Russell Collection of Early
Keyboard Instruments

HT1-SB1627.4: Three-manual harpsichord, Stefano Bolcioni.
Prato, 1627.

Towards establishing the original state of the three-manual harpsichord
by Stefano Bolcioni, Florence, 1627, in the Russell Collection
of Early Keyboard Instruments, Edinburgh.

In the previous article I attempted to show that a determination of the unit of measurement used in the construction of a stringed keyboard instrument can be used as a powerful tool in the analysis of how the instrument was designed and built. A determination of the unit of measurement can also be used to aid in the attribution of an instrument of doubtful authorship, and to determine the centre in which an unsigned instrument was made. Analogously it can also be used to help to establish where known makers lived and worked when there is otherwise no biographical information about them. All of these methods rely on a reliable and impartial determination of the local unit of measurement used in the design and construction of the instrument concerned. I was able to show that it is a relatively easy matter to determine this unit of measurement for any given instrument. From the plethora of measurements which one could take of an instrument, the use of simple geometry and the measurement of the orthogonal components of the tail angle of a harpsichord baseboard or the end corners of a polygonal virginal baseboard can be used to get an initial estimate of the length of the unit of measurement used in its design and construction. This can then be refined using the other larger dimensions of the baseboard and instrument which were originally measured out by the maker.

What I would like to show in this paper is that an analysis of the unit of measurement may also be used as a valuable tool in the determination of the original state of a drastically-altered instrument. A harpsichord in the Russell Collection of Early Keyboard Instruments at the University of Edinburgh signed 'STEFANVS o BOLCIONIVS o PRATENSIS o F o AoD o MoDoCoXXVII F¹ is a good example of an instrument which has had a chequered history and which, in its present state, does not in any way represent its original nor any intermediate historical state.

The Bolcioni harpsichord currently has a disposition of 2 x 8', 1 x 4' with three uncoupled keyboards and three registers, one per keyboard. It has an elaborately-decorated outer case in a kind of Italian vernis-martin mannerist style, and a complex French-style stand in the style of Louis XIV (see Plate 1). A photograph of this instrument appears in the catalogues of Leopoldo Franciolini² (Plate 2) with three keyboards and the same outer case but with a totally different decoration and stand³ . It is clear that the present state is totally inauthentic and dates from a 're-working' of the instrument around the time when it was offered for sale by Franciolini at the end of the nineteenth century. Because of the extent of the drastic alterations to the instrument it has hitherto been very difficult to establish the original compass, disposition, scalings and pitch of this instrument⁴.

As it presently exists the signature is written upside down on the back of the nameboard at a level above the top of the wrestplank so that it is visible and readable when viewed from a standing position at the keyboard end of the instrument. This unusual arrangement is, however, easily explained. The nameboard had to be narrowed considerably in order to make room for the height of the three inauthentic keyboards. If the nameboard had been cut away at its original bottom edge to make way for the extra keyboards, the signature would have been destroyed altogether in the process. The nameboard was therefore rotated end-for-end turning it upside down, and a new cap moulding was added to the original bottom of the nameboard so that it could serve as a normal nameboard in the usual way. The replacement nameboard cap moulding clearly comes from a different instrument and matches a non-original moulding on the non-original sloping cheeks, and that of a repair to the tail of the instrument. This moulding does not correspond to that on any of the other Bolcioni instruments. However, the moulding on the original lower front part of the nameboard has the same profile as the moulding on the inside of the spine below the cap moulding. Since the nameboard moulding is cut from the solid wood and not applied, it belongs to the same piece of wood onto which the signature is written. The fact that this signature is very similar to that found on the only other extant Bolcioni harpsichord⁵ and the fact that the moulding on the (original) lower side of the namebatten matches that on the inside of the spine of the case leaves little doubt that the signature is original and that the instrument is indeed by Bolcioni. This is further confirmed, as will be shown below, by the use in this instrument of the same unit of measurement used in the other instruments made and designed by Bolcioni.

This paper is an attempt to show how the original dimensions of the baseboard used by Bolcioni to design and construct this instrument can be determined using the Florentine soldo⁶ and comparison with the only other surviving Bolcioni harpsichord in the University of Yale (click here to see my previous paper). This is a procedure not previously applied to this radically-altered instrument (see footnote 4). Fortunately Bolcioni left a number of construction marks in various places and on various parts of the instrument which can be used in conjunction with the use of the unit of measurement analysis. Comparison with the only extant Bolcioni harpsichord, an understanding of these construction marks, and an understanding of the use of the soldo in its design and construction then enables the original case dimensions, the original compass, keyboard layout, string scalings and plucking points to be re-constructed.

