The Statistical Analysis of the Lateral String Spacing in Some Neapolitan and Flemish Seventeenth-Century Harpsichords

 

 

 

Introduction

         The way a maker marks out the lateral spacing of the strings in a harpsichord, spinet or virginal is perhaps one of the most characteristic features of his work.  By lateral string spacing I mean the distance which separates the strings in a direction perpendicular to their length.  In most, but not all, instruments the strings in the tenor, alto and treble are parallel to the spine of the instrument.  However, in the bass the strings on the bridge are usually angled away from the spine at the  end furthest from the player.  The reason for this is clearly to make extra space between the bass end of the bridge and the spine side of the instrument.  In order to improve the quality of the extreme bass notes it is necessary to make the area of soundboard around the bass end of the bridge as large and flexible as possible.  Angling the strings away from the spine so that the bass end of the bridge is distanced from the spine and spine liner achieves the required area and flexibility in the bass part of the soundboard.  This therefore means that the lateral bridge-pin spacing is different in the bass from that in the rest of the compass.

         Normally the bridge- and nut-pins are very regularly spaced and so an analysis of their spacing lends itself naturally to statistical methods giving a result of high accuracy and low error.  What I would like to show here is that the value of the lateral string spacing can, in turn, be used to establish the maker’s workshop unit of measurement to a high degree of accuracy.  Normally the unit of measurement used in a maker’s shop is close to the unit of measurement used in the city or region in which he worked.  But the high degree of accuracy of the determination of the unit of measurement using the lateral string spacing statistical method enables the work of two or more makers working in the same city or region to be distinguished from one another.  Indeed it is likely that the workshop unit of measurement determined in this way is even more characteristic of a maker’s work than the mouldings he used since there is no evidence to show that these were not ‘bought in’ to individual workshops by several different makers from a common supplier.

         For example, Stefano Bolcioni, Francesco Poggio and Bartolomeo Cristofori were all working in Florence together during the same period.  All of them used a value of the soldo used in Florence close to 27.56mm.  However an analysis even of the case measurements shows that each of them used a value of the soldo slightly different from the other and characteristic of the individual maker.  The difficulty with an analysis of the case measurements is that the unit of measurement derived in this way has a rather large error and this makes a positive distinction between workshops in the same centre rather difficult.  This difficulty is solved using an analysis of the lateral bridge- and nut-pin spacing because of the high accuracy resulting from a statistical analysis of the lateral pin position measurements.

         To my knowledge the analysis of the lateral string spacing using statistical methods has not so far been done by anyone else.  What I hope to show in this paper is how this new and powerful method is carried out, how the method can be used to distinguish one maker’s work from another, and also how it can be used to identify an individual maker.

         Before beginning on an example of the use of these statistical analyses I would like to review some simple mathematical concepts.

 

The concept of the slope of a straight line graph

         A simple concept, fundamental to the analysis of the bridge- and nut-pin spacing in a harpsichord, spinet or virginal is that of the slope of a straight line graph.  The slope is defined simply as the change in the y co-ordinates of the beginning and the end of a line divided by the change in the x co-ordinates of the beginning and end of the straight line.

 

 

In the straight-line graph shown in Figure 1 below the slope of the graph is given by

 

 

Hence if this were a graph of the pin spacing of an instrument, then the slope would give a spacing of 13.83.  The 36 notes in three octaves of strings with this spacing would therefore have a width of

 

 

and this is a typical 3-octave span suitable for human hands of average size.

 

 

Figure 1 - The slope and intercept of the line y = mx + b

 

This graph and this example show how the slope of a graph could be used as a measure of the lateral string spacing.  What I would like to do now is to apply this method to a real instrument.

 

Lateral string spacing in the 1651 single-manual harpsichord by Onofrio Guarracino belonging to Prof. Andrea Coen in Rome.

         A good example of the use of the lateral string spacing which both helps to understand how a typical 17th century harpsichord builder worked, and also how the lateral string spacing can be used as one of the characteristic workshop features of a particular maker is the 1651 single-manual harpsichord by Onofrio Guarracino belonging to Prof. Andrea Coen in Rome.  This instrument possesses many of the characteristics of Neapolitan construction which I won’t repeat here.  Neither will I describe all of the features of the instrument and its measurements for the purposes of this discussion.

