia 22.575 Co
Table 3 - Units of measurement used in the Italian peninsula in
the historical period[5]
*The abbreviations used in the table
above refer to the
following:
Ca Hercule Cavalli, Tableaux comparatifs des mesures, poids et monnaies modernes et anciens…,
(Paul Dupont, Paris, 2/1874).
Cha Chambers, Ephraim, ‘Measures’, Ciclopædia:
or An Universal Dictionary of Arts and Sciences, Vol. 2 (London,
1728; 4/1741; 5/1743).
Co Colonel Cotty, Aide-mémoire
a l’usage des officiers d’artillerie de France, 2 (Paris, 1819) 896-7.
Cr 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).
Did Denis Diderot and Jean Henri le Rond
d'Alembert, ‘Pied’, Encyclopédie ou
dictionnaire raisonnée des arts, sciences et métiers, 7 (Paris, 1751-65)
562-563. Diderot gives his measurements
as 1440-th parts of the Paris pouce,
and Colonel Cotty’s military manual was used for the length of the pouce.
Dou Horace Doursther, Dictionnaire universel des poids et mesures anciens et modernes,
(M Hayer, Brussels, 1840).
Eu Ludovico Eusebio, Compendio di Metrologia Universale e Vocabolario Metrologico,
(Unione Tipografico Editrice Torinese, Turin, 1899; reprint by Forni Editore,
Bologna, 1967).
Ga Giovanni Gandolfo, Tavole di ragguaglio ovvero prontuario di
computi fatti di pesi, misure e monete legali italiane, (Naples, 1860).
GDE Anon., ‘Misure’, Grande dizionario enciclopedico,
12 (Unione Tipografico-Editrice Torinese, Turin, 1970) 626.
Kr Johann Georg Krünitz, Öconomische Encyklopädie oder allgemeines
System der Staats-, Stadt-, und Landwirtschaft, in alphabetischer Ordnung,
15 (Jospeh Georg Traßler, Brünn, 1788) 519-22.
Given as 1440-th parts of the Paris pouce;
Co used for pouce. See Did.
Mal L. Malvasi, La metrologia italiana ne' suoi cambievoli rapporti desunti dal
confronto col sistema metrico-decimale, (Fratelli Malvasi, Modena,
1842-44).
Mar Angelo Martini, Manuale di metrologia, (E. Loescher, Turin, 1883; reprint Editrice
Edizioni Romane d’Arte, Rome, 1976).
Or Barnaba Oriani, Istruzione su le misure e su i pesi che si usano nella Repubblica
Cisalpina, (Milano, 1891).
Pa Luigi Pancaldi, Raccolta ridotta a dizionario
di varie misure antiche e moderne coi loro rapporti alle misure metriche…,
(Sassi, Bologna, 1847).
Figure 2 below shows the measurements
of the baseboard and of some of the scribed lines on the baseboard measured in
millimetres on the left and in units of the Neapolitan oncia as
determined above.
Figure 1 - The
scribed lines and dimensions of the baseboard in millimetres (on the left)
and in nominal units of the Neapolitan oncia = 21.995mm (on the right).
Anonymous single-manual harpsichord, Naples, c.1620
Property of the Markiezenhof Museum, Bergen op Zoom, The Netherlands
Endnotes:
[1] See: Herbert Heyde, Musikinstrumentenbau, 15.-19. Jahrhundert. Kunst Handwerk Entwurf, (VEB Deutscher Verlag für Musik, Leipzig, 1986).
[2] In the North-European tradition where the case sides are much thicker than in Italian practice, the top moulding is often cut into the wood of the case side itself, and the case sides are usually (but not always) applied to the top of the baseboard. In Italian instruments it is therefore the case height less the thickness of the top cap moulding that the maker would measure out using a simple number of local units; for North-European instruments it is the case height less the thickness of the baseboard onto which the case sides are placed.
[3] See my article ‘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’, The Galpin Society Journal, 52 (1999) 108-171 which is given here at Geometry and the Unit of Measurement.
[4] There was a decimal division of the oncia in Naples. Often a fifth of an oncia called a minuto was used. But clearly halves and quarters of the oncia was also used as well as the division into tenths.
[5] See my article quoted in footnote 3 and the database of the Italian units of measurement in Table 11 with further information in Appendix 2.
- Grant O’Brien
- Edinburgh, October, 2000