The original baseboard layout of the Edinburgh Bolcioni harpsichord
The 1627 Bolcioni harpsichord has unusual sloping cheekpieces beside the keyboards instead of the usual keywell scrolls. Close examination shows that these are not original but have been added on with lap joints to the main spine and the cheek sides. Because of the existence of the inauthentic three keyboards in the instrument the apparent explanation for these added cheekpieces is that they were added on to the sides of the case to provide the additional length necessary for the additional two keyboards.

However, a cursory examination shows that this is not at all the true situation! A number of features indicates that, in fact, the case has been shortened and not lengthened:

1. The present original baseboard extends beyond the spine and cheekpiece lap joints right up to the present front of the instrument and does not stop short at the point where the cheeks have apparently been extended.
2. Construction marks on the top surface of the baseboard indicate the original position of the front of the wrestplank, the angled nut, the register gap, and the lower belly rail behind the keyboard. This makes it clear that the front of the wrestplank has been moved back about 255mm and that the belly rail has been moved back about 99mm. As a result the present wrestplank is also very slender and probably about 84mm narrower than the original wrestplank at the bass end, and is also not tapered in width as it was originally. It is clear therefore that the additional space for the three keyboards was gained by narrowing the wrestplank and moving it and the belly rail some distance toward the rear of the instrument. This involved cutting away some of the original front edge of the soundboard including the part on which the treble end of the original bridge was located. The scribed line on the baseboard indicating the position of the nut is therefore now left well out in front of the present wrestplank in the new larger keywell space.
3. The case widths of the University of Yale and of the Edinburgh Bolcioni harpsichords are almost the same. The original compass of the Yale harpsichord was C/E to f³, and therefore it is possible that the compass of the Edinburgh harpsichord was either the same or that it had the same number of naturals in order to give it the same overall width. There are 7 staggered and badly-drilled holes in the baseboard, clearly for pedal pull-downs for the 7 notes of a keyboard with a C/E short octave: C, F, D, G, A, B and B. The lowest hole for the C/E pull-down is centred about 50mm from the spine side of the case indicating that there must have been very wide keyblocks beside the keyboard which had these pull-downs. If this keyboard was placed with the bass short octave keys above the holes and located roughly centrally in the keywell, then the space left for the keyboard would have been about 635mm. The 27 naturals of a C/E to c³ keyboard placed in this space would have a 3-octave span of about 494mm, a normal value for the keyboard of an Italian instrument. Any larger compass would have had an unusually small octave span. A C/E to d³ compass, for example, would have had a 3-octave span of only 476mm. The keyboard used with the pull-downs could therefore not have reached higher than c³ in the remaining space. It appears therefore that the keyboard for which the holes for the pedal pull-downs were drilled was not the original keyboard but one from an early alteration to the harpsichord. Further evidence of this fact is provided from the boxslide registers. A compass of C/E to c³ has 45 notes (or 47 notes even assuming a C/E to d³ compass), and yet the registers for this instrument have 53 jackslots⁷. The holes for the pull-downs are also placed very far back from the present front of the case, all of which, along with the roughness of the workmanship, suggests non-original work.
4. Examined from underneath, the present front edge of the baseboard is very coarsely cut in a manner atypical of the careful workmanship of the original parts of the rest of the instrument. This suggests that it was not sawn by Bolcioni but by the later worker who replaced the original keyboard and installed the keyboard with the pedal pull-downs. There is also no transverse batten between the front case moulding and the front edge of the baseboard as is normal Italian practice and as is found in the Yale Bolcioni harpsichord⁸. Apparently the replacement keyboard had short keyplates and keylevers so that it was necessary to shorten the case in order to accommodate these short keylevers with short keyplates. Cutting away the front of the baseboard and removing the batten from behind the front moulding would have spoiled the original keywell scrolls and necessitated their replacement with the present sloping cheek-pieces. Indeed although the tail, the width of the instrument and the case height were all clearly designed using simple numbers of the Florentine soldo already found for Bolcioni (see the analysis below), neither the present length of the spine nor the length of the cheek corresponds to simple measurements in soldi. The length of the baseboard has therefore clearly been shortened.

However, if it is assumed that the keywell scrolls on the Edinburgh Bolcioni where the same length as those on the Yale harpsichord, and that Bolcioni used the same thickness of batten at the front of the keywell behind the front case moulding, then there must now be about 20½mm missing from the front of the baseboard of the Edinburgh harpsichord. Adding this missing 20½mm results in the measurements given in Table 1.