 

         The instrument is signed “[Hon]ofrius Guarracino fecit 1651” in ink on the top surface of the c3 keylever behind the balance point.  The first part of the signature is covered over by a non-original piece of cloth covering the tail part of the keylever on which the jacks rest, and the number ‘45’ is written to the right of this near the balance point.

 

Figure 2 – Photograph showing the signature on the top of top c3 keylever.

Single-manual Italian harpsichord by Onofrio Guarracino, Naples, 1651

Property of Prof. Andrea Coen, Rome

 

         The soundboard rosette is made of parchment and wood (probably pear?) and is of the usual Neapolitan ‘wedding cake’ style of construction in four different levels each of 2 or 3 layers of parchment and wood.

 

Figure 3 – Two photographs showing a plan view (left) and a side view (right) of the soundboard rosette

Single-manual Italian harpsichord by Onofrio Guarracino, Naples, 1651

Property of Prof. Andrea Coen, Rome

 

         The case is constructed in the usual Neapolitan style with the baseboard raised about 3½mm above the edges of the case sides and the lower outer moulding.  The nameboard does not have a central excavated portion as is more usual with Guarracino and many other Neapolitan instruments but has both the top and bottom mouldings added on.  There are carved figures at either end of the keywell representing Neptune riding a hippocampus.  Also like many Neapolitan instruments and all of the instruments of Guarracino that I know the keyboard withdraws from the instrument like a drawer, rather than being lifted up vertically (see Figure 4).

 

Figure 4 – Photograph showing the keyboard partly withdrawn, drawer fashion, from the instrument

Single-manual Italian harpsichord by Onofrio Guarracino, Naples, 1651

Property of Prof. Andrea Coen, Rome

 

 

The determination of the unit of measurement used to construct this instrument

         Like virtually all other Italian builders, Guarracino began the process of construction by measuring out the baseboard.  This he did using simple units of the Neapolitan oncia.  It is therefore the measurements of the baseboard that are used in the determination of the unit of measurement used in the design and construction of this instrument.  The dimensions of the baseboard and of the case sides without the top moulding are given below:

 

                                                                   Length of spine side:         1848

                                                                  .   Width at the front:         684½

                                                                           Width at cheek:         684½

                                                                  Length of cheek side:         501½

                                                          Length of oblique tail side:         464½

                                      Component of the tail, parallel to spine:         403½

                           Component of the tail, perpendicular to spine:         232½

                                                                                   Tail angle:         30º

                                                              Height of the case sides:         205

Table 1 - Dimensions of the baseboard and case height in millimetres

Single-manual Italian harpsichord by Onofrio Guarracino, Naples, 1651

Property of Prof. Andrea Coen, Rome

 

         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.  This angle is 30º and sin 30º = ½, suggesting that the side opposite the tail angle and the length of the tail itself have lengths in the ratio of 1:2.  A process of elimination by trial and error shows that the ratio that gives an oncia which applies to the other dimensions of this instrument is that of .  Measurement of these two sides in mm enables the calculation of 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 including the lateral string spacing.  A summary of the measurements of the baseboard and case height in once are given in the following table:

 

 

                                                                Measurement          Measurement                                                                      Length of

                                                                           in mm          in local unit                                                                        oncia in mm

                                                 Tail length:          464½    =   21½ once                Þ                                                          21.61

                             Tail side opposite angle:          232½    =   10¾ once               Þ                                                          21.61

                                                  Spine side:           1848    =   85½ once                Þ                                                          21.61

                                       Baseboard width:          684½    =   31 once               Þ                                                          21.62

                     Baseboard cheek (short side):          501½    =   23¼ once                Þ                                                          21.57

                                       Case sides height:             206    =   9½ once                 Þ                                                          21.58

                                                            Total         3937    =   182 once      Average:                                                        21.61mm ± 0.013mm

Table 2- Baseboard measurements used to calculate Guarracino’s  unit of measurement

Single-manual Italian harpsichord by Onofrio Guarracino, Naples, 1651

Property of Prof. Andrea Coen, Rome

 

 

         These measurements are shown in the diagram on the next page where the actual measurements of the baseboard in millimetres are shown on the left, and the measurements in Guarracino’s unit of measurement are shown on the right.  According to most reliable sources, in Naples the palmo, divided into 12 units, had a length of 262.01mm[1].  Hence the oncia had a length of:

The difference between this and the oncia found here is only of the order of 1% and therefore there is very good agreement between the value found here and the text-book value of the Neapolitan oncia.

 

         I have, however, measured a number of other instruments made by Onofrio Guarracino.  From these measurements it seems clear that Guarracino had his own workshop unit of measurement which is somewhat different from the ‘textbook’ value of the Neapolitan oncia found above.  I have been able to calculate an average value of the oncia used by Guarracino in his workshop[2] as 21.61mm so that the palmo would be:

                                                                   

This value of the oncia is only 0.05% different from that found here and is a very good indication that this instrument is indeed by Guarracino!

 

Figure 5 - Dimensions of the baseboard in mm (left) and in units of the Neapolitan oncia (right)

Single-manual Italian harpsichord by Onofrio Guarracino, Naples, 1651

Property of Prof. Andrea Coen, Rome

 

Lateral spacing of the bridge pins and strings:

         Although it is now disposed with 2x8', the instrument originally had only one set of strings and these seem to have been the present long set as is usual.  The distance from the spine of each of the bridge and nut pins was measured and these are given in the table below:

 

Note

Long 8' bridge pin

Long 8' nut pin

c3

640½

646

b2

626½

632

bI2

611

618½

a2

599

603½

gT2

585

589½

g2

571½

575

fT2

557

562

f2

543½

549.

e2

531

536

eI2

517

522

d2

503

509

cT2

490

496½

c2

475½

482½

b1

462

466½

bI1

448

452

a1

434

439

gT1

421

424½

g1

408

410½

fT1

394

398

f1

380

385

e1

365½

372

eI1

352½

358½

Note

Long 8' bridge pin

Long 8' nut pin

d1

339

343

cT1

325½

329½

c1

311

315

B

297

303

bI

284

289

A

271

275½

gT

257

261½

G

244

247

fT

230

233

F

216½

219

E

203

205

eI

190

192

D

176

178

cT

163

164½

C

148

150

B

136

136

BI

121

121½

A

109½

106½

E/GT

95½

93

G

81

79

D/FT

69

64

F

56½

50

C/E

43

35½

Table 3 - Distance of the bridge and nut pins from the spine in mm

Single-manual Italian harpsichord by Onofrio Guarracino, Naples, 1651

Property of Prof. Andrea Coen, Rome

 

         It should be noted from the measurements in Table 3 that for the notes around tenor B to tenor c, the strings are parallel - that is the distance of the nut and bridge pins from the spine are equal.  Below tenor c the nut pins are nearer to the spine than the corresponding bridge pins and above tenor c the nut pins are further from the spine than the bridge pins.  This is the first clear indication that the strings are angled away from the spine in order to increase the area of freely vibrating soundboard area around the bass end of the bridge.  Indeed for this instrument the strings are angled away from the cheek as well to increase the area of soundboard around the treble end of the bridge.  These distances are plotted below in Figure 6. 

 

          The pin spacing of both the bridge and of the nut (see Figure 7) falls into two distinct sections.  Above the note tenor c, the pins have one regular spacing relative to one another, whereas below tenor c they have another, slightly different spacing.  This difference is indicated by the slight but significant change in the slope of the line that joins the plotted points above and below the note tenor c.

 

         The slight change in the spacing of the bass bridge pinning shown in Figure 6 above is the result of Guarracino’s desire to improve the quality of the lowest bass notes by moving the bass end of the bridge away from the spine side of the instrument as discussed above.  Therefore, the strings have a different relative spacing above and below the played note tenor c.