Analysis of the unit of measurement used in the construction of the Edinburgh Bolcioni harpsichord, originally a single-manual instrument:
The value of the Florentine soldo used in the Edinburgh Bolcioni can be calculated in the usual way which has been demonstrated in my article in the previous volume of this Journal. The tangent of the tail angle is . The numbers ⁴/₅ when applied to the component measurements of the tail give a soldo greater than any known historically in Italy. But the ratio ⁸/₁₀ suggests that the two orthogonal components of the triangle that form the tail angle are 8 soldi and 10 soldi which, mathematically, would form an angle of 38.66º. Not surprisingly this angle is very close to the measured angle of 38½º, and well within the error of measurement. The length of the two orthogonal sides constituting the components of the tail side (see Table 1) gives an approximate estimate of the size of the soldo which can then be applied to the other measurements of the baseboard, the original wrestplank, the original string scalings, and all of the other original parts and design features of the instrument in a way similar to that already described for the other instruments discussed in my paper in the previous volume of this Journal. A summary of the original measurements of the baseboard, baseboard construction lines and the case height in soldi is given in Table 2, where the lengths of the soldo calculated from each of these are shown at the right:

	Measurement in mm		Local unit		Length of soldo
Tail angle component parallel to spine:	273½	=	10 soldi		27.35
Tail angle component perpendicular to spine:	220	=	8 soldi		27.50
Spine (long bass side)*:	1981½	=	72½ soldi		27.33
Baseboard width:	756½	=	272/3 soldi		27.34
Cheek (short treble side)*:	537½	=	192/3 soldi		27.33
Case sides height:	219	=	8 soldi		27.38
Case front to nut line (bass side)*:	164½	=	6 soldi		27.42
Case front to nut line (treble side)*:	273½	=	10½ soldi		27.35
Case front to belly rail (bass side)*:	391½	=	141/3 soldi		27.31
Case front to belly rail (treble side)*:	373½	=	132/3 soldi		27.33
Total:	5191	=	1895/6 soldi	Average: 27.345mm

This calculation gives a value of the soldo that compares with a value of 27.29mm found for the 1631 Bolcioni harpsichord in Yale University, a value of 27.34mm found for the 1641 Bolcioni virginal in the Musikinstrumentenmuseum in the University of Leipzig ( for both of these see the analyses in my paper in the previous volume of this Journal), a value of 27.341mm given by both Diderot (1751) and Krünitz (1788)⁹, a value of 27.408mm given by Larousse¹⁰ and the value of 27.53mm given by Colonel Cotty (1819)¹¹. The similarity to one another of the values of the soldo found for the various Bolcioni instruments, and the similarity of these to the values given in the historical sources of metrology, confirms that they were all made in Florence using the Florentine braccio and soldo, and this fact also helps to confirm that the instruments were indeed all made by Bolcioni¹² .

The measurements from Table 2 are shown in Figure 1 where the actual dimensions in millimetres with the measured tail angle are shown on the left. The same measurements in units of the Florentine soldo, and the nominal tail angle resulting from these are shown on the right.

The shaded portion at the front of the baseboard seen in Figure 1 shows the amount which seems to have been removed in order to accommodate the non-original C/E to c³ keyboard with pedal pull-downs. This shortening of the baseboard occurred in one of the numerous intermediate states of the instrument. The strongly-angled line indicates the original position of the nut, and the double lines behind this indicate the original position of the sides of the lower belly rail. Clearly, if my assumption about the scroll of this harpsichord having originally been the same as that on the University of Yale Bolcioni so that 20½mm were removed from the baseboard of this instrument, the nut and the belly rail were also positioned using simple integers and fractions of Florentine soldi as would be expected.

The position of the front of the belly rail involves thirds of a soldo, rather than the more common halves and quarters. This is, however, not as unusual as it seems at first. As explained in footnote 6 the soldo was divided into 3 quattrini (so-called because one quattrino = 4 denari). The quattrino, equal to ¹/₃ of a soldo, was a unit of measurement that was in common use in Florence, and often quoted when describing the sizes of objects in Florentine documents and inventories. It is therefore not at all surprising to see measurements among those found in the layout of the baseboard of this harpsichord involving quattrini or thirds of a soldo. The fact that all of the measurements after correction are simple rational numbers in units of the soldo or its common division indicates that the assumed reduction in the length of the baseboard of 20½mm is indeed correct. It would be an unusual coincidence for the numbers to work out this tidily if the assumed correction were incorrect.

Figure 2 shows a schematic representation of the cheek section, and of the probable original form of the keywell for the Edinburgh Bolcioni. Here the keywell scroll of the Yale University Bolcioni harpsichord of 1631 has been added on at the point where the present join in the cheek begins (dashed line) and the batten in front of the baseboard of the Yale University Bolcioni has been drawn in (shaded). An added section 20½mm wide (shaded) has had to be added to the length of the baseboard in order to accommodate the Yale cheek piece as discussed above.