Figure 6 - Graph of the lateral spacing of the bridge pins from the spine

Single-manual Italian harpsichord by Onofrio Guarracino, Naples, 1651

Property of Prof. Andrea Coen, Rome

  

         Clearly if the bass bridge pins are moved away from the spine, the strings also move away from the spine along the line of the jacks at the register.  This would have the effect of pushing the strings towards the jacks and would require shorter quills there.  In order to avoid this problem the strings were moved away from the jacks by positioning the bass nut pins further apart for the notes below tenor c.  This is shown in Figure 7 below where there is again a small but significant change in the slope of the line joining the points above and below tenor c.  The difference is that, in this case, the spacing of the nut pins is greater below the note tenor c than it is above tenor c.

Figure 7 - Graph of the lateral spacing of the nut pins from the spine

Single-manual Italian harpsichord by Onofrio Guarracino, Naples, 1651

Property of Prof. Andrea Coen, Rome

  

         Here, in order to calculate the average lateral spacing of the bridge and nut pins in each part of the compass, the analysis has been based on a statistical method slightly more complicated, but giving a much higher accuracy than simply using the coordinates of the beginning and end of each of the lines.  In this type of analysis the measured points have been fitted to a straight line using a regression analysis and the method of least squares.  Each section of the graphs shown in Figure 6 and Figure 7 can be represented mathematically by a simple, straight-line equation of the form y = mx + b like that shown in Figure 1 above.  By using each of the points on the graph and by fitting the best possible straight line to all of the points in each section of the graph, the regression analysis gives the best average slope, and greatly increases the accuracy of the determination of this slope.  Hence a very accurate value of the lateral string spacing was obtained for each of different sections of each of the two graphs.

          The results are shown in Table 2[3] below.

 

                                       Bass section below tenor c Middle and treble section above tenor c

                                                m                     b                                         m                    b

                      Bridge:       13.18±0.8%         -168.2                          13.648±0.07%  -179.4

                          Nut:       14.31±0.3%         -193.3                          13.74  ±  0.1%  -178.9

Table 4 - The values of the constants m and b in the straight-line equation y = mx + b found from the regression analysis of the bridge and pin positions for the bass and treble sections

Single-manual Italian harpsichord by Onofrio Guarracino, Naples, 1651

Property of Prof. Andrea Coen, Rome

 

 

         Of interest in this analysis are the regular spacings of the strings, given by the constant m, for the nut and for the bridge and for each section of the pinning above and below the note tenor c.  The percentage error calculated during the regression analysis procedure has been given here for each of the values of m, but not for b which is not of interest in this particular analysis.  The value of m for the sections of the pinning in the bass below tenor c are clearly quite different and have a larger percentage errors (since there are far fewer measurements to contribute to the averages) from the treble  bridge-pin and  nut-pin spacing.  The values of m for the pinning above tenor c are very nearly the same, but differ significantly from one another.  Indeed the difference between them is greater than the error for each and so they need to be considered separately.  In other words the middle and treble strings have a different spacing at the bridge end from that at the nut end and are therefore not exactly parallel to one another.  In this case it is clear that they have a slightly greater spacing at the nut than they do at the bridge.   

         I now want to consider each of the lateral string spacings separately in order to see how each of them is related to the unit of measurement used by Guarracino.  First of all let’s consider the average middle and treble  bridge-pin spacing expressed in terms of Guarracino’s workshop oncia found above[4].  This gives

                                                                Equation 1

Although at first sight this spacing seems rather strange and arbitrary, this is very close to the spacing that would be obtained if Guarracino had spaced exactly 19 notes in one palmo:

                                     (Equation 2)

The close agreement (error = 0.02%!) suggests very strongly that Guarracino spaced out the middle and treble bridge pins so that 19 of each occupied a space of one palmo.  The difference is smaller than the experimental error and so is a good indication that this interpretation is correct.

 

         In the bass the  bridge-pin spacings have to be analysed separately from those found in the treble.  Here, the bass  bridge-pin spacing, again expressed in terms of Guarracino’s workshop oncia, is:

                                                                           (Equation 3)

This is very close to the spacing that would be obtained if Guarracino had spaced 9 notes in exactly 5½ once (error = 0.3%):

                                                         (Equation 4)

and this, in turn, suggests that Guarracino spaced out the bass bridge pins so that 9 pins occupied a space of 5½ once.  The reader is reminded at this point that there are exactly 9 notes from C/E to tenor c, and it is precisely these 9 notes that are spaced out in 5½ once.