The present boxslide registers and the original compass
The present boxslide registers fit perfectly into the width of the instrument with a roughly equal amount of space between the ends of the registers and the first and last jackslots. The equal spacing at the ends of the registers is a good indication that the registers are original since a maker normally designed the string band of his instruments to be positioned centrally between the side case walls. These registers, despite the drastic falsification of the instrument which occurred around the time it was sold by Franciolini, and despite at least one and perhaps several more intermediate-state replacements of the original keyboards, do indeed seem to be original on the basis of the following further evidence.

These registers were sliced through longitudinally about half-way down from the top of the register so that, from the original two registers, four new registers were made. Presumably one of these half-registers was discarded and the other three were used as the new registers for the inauthentic 3-keyboard state. However, the top sections of both registers survive, and both have marks beside some of the jackslots made with a sharp pointed tool to locate the string directly above the mark. These marks appear from their irregular spacing along the registers to indicate each of the notes c and f throughout the compass¹⁴. One register has the marks placed to the right of the jackslots, the other on the left of the jackslots to indicate the quill directions plucking to the left and to the right in the usual way. This indicates clearly that the instrument had two choirs of strings, and the absence of any marks either for a 4' bridge or for 4' hitchpins on the soundboard means that it must originally have been disposed with two sets of 8' strings¹⁵ . Even in the absence of the evidence provided by the scribed markings on the baseboard to the same effect, this strongly suggests that the instrument originally had only one manual as is usual with Italian harpsichords.

Figure 3 indicates one of the registers in its present orientation at the top of the diagram, and the same register rotated through 180º in what is likely its original orientation. If the disposition of the two registers of the Edinburgh Bolcioni was the same as that of the 1631 Bolcioni in the University of Yale then this would be the register located nearest to the player which clearly, from the position of the indentation markings on the right-hand side of the jackslots, would have plucked the short set of 8' strings.

In the present orientation of the register (top part of the diagram), the compass implied by the construction marks beside the jackslots would read from F to d³, four octaves less a minor third but apparently including a number of split accidentals. This is a very unusual compass historically and is both very old-fashioned at the bass end of the compass and very advanced in the treble for an instrument of 1627. It would be necessary to postulate a number of split accidentals including all but one of the accidentals between f² and c³ in a part of the compass where split accidentals are normally not found in other extant instruments. It would also imply the use of a bass octave beginning at F, but with split accidentals higher up in the compass. This is most unlikely since split accidentals imply the use of a broken short octave in the bass with both a compass down to C and with split D/F and split E/G. The extra notes of the broken short octave provide roots to the additional chords and playable tonalities in meantone tuning provided by the extra accidentals used harmonically higher up in the compass. Also, if it is assumed that this orientation is correct, it would be necessary to postulate that Bolcioni made a mistake and marked both b² and c³ on one of the registers, an unlikely possibility for an otherwise careful and accurate professional maker.

All of these problems disappear, however, if it is assumed that the registers have been incorrectly placed in the instrument in an orientation rotated through 180º. The two adjacently-marked register slots are then clearly the notes C[/E] and F of a normal short octave, and the marked slots above this correspond to the remaining c and f notes. Between F and c there are jackslot spaces for D/F and E/G of the usual broken octave. Above this the number of jackslots available implies that there are two extra notes in the next two octaves which, in analogy with the other instruments made by Bolcioni, must have been d /e and g /a in the second octave and d¹/e¹ and g¹/a¹ in the third octave where these notes would be needed harmonically¹⁶ . Because of the presence of these split accidentals it would be both useful and necessary to have split keylevers for D/F and E/G to provide roots to the chords in the tonalities and modulations possible with the additional enharmonically-related notes provided by the split accidentals in the middle of the compass. The top octave from c² to c³ has no split accidentals as would be expected since the accidentals here are normally used melodically and not harmonically. The compass implied by the marks on the register in this orientation is therefore clearly C/E to c³ with two keys below the low C which could be tuned to any note required by the music in a manner similar to that adopted for the lower diapason notes of the theorboed lute. I have assumed here that these keylevers would play strings tuned to G₁ and A₁ but they might have played any of the notes F₁, G₁, A₁, B₁, B and E, all of which could be used as the roots to the major and minor chords (except for b minor and e minor) playable in the tonalities possible in meantone temperament with the notes available elsewhere in the compass¹⁷.

It is impossible now to tell with certainty whether the two keylevers below the low C full-width natural were placed side-by-side, or whether the two notes were played by the front and rear section of a split natural. Given the amount of space available in the keywell it seems likely that the two keylevers were placed side-by-side¹⁸. This would then give the front of the keyboard a width of 29 naturals. If these 29 naturals had a width designed by Bolcioni to be 25 soldi = 684mm, then the resulting span of the keyboard would be 495mm, intermediate between the 3-octave spans of the other Bolcioni instruments which vary from 488mm to 512mm¹⁹. A 25 soldi keyboard width would leave a space for the keywell scrolls and keyblocks of about 36mm on either side of the keyboard²⁰. Figure 4 shows the compass and probable original arrangement of keylevers for this harpsichord.

This unusual compass with the two keylevers below the C/E keylever, and with a broken octave above this and then the split d /e and g /a notes in the next two octaves, would have become out-of-date by the end of the seventeenth century. This is clearly the reason that the original keyboard with this extraordinary compass was replaced by the straightforward C/E to c³ keyboard with the added pedal pull-down cords. And the replacement of the original keyboard, it will be remembered, is the reason that the case length was shortened, and that the original keywell scrolls were replaced with the present sloping cheekpieces.

The original string scalings of the Edinburgh Bolcioni harpsichord
The single angled scribed line on the baseboard marking the position of the nut indicates clearly that, for the Edinburgh harpsichord at least, Bolcioni intended that there should be only one nut and not two as in the 1631 Bolcioni single-manual harpsichord in Yale University²¹. The position of this line is very clear and unambiguous. The soundboard, however, has many scratched lines and indentation marks made either as construction marks or from bridge pins which have penetrated through their bridge and into the wood of the soundboard. It is not easy to decide by simple observation which of these marks correspond to the original state and which to one of the intermediate states of the harpsichord. A more analytical method is required to decide which of the marks belong to the original state.

In order to resolve the problem of deciding which of the soundboard markings belong to the original state of the instrument, a kind of string-band strip was made of the indented construction markings beside the jackslots on the registers²². This was done by using the cheek side of the instrument as a datum line to mark out the position of each of the indented construction marks from the box-slide onto the string-band strip for both registers. Then the marked-out string-band strip was rotated by 180º and the spine side of the instrument was used as the new datum line. In this orientation the markings on the strip then indicated the original position of each of the long and short c and f strings relative to the spine. Holding it perpendicular to the spine and moving the string-band strip across the soundboard area showed clearly and unambiguously that there are similar construction indentations made with a sharp pointed tool on the soundboard corresponding to the register construction marks for the short string positions²³ marked on the string-band strip. Hence Bolcioni clearly intended the strings to run exactly parallel to the spine except for the lowest bass strings which angle away from the spine in the usual way (see footnote 24). The position of the soundboard indentation mark for the note f is now covered over by the present bridge dating from the Franciolini period. The marks for the top notes f² and c³ are missing altogether since the section of the soundboard in the extreme treble where they once existed was cut away when the three inauthentic keyboards were added. It is clear that none of the observed scratched lines on the soundboard corresponds to the position of the original bridge position, and most of the indentation marks are, in fact, imprints left by bridge pins which have penetrated through the bridges of the numerous intermediate states of the instrument. However, although not marked on the register, a construction mark for the lowest note [here assigned to be G₁] also seems to exist²⁴ on the soundboard. This then locates the position on the soundboard of the bridge pins for the short strings of most of the c and f notes throughout the compass, as well as the bridge pin for the lowest note [G₁].

In order to analyse the scalings of the harpsichord, use was made of the diagram of the baseboard of the instrument shown here in Figure 1. The positions of the short strings were projected back into the soundboard area using the rotated orientation of the near register which originally served the jacks plucking the short set of 8' strings (see Figure 5). The positions of the soundboard construction marks were transferred onto the same diagram by measuring their locations using the present front of the instrument as a reference line. These are each indicated by arrowheads beside the bridge line in Figure 5²⁵ . The distance from the scribed line giving the nut position to each of the soundboard construction marks was then measured using the facilities provided by the drawing programme being used²⁶ . This gives a c² scaling for the short 8' string, measured by the drawing by the programme, of 300.9mm. The position of the missing bridge pins for the notes c² and c³ were calculated assuming Pythagorean scalings in the region from ² and c³. The position of the covered mark for the note f between the notes c and c¹ was assumed to be on a smooth curve also fitted using the drawing programme and the visible marked short c and f bridge pin positions. The missing indentation marks are indicated on the diagram beside the bridge curve with short horizontal lines. These are all shown on the diagram in Figure 5 along with the short 8' string lengths of the c and f notes measured by the drawing programme.

The position of the bridge found from the construction marks on the soundboard forms a smooth curve on the diagram of the baseboard which is quite accurately parallel to the bentside. This is a strong indication that these markings do indeed represent the original bridge position and shape since it is normal for the maker to position the bentside at a more-or-less constant distance from the bridge. The c² scaling of 300.9mm found using this method is very close to 11 Florentine soldi = 300.8mm suggesting that 11 soldi was the design scaling used by Bolcioni when laying out the construction marks for the 8' short string lengths (see further the graph of the original scalings shown in Figure 7).