 

         The analysis of the lateral nut-pin spacing follows along similar lines.  The tenor, alto and treble nut-pin spacing is 13.74mm/string.  This gives:

                                  (Equation 5)

The close agreement (error = 0.09%) is within the calculated experimental error and suggests that Guarracino spaced out the middle and treble nut pins so that 11 strings occupied a space of  7 once.

 

         Again the bass the nut-pin spacings have to be analysed separately from those found in the treble.  Here, the bass  nut-pin spacing, again expressed in terms of Guarracino’s workshop oncia, is:

                                      (Equation 6)

This is very close to the spacing that would be obtained if Guarracino had spaced out the 9 notes of the bass short octave in exactly 6 once (error = 0.7%) instead of the 5½       once already found above for the bass bridge spacing.

 

         On the other hand the simplicity and elegance of the way the pins were spaced on the bridge and nut is striking.  Use of the value of the 21.61mm oncia found from the analysis of the case dimensions suggests how the instrument’s string spacing was designed and carried out.  However, this value of the oncia, measured from the case dimensions, does not have the same high accuracy as that to which the value of the  bridge-pin spacings have been calculated.  Indeed the value of the oncia used by Guarracino to mark out the sticks he used to position the bridge pins can be calculated by assuming an exact spacing of 19 notes in 12 once for the middle and treble  bridge-pin spacing and of exactly 9 notes in 5½ once for the bass  bridge-pin spacing.  For the middle and treble bridge pins:

                                                     (Equation 7)

or

                                               (Equation 8)

And for the bass bridge pins:

 

                                                       (Equation 9)

or

                                                       (Equation 10)

         The two values of the oncia calculated above are in agreement with one another to within the statistical error calculated using the regression analyses.  The value calculated here for Guarracino’s oncia = 21.607mm±0.015mm is the most accurate value of his workshop oncia calculated so far by any means of analysis.  The high accuracy of this result also makes it possible to say definitively that Guarracino’s workshop unit of measurement was not the ‘text book’ value[5] of the Neapolitan oncia = 21.834mm.

 

         The lateral string spacing, given in terms of the unit of measurement used by Guarracino is summarised in Table 5 below

 

                                     Bass section below tenor c            Middle and treble section above tenor c

                      Bridge:            9 notes in 5½ once                                     19 notes in 12 once

                          Nut:              9 notes in 6 once                                         11 notes in 7 once

Table 5 - Lateral string spacing expressed in terms of Guarracino’s unit of measurement

 

         Table 6 below shows the unit of measurement calculated using the case measurements and the lateral string spacing for a number of Guarracino instruments.  The measurements for the 1651 Guarracino belonging to Andrea Coen are highlighted in green at the top of the table.  These have a very low error.  The virginals below this have errors in the calculated unit of measurement that are somewhat higher because of the smaller measurements involved and the smaller number of strings in a virginal which can be used in the determination of the lateral string spacing.  However they all form a consistent set of analyses for instruments spanning the 41-year period of Guarracino’s activity, and they all show that Guarracino’s workshop unit of measurement was consistently different over this long period from the ‘text book’ unit of measurement for Naples.

         The instruments highlighted in orange at the bottom of Table 6 are all instruments which have numerous features of Neapolitan harpsichords in general and of the workshop of Onofrio Guarracino in particular.  The woods used, the method of marking out, the order of construction, the geometry of the tail, and the sectional shapes of a number of the mouldings used are all similar.  But in addition to these the workshop unit of measurement calculated for these instruments is the same unit close to 21.61mm and is within the experimental error for each determination of the unit of measurement to that normally used by Guarracino.  This, to me, strongly suggests that these five anonymous instrument have all been correctly attributed to Guarracino.