In a similar way the position and length of the long set of 8' strings was drawn on the diagram of the baseboard of the harpsichord by assuming a symmetrical position of the long c and f strings beside their respective jackslots relative to the marked short-string positions²⁷ (see Figure 9). These lengths were then also measured using the drawing programme. The same diagram was then further used to find the original plucking points along the strings as seen in Figure 6. It was assumed for this purpose that the plucking directions of the two registers were the same as the original plucking directions of the jacks on the Yale University Bolcioni harpsichord:

Back Row:		8'
Front Row:		8'

The gap space marked on the baseboard is about 1½mm wider than the combined thickness of the two existing registers, and so two dotted lines were drawn onto the baseboard diagram at positions exactly ¼ and ¾ of the width of the marked gap space. It was then assumed that the near register of jacks plucked the short set of strings at the position of the nearer dotted line, and that the far register plucked the long strings at the position of the further dotted line. In the diagram, for clarity, only the plucking-point distances for the c² strings have been measured by the drawing programme and indicated in the figure.

The string scalings and plucking points for both sets of 8' strings as measured using the drawing programme are given in Table 3 rounded off to the nearest half-millimetre:²⁸

The scalings of the short strings, clearly the ones used to design this harpsichord by Bolcioni, are plotted in the graph of Figure 7. A straight line has been added to the plotted scalings which corresponds to accurately Pythagorean scalings based on c²= 11 soldi = 300.8mm. This graph shows both that the reconstructed scalings obtained in Figure 5 were designed to be Pythagorean all the way from the bass bridge mitre right up to the top note, and that these scalings were almost certainly based in a design by Bolcioni with a short c² = 11 soldi (or c¹ = 22 soldi, etc). Taken together these two facts give added confidence in the accuracy of the reconstruction of the scalings of this instrument.

The plucking points given in Table 3 result from positioning the line of the nut and the register gap on the baseboard so that measurements in Florentine soldi give their locations relative to the front of the baseboard along the spine and cheek sides (see Figure 1). (In fact, of course, the plucking position is related to which of the two registers plucks to the left and which to the right, and on where in the gap the registers position the jacks and quills.) The line of the nut and the lines marking the register gap slope in opposite directions and this, combined with the irregular transverse spacing of the c notes along these lines, means that the plucking points were not designed to give simple measurements in Florentine soldi. The plucking points result instead from the geometry of the lines drawn out on the baseboard, the plucking directions, and the position of the jacks in the gap, and give irrational and otherwise unrelated numbers when expressed in . However it is clear from the accurately-Pythagorean nature of the scalings, and the accuracy of the lengths when expressed in units of Florentine soldi, that the bridge was positioned by measuring the string lengths out from the nut position at the irregularly spaced c string locations. I find this a very interesting aspect of the design procedure used by Bolcioni, and an aspect which is revealed only by a careful analysis of the use by him of his local unit of measurement.

A comparison of the scalings of the Edinburgh Bolcioni harpsichord with the other Bolcioni instruments in order to try to understand the intended pitch relationship between them proves to be very difficult. For a start the Edinburgh harpsichord is the only Bolcioni instrument which is designed around the lengths of the c strings rather than on the lengths of the f strings. All of the other instruments have compasses going to f³ in the treble and the measurements in Florentine soldi used to mark out the scalings are all based on the f notes. Although the lengths of the c and f strings in a given instrument should have a length ratio for Pythagorean or just tuning and scalings of 4:3, there can be no guarantee that two instruments, one designed using the c strings as the basis of its design, bears this relationship to another instrument which uses the f string lengths as the basis of its design. It is therefore not completely clear what the pitch-relationship between such instruments should be. The 1631 Yale harpsichord has an f² scaling designed by Bolcioni to be 7 Florentine soldi; the 1629 Edinburgh harpsichord has a short c² scaling designed by Bolcioni to be 11 soldi. The f²-equivalent scaling of the Edinburgh harpsichord is therefore 11 x ¾ = 8¼ soldi. The pitch relationship between 7 soldi and 8¼ soldi is 284 cents, or about 80 cents larger than a major Pythagorean second, so that it is unlikely that Bolcioni intended these two instruments to sound at pitches a whole tone apart²⁹ . I have been able to show elsewhere that the difference between iron and brass scalings in a harpsichord which I have attributed to Marco Jadra³⁰ corresponds to about 265 cents. It therefore appears at first sight that Bolcioni must have intended these two harpsichords to sound at the same pitch, but for the Edinburgh harpsichord to be strung in iron with the Yale harpsichord strung in brass. However, in fact, it is the short strings of the Edinburgh harpsichord which are designed to have a length equivalent to f² = 8¼ soldi and not the long, critically-stressed strings. This totally confuses any possible pitch or stringing assignment, and is only made more unclear by the fact that the Munich and Leipzig Bolcioni virginals have f² scalings of 9 soldi and 8¾ soldi respectively³¹ . The latter lengths have no pitch or stringing relationship either to one another nor to the 7 soldi f² scaling of the Yale harpsichord or the 8¾ soldi f²-equivalent scaling of the short strings of the Edinburgh Bolcioni harpsichord. It would therefore appear that clear and simple conclusions can be drawn neither about the stringing materials nor about the pitch relationships which underlie Bolcioni's design for these instruments.

Another method of determining the Florentine soldo from the Edinburgh Bolcioni harpsichord
Because the use of the Florentine soldo enters into all aspects of the construction of the Bolcioni harpsichord, there are other methods of determining the value of the unit of measurement, and what method is used to make this determination is limited only by the ingenuity and imagination of the investigator. One such method was noted at the time that I was working on the Edinburgh Bolcioni harpsichord discussed in detail above, and involves the regular spacing of the jackslots in the boxslide register. The position of each of the register slots was measured from the original bass end of one of the registers. These are given in Table 4 below and are plotted in the graph shown in Figure 8.

c³	722.1	c¹	377.5
b²	709.9	b	364.3
b²	695.9	b	351.0
a²	682.7	a	337.8
g²	669.8	a	325.0
g²	656.3	g	311.6
f²	643.0	g	298.9
f²	629.3	f	285.5
e²	616.6	f	272.1
e²	603.4	e	259.1
d²	590.2	e	246.0
c²	577.0	d	233.1
c²	563.7	d	220.0
b¹	550.8	c	206.4
b¹	537.5	c	193.7
a¹	524.0	B	180.8
a¹	510.7	B	167.2
g¹	497.7	A	154.1
g¹	484.2	G	141.4
f¹	470.8	E	128.1
f¹	457.2	G	115.6
e¹	444.1	F	102.7
e¹	430.7	D	90.0
d¹	417.7	F	77.2
d¹	403.9	[A1]	52.4
c¹	390.2	[G1]	39.4

The graph of Figure 8 is clearly a straight line and, since both axes are linear in scale, the slope and the intercept can be calculated for this line. The use of the method of least squares and the usual regression analysis enables an accurate and unbiased determination of these two factors. This has been done and the slope of the line is found to be 13.1815mm per slot. Using the value of the soldo already calculated for this instrument of 27.345mm from Table 2, this is equivalent to 0.4820 soldi per slot. This does not correspond to an exact, simple number of soldi per single register slot, but it does correspond to 24.10 soldi in a width of 50 jackslots. This strongly suggests that Bolcioni intended 50 jackslots to have a width of exactly 24 soldi³² . Assuming this to be the case then the slope of the graph should, in theory, be exactly 0.480 soldi per jackslot:

Hence:

The braccio with 20 soldi as used by Bolcioni would therefore have a length of 549.23mm. This is only about 0.2% different from the braccio given in the reference in footnote 11 of 550.6371mm (1 soldo = 27.53mm since 1 braccio = 20 soldi). If it is assumed that there was an error in the measurement of the position of each of the register slots of 0.1mm and that Bolcioni made about this same error when he cut the register slots, then, if my assumptions about the separation of the jackslots chosen by Bolcioni is correct, the value of the soldo determined from the regression analysis of the slope of the graph shown in Figure 8 has an error of only 0.08% or 0.02mm. Hence the size of the soldo used by Bolcioni has been determined by this method to an extremely high degree of accuracy. The use of this method has been found to apply in other instruments³³ and points the way to other methods of determining the size of the local unit of measurement, or of refining it.

Conclusions
Using the methods outlined here it has been possible to determine with a high degree of certainty the original dimensions of the baseboard, the original compass, and the original string scalings of the 1627 Bolcioni harpsichord in the Russell Collection. This was made possible only by knowing the size of the local unit of measurement, in this case the Florentine soldo, being used by the builder of this instrument. Assuming that the jacks plucked in the same directions as those in the 1631 Yale harpsichord it was further possible to determine the probable original plucking points for the Russell Collection Bolcioni, although this is clearly dependent upon this assumption.

What I have not shown here, but what seems evident from my analysis of the work of the Florentine makers Francesco Poggio and Bartolomeo Cristofori, is that each of these makers was using a workshop ruler divided up to give a value for the Florentine soldo that was close to the value given by the reference works that I have consulted, but which differed slightly from it. In each case the values are consistent within each workshop, sometimes having values slightly higher or lower than the quoted reference values, but constant and consistent for instruments all coming from the same workshop. This seems to suggest that the methods outlined here, especially for the type of statistical analysis carried out for the register spacing analysis, for example, are capable of giving the size of the unit of measurement of the actual ruler or rulers being used within one workshop. Because there would have been a slight error when dividing up the rulers into their sub-units when doing this by hand, the lengths of the rulers and their sub-divisions would have varied slightly, and this would have resulted in individual variations in the length of the units of measurement which become evident from the type of analysis carried out here. Indeed the slight variations in the quoted values of the units of measurement given by the reference sources also probably have similar origins.