 


 


 

oncia

Error

Error

 

Instrument

mm

mm

%

Method

1651 Guarracino harpsichord, Coen,  Rome

21.61

0.02

0.093

Case measurements

1651 Guarracino harpsichord, Coen,  Rome

21.607

0.015

0.069

Lateral string spacing

1663 Guarracino virginal, Tagliavini, Bologna

21.608

0.015

0.069

Case measurements

1663 Guarracino virginal, Tagliavini, Bologna

21.61

0.13

0.602

Lateral string spacing

1668 Guarracino virginal, Museo Naz., Rome

21.61

0.02

0.093

Case measurements

1668 Guarracino virginal, Museo Naz., Rome

21.58

0.13

0.602

Lateral string spacing

1677 Guarracino virginal, Museo Naz., Rome

21.664

0.015

0.069

Case measurements

1689 Guarracino virginal, Roger Mirrey, London

21.62

0.015

0.069

Case measurements

1692 Guarracino virginal, Museo Naz., Rome

21.61

0.015

0.069

Case measurements

1692 Guarracino virginal, Museo Naz., Rome

21.58

0.05

0.232

Lateral string spacing

 n.d. ‘Guarracino’ harpsichord, Gemeentemuseum

21.649

0.04

0.185

Case measurements

n.d. ‘Guarracino’ harpsichord, RCM 175, London

21.637

0.019

0.088

Case measurements

n.d. ‘Guarracino’ harpsichord, Giulini, Milan

21.612

0.011

0.051

Case measurements

n.d. ‘Guarracino’ harpsichord, MMA, New York

21.65

0.03

0.125

Case measurements

n.d. ‘Guarracino’ harpsichord, BMFA, Boston

21.60

0.03

0.13

Case measurements

Average:

21.616

0.010

0.045

 

Table 6 – Calculation of Guarracino’s averaged workshop unit of measurement


A comparison of the lateral bridge- and nut-pin spacing of the 1638 Ioannes Ruckers and an anonymous Franco-Flemish harpsichords

 

                      

Figure 8 - The 1638 Ioannes Ruckers harpsichord, Russell Collection, Edinburgh (left)
and the anonymous Franco-Flemish ravalement harpsichord, Antwerp, 1617 (private ownership, London).

 

         These two instruments, although now physically very different, do have many features in common.  The 1638 Ioannes Ruckers harpsichord is in almost unaltered condition since the time when it was first made in Antwerp.  In particular, the pinning of the bridges and nuts has never been changed.  Because of this the lateral string spacing and the lateral pinning of the bridges and nuts can be used as a kind of standard for the Ruckers’ workshops.  The second instrument has been much altered, but the original pinning of the bridges has never been changed.  In a paper in the Early Keyboard Journal[6] I have been able to show that it was originally a non-aligned or a so-called ‘transposing’ harpsichord and that, despite the fact that this instrument bears a genuine Ioannes Ruckers in the soundboard, it was made in Antwerp, although it is not by a member of the Ruckers family.

         The lateral bridge-pin spacings of these two instruments are shown in the graphs of Figure 9 and Figure 10 below.  Comparing the lateral bridge-pin spacing of the 1638 Ioannes Ruckers harpsichord with that of the Guarracino harpsichord analysed above, it can be seen that, despite the enormous differences in the construction style, string scalings, and unit of measurement used to design the instruments, the lateral string spacings of the mid- and treble-string spacings are very similar:  13.86mm and 13.84mm for the 1638 Ioannes Ruckers harpsichord and 13.684mm for the 1651 Guarracino harpsichord.  The determining factor here is obviously the stretch of the human hand:  no matter where the instruments are made and designed and what the unit of measurement used is, the lateral string spacing and the octave span of the keyboard is, in the end, determined by the size of the human hand.

  

Figure 9 - The lateral string spacing of the 8' and 4' bridge pins

1638 IR double-manual harpsichord, Russell Collection of Early Keyboard Instruments

 

 

Figure 10 - Lateral 8' and 4' bridge pin positions

Anonymous double-manual Franco-Flemish harpsichord, Antwerp/France, c.1620/1756

         Before going on I would like to point out that the change in the slope in the graph of the 1638 Ioannes Ruckers harpsichord shown inFigure 9 occurs at the upper-manual note GT or at the lower-manual note cT.  Given that the instrument was designed on the basis of the low-pitch lower manual keyboard, this is the same note at which the stringing changed from yellow brass to iron.  Indeed for all models of clavecimbel listed in Douwes, the change from yellow brass stringing to iron stringing occurred between the notes cT and d.  The change in the slope of the graphs of the Franco-Flemish harpsichord (the pitches in the graph are one semitone to high relative to the original pitch of the strings of the upper manual because the maker would have had to overcome the van Blankenburg problem[7]) occurs much higher up in the compass at the lower-manual note f.  This suggests that for the maker of the Franco-Flemish harpsichord there was no relationship between the brass to iron transition and the change in the lateral spacing of the bass and treble bridge and nut pinning.

 

 

                                                                      Bass section     Middle and treble section

                        1638 IR 8' bridge:                10.01 mm/note                      13.86 mm/note

                        1638 IR 4' bridge:                11.43 mm/note                      13.84 mm/note

            Franco-Flemish 8' Bridge:                12.67 mm/note                      14.18 mm/note

            Franco-Flemish 4' Bridge:                12.89 mm/note                      14.17 mm/note

Table 7 - Slopes of the graphs of lateral bridge spacing from Figure 9 and Figure 10

 

         Table 7 shows clearly that the lateral string spacings of the pins on the bridge and nut of the 1638 IR and the Franco-Flemish harpsichord are totally different.  Nonetheless it is interesting to look at their similarities.  In both instruments the spacing of the middle and treble pins are the same for the 8' pins and the 4' pins.  This is entirely to be expected so that the 8' and 4' strings run parallel to one another with a constant relative spacing.  In each case therefore an average was taken of the middle and treble section lateral spacings.

         Although not shown here, the errors in the results for each of the 8' and 4' slopes of the bass sections of the Franco-Flemish harpsichord are large enough that the errors overlap to the extent that they are not significantly different from one another.  Therefore it is necessary to consider the 8' pins to have the same spacing as the 4' pins.

        In the bass the situation is somewhat different.  Here, because of the smaller number of pin positions being analysed, the error in the slopes is considerably greater.  Nonetheless, the slopes of the bass sections of the 8' and 4' bridges of the 1638 IR are significantly different and therefore need to be analysed separately.  On the other hand in the Franco-Flemish harpsichord, although the difference in the slope of the bass section of the 8' and 4' differ by about 1.7% the statistical error in the determination of these values using the regression analysis is even greater than this showing that there is no significant difference between these two.  They were therefore averaged in the analysis below.

         Just as the spacing of the strings was determined in units of Guarracino’s oncia, the spacings in Table 7 can also be determined in units of the Antwerp duim.  In my work on the instruments of the Ruckers family I found that there seemed to be two workshop units of the duim used in the Ruckers workshops.  These were the large duim = 25.88mm and the small duim, used for the measurements of the case height and string scalings = 25.48mm.  Using the latter value to calculated the average middle and treble lateral string spacing of the 1638 IR harpsichord shows that:

 

In other words Ruckers spaced out the middle and treble notes so that each octave took up a space of 6½ duimen.

         The other measurements in Table 7 can be calculated in terms of the Antwerp duim in a similar way, and the results of these calculations are shown below in Table 8.

 

                                                                      Bass section     Middle and treble section

                        1638 IR 8' bridge:              5 notes in 2 duimen          12 notes in 6½ duimen

                        1638 IR 4' bridge:            5 notes in 2¼ duimen        12 notes in 6½ duimen

            Franco-Flemish 8' Bridge:            22 notes in 11 duimen         20 notes in 11 duimen

            Franco-Flemish 4' Bridge:            22 notes in 11 duimen         20 notes in 11 duimen

Table 8 - Lateral string spacing expressed in terms of the Antwerp duim

 

         Table 8 above shows that the makers who made these two instruments, although both worked in the same centre and used the same duim, they thought about the lateral string spacing in a totally different way.  Ioannes Ruckers considered each octave of strings in the treble part of the compass and made each octave of strings occupy a space of 6½ duimen.  In the bass the 8' bridge pins are spaced very closely together in order to move the bottom bass bridge pin a long distance from the spine and spine liner.  But here the 4' strings have a different bass lateral spacing so that the 4' strings end up being slightly closer to the spine, but are closely parallel to the 8' strings.  This is a very sophisticated refinement and is an indication of the care and attention that the Ruckers paid to this aspect of the string-band layout.