Postscript
I cannot emphasise too strongly at this point that the normal case and keyboard measurements usually quoted for Italian harpsichords, virginals and spinets in catalogues and normal instrument descriptions do not bear any relationship to the unit of measurement used in their design and construction. This is most unfortunate as the sort of analysis carried out in my paper published in the previous volume of this Journal, and for the instrument discussed above, requires a re-measurement of the instrument in order to obtain the necessary baseboard, case-height and other constructional dimensions.

As mentioned in my previous paper, the analyses that I have carried out thus far of a number of instruments made in various centres in Italy has also shown that the design measurements used by the makers do not bear any relationship to any of the numbers from the Golden Series as found by Hubert Henkel in the new catalogue of the keyboard instruments in the Deutsches Museum, Munich³⁴. In his discussion of the Stefano Bolcioni virginals in Munich Henkel suggests, using methods which I feel are open to suspicion, a length for the soldo³⁵ used by Bolcioni of about 29mm. The calculation of this length for the Florentine soldo is based by him, not on the measurements of the baseboard from which Bolcioni began the construction of this instrument, but of the resultant measurements of the outside of the case after the sides were added to the edges of the baseboard. The apparent size of such a unit is therefore larger than the actual size of the unit actually being used. Henkel seems therefore to imply that the instrument is made using the same measurement of the Florentine soldo as that given by a number of authors of 29.18mm³⁶, considerably larger than the value of the soldo of about 27.4mm found here and for other Florentine instruments. However the 29.18mm measurement corresponds to the length of the unit used in Florence after the standard of length there was changed as a result of legislation passed on 2 July, 1782³⁷ , and therefore not the unit being used in the historical period of harpsichord and virginal building. As shown here, and as given in a number of highly-reliable sources not the least of which is Diderot, the Florentine soldo being used at the time of Bolcioni and a number of other makers working in Florence during the historical period was close to 27.4mm. However, it is more likely in the opinion of Henkel, that Bolcioni was using a unit of 22.197[sic]mm to design and build this instrument. But I have found no reference to a unit of this length, nor to a length anywhere near this value, being used in Florence or even anywhere else in Tuscany among the 20 or so references to Italian metrology that I have consulted. Using this length leads Henkel to believe that some of the measurements of the instrument expressed in this totally spurious value for the Florentine soldo, most of which are anyway not those with which Bolcioni began the design of the instrument, belong to numbers which make up the Golden Series!

In my opinion Henkel's deduction of the use of the numbers of the Golden Series in the design of the instruments in the Deutsches Museum in particular, and of historical stringed-keyboard instruments in general, is extremely dubious. In practically all cases he does not use the measurements with which the makers began the design of their instruments but rather of consequent measurements resulting from the addition of case sides, mouldings, baseboard thicknesses, etc. to the parts that were originally measured out in simple numbers of local units by the instrument builder. It is my opinion that the design of these instruments was based on simple, easy-to-remember numbers which resulted from the basic pragmatic problems faced by the maker when fitting the case of the instrument around the string band.

The instrument design began with the string band which was calculated to give the correct pitch and plucking points. Normally either or both the length of the c or the f notes were marked out and used as the basis of the design. In virginals the transverse spacing of the jackslots in the boxslide was made to match the spacing of the key tails. Using some convenient lateral spacing of the jackslots that was suitable to give the jacks and strings sufficient clearance, and angling the strings by a convenient and desired amount³⁸ , the position of the left- and right-hand bridges could be located by measuring out from marks made on the soundboard surface according to the design requirements for the plucking distances and the string scalings. The maker then fitted the case walls around the string band, and the keyboard into the space underneath the register. Similarly for the harpsichord the lateral spacing of the keys and strings had more mundane origins, and depended ultimately on the anatomy of the human hand and not on a desire to use a keyboard width equal to one of the numbers from the Golden Series or even, for that matter, an integral number of units of whatever the local measurement was. The plucking points were either chosen first, as in the case of the Edinburgh Bolcioni harpsichord, and then the string scalings were measured out and marked in the soundboard area either directly onto the baseboard or onto the soundboard placed temporarily in its final position in the instrument.

Theoreticians like Arnault de Zwolle³⁹ may have used numbers from the Golden Series in their description of the design of keyboard instruments but, by the time in which the first extant instruments were built some 100 years later, the majority of the practical work-a-day instrument makers were much more pragmatic in their approach.

Footnotes:

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