         In the Franco-Flemish harpsichord the middle and treble lateral bridge-pin spacing is based not on the octave span, but on the voet.  In this case the maker spaces out the treble strings so that there are 20 notes in one voet.  In the bass the strings are spaced so that there are 22 notes in 1 voet (= 11 duimen), so that the lateral spacing of the 4' bridge pins is just ½ duim.  However, in this case the lowest  8' bridge pin and the lowest 4' bridge pin are the same distance from the spine.  The 8' and 4' strings therefore cannot possibly be parallel.  This is not a problem as the spacing of the 8' and 4' strings is important only where they pass the jacks.  This is, in turn, determined by the nut-pin spacing which was not recorded here because the original nut is now missing.

         The main thrust of my argument is, however, that the makers of these two instruments thought about the lateral string spacing in two totally different ways.  Because of this there is clearly no possibility that the Franco-Flemish harpsichord was made in the Ruckers’ workshops.  The characteristic way that each maker uses his own workshop unit of measurement, that each changes the note at which the bass and treble spacing changes, and the characteristic way that each designs the lateral string spacing in his instruments underlines the importance and usefulness of this method of analysis.  Examination by me of numerous other instruments shows that the same lateral string-spacing analysis can be applied to instruments in all of the different workshops, regions and schools of harpsichord building throughout Europe.  It shows that this is a valid and important part of the authentication and attribution of instruments as well as to an understanding of how harpsichord makers throughout all of Europe thought and worked. 

                                                           - begun in Zanzibar, March 2006, finished in Edinburgh, April 2006

                                                           - © Grant O’Brien 2006                                                                      

FOOTNOTES:

[1] See: Horace Doursther, Dictionnaire universel des poids et mesures anciens et modernes, (M Hayer, Brussels, 1840) and Hercule Cavalli, Tableaux comparatifs des mesures, poids et monnaies modernes et anciens…, (Paul Dupont, Paris, 2/1874).  Both of these authors give the same value for the Neapolitan oncia.

[2] See the section concerning the Royal College of Music Neapolitan harpsichord on my website http://www.claviantica.com/Publications_files/Cristofori_Naples.htm for a calculation of the average unit of measurement used by Guarracino.

[3] In Table 4, the errors are the standard deviation errors calculated during the regression analysis for each of the results.  These are expressed here as a percentage rather than as an absolute value.

[4] See the results calculated above.

[5] Hercule Cavalli, Tableaux comparatifs des mesures, poids et monnaies modernes et anciens…, (Paul Dupont, Paris, 2/1874) gives a value of the Neapolitan oncia of 21.813mm; Cavalli (op. cit.), Ephraim Chambers, ‘Measures’, Ciclopædia:  or An Universal Dictionary of Arts and Sciences, Vol. 2 (London, 1728; 4/1741; 5/1743), Horace Doursther, Dictionnaire universel des poids et mesures anciens et modernes, (M Hayer, Brussels, 1840),  Barnaba Oriani, Istruzione su le misure e su i pesi che si usano nella Repubblica Cisalpina, (Milano, 1891) and Luigi Pancaldi, Raccolta  ridotta a dizionario di varie misure antiche e moderne coi loro rapporti alle misure metriche…, (Sassi, Bologna, 1847) all give a value of 21.834mm and 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) and Doursther (op. cit.) both give a value of 21.835mm.

[6] See:  Grant O’Brien, ‘An analysis of the origins of a large Franco-Flemish double-manual harpsichord.  Would a Ruckers by any other name sound as sweet?’, Early Keyboard Journal, 22 (2004): 49-90.

[7] See my book Ruckers.  A harpsichord and virginal building tradition (Cambridge: Cambridge University Press, 1990) p. 209, 213, 214, 216, 217, 232, 249, 254, 255 where the van Blankenburg problem is discussed in detail.