The use of simple geometry and the local unit of measurement in the design of Italian stringed keyboard instruments:

an aid to attribution and to organological analysis

 

Grant O'Brien

 

A harpsichord dated 1631 by Stefano Bolcioni, Florence in the Yale University Collection of Musical Instruments, New Haven, Conn.

          An unusual harpsichord in the Yale University Collection of Musical Instruments[30] bears the signature ‘STEFANVS BOLCIONIVS PRATENSIS F MDCXXXI F’ written in ink in Roman capitals on the lower back part of the nameboard.  Below this in small cursive script is a second signature ‘1631 Stefanus · Bolcionius · Pratensis fecit’[31].  The compass is now C to f3 chromatic, but was originally the common C/E to f3 chromatic compass, and the original c2 scalings were 262/263mm.  Figure 9 shows a schematic representation of the cheek section and of the keywell scrolls of this harpsichord.

          The most unusual aspect of this harpsichord is that it has two nuts on the wrestplank.  The nut nearest to the player serves the right-hand choir of strings and is slightly higher than the nut further from the player which carries the left-hand choir of strings.  The two nuts are very close together in the treble and indeed one of them is partly sliced away in order that the two can be separated by the correct amount.  Further down in the bass the two nuts gradually diverge until, at the lowest note, there are several centimetres separating them.  The near, higher nut has scallops cut out of it to allow the strings of the far nut to pass by unimpeded to their tuning pins.  The tuning pins are not arranged as normal, but are widely separated and the rear row of pins tunes the left-hand (what would normally be the long) choir of strings.  The strings therefore diverge from the nut towards the tuning pins instead of remaining parallel as is more usual.[32] 

          The scalings of this harpsichord produced as a result of this unusual arrangement of the two nuts are given in Table 6:

  

                                    Left-plucking 8'                  Right-plucking 8'           Comparison of string lengths[33]

                                  String        Plucking               String        Plucking             Nominal              Florentine

                                 Length          Point                 Length          Point                   mm                     soldi

                    f 3             97                45                       96                28                      96.4                     3½

                    c3            122               57                      129                44

                    f 2            194               74                      194                63                    192.7                    7

                    c2            262               86                      263                79

                    f 1            399              102                     399               100                   399.2                 14½

                    c1            532              113                     530               114

                     f             783              127                     776               131                   784.6                 28½

                     c            1039             137                    1017              140

                    F            1472              150                   1450               153                  1472.9                  53½

                  C/E          1486             152                   1497               155

Table 6

Scalings in mm of the original C/E to f 3 state (the present state has been ignored)

Single-manual harpsichord by Stefano Bolcioni, Florence, 1631

Yale University Collection of Musical Instruments, Catalogue No. 4889.72

 

          It is clear from Table 6 that the intention of the maker was to equalise the scalings of the two 8' registers by a correct positioning of the two nuts.  In the middle of the compass around f1 Bolcioni achieves both scalings and plucking points which are essentially the same for both sets of 8' strings.  Clearly string scalings and plucking points were important to Bolcioni and aspects which occupied a significant role in his (and that of most other harpsichord and virginal maker’s) overall design.  And this design was clearly based on the Florentine soldo.

 

 

Figure 9

Schematic representation of the cheek section and the keywell scrolls

Single-manual harpsichord by Stefano Bolcioni, Florence, 1631

Yale University Collection of Musical Instruments, Catalogue No. 4889.72

 

          The measurements of the baseboard and case height are given in Table 7 below:

 

                                                                                               Measured

                                                                                                 dimension

                                                                                                     mm

                                                                          Length:               1827

                                                                           Width:                778½

                                                                          Cheek:                 422

                                                                               Tail:                212

                                                                      Tail angle:                75º

             Component of tail perpendicular to the spine:               205

                        Component of tail parallel to the spine:                56

                                                                   Case height:               184

tan 75º = 3.732 ≈ 3.75 =

 

Table 7

Baseboard dimensions and case height

Single-manual harpsichord by Stefano Bolcioni, Florence, 1631

Yale University Collection of Musical Instruments, Catalogue No. 4889.72

 

 

Analysis of unit of measurement used in the construction of the Yale Bolcioni single-manual harpsichord:

          The procedure for determining the unit of measurement used to construct this harpsichord begins with the measurement of the angle of the tail, which was found to be 75º.  The tangent of this angle is tan 75º = 3.732 ≈ 3.75 = .  This suggests that the two sides of the triangle that were used to construct the tail angle are 7½ soldi[34] and 2 soldi which, mathematically, would form an angle of 75.19º.  This angle is very close to the measured angle and well within the error of measurement.  Measurement in millimetres of the length of the two sides constituting the orthogonal components of the tail side gives an approximate estimate of the size of the soldo 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.  A summary of the measurements of the baseboard and case height in soldi is given in Table 8:

 

 

                                    Left-plucking 8'                   Right-plucking 8'         Comparison of string lengths[1]

                                  String        Plucking               String        Plucking             Nominal     Florentine

                                 Length          Point                 Length          Point                   mm             soldi

                    f 3             97               45                        96               28                       96.4             3½

                    c3            122              57                       129              44

                    f 2            194              74                       194              63                      192.7              7

                    c2            262              86                       263              79

                    f 1            399             102                      399             100                     399.2           14½

                    c1            532             113                      530             114

                     f             783             127                      776             131                     784.6           28½

                     c            1039            137                     1017            140

                     F            1472            150                     1450            153                   1472.9          53½

                  C/E          1486            152                     1497            155

                                             tan 75.19° = 3.75 =           arctan  = 75.19°

Table 8

The calculation of the local unit of measurement

Single-manual harpsichord by Stefano Bolcioni, Florence, 1631

Yale University Collection of Musical Instruments, Catalogue No. 4889.72

 

          These measurements are shown in the diagram in Figure 10 where the actual measurements in millimetres are shown on the left, and the measurements in units of the local measurement are shown on the right.

          For Florence Johann Georg Krünitz[35] mentions the use of the bavelle which is clearly equal to a palmo or half a Florentine braccio[36].  As the braccio was divided into 20 soldi, the bavelle, like the palmo, must have had a length of 10 soldi.  The calculated length of the bavelle given by Krünitz is 273.41mm, so that the soldo must therefore have had a length of 27.341mm.  This seems clearly to be the unit being used by Bolcioni (the difference between this and the unit found here for the Yale harpsichord is only 0.2%).

          A further look at Appendix 2 giving the units of measurement used in the various centres in Italy during the historical period shows that in Florence the braccio, divided into 20 units, had a length according to Angelo Martini[37] of 551.202mm.  Hence the soldo had a length of:

 

                                                                

The length of the braccio is also variously given as 550.6371[38], giving a soldo of:

 

                                                                 

These are both close (error @ 0.8%) to the length of the soldo found here and seem to confirm that the instrument was indeed made in Florence. 

 

 

Figure 10

Baseboard measurements in millimetres (left) andin units of the Florentine soldo used by Bolcioni = 27.29mm (right)

Single-manual harpsichord by Stefano Bolcioni, Florence, 1631

Yale University Collection of Musical Instruments, Catalogue No. 4889.72

 

 

Click here to go to the next section

 

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

 

Endnotes:

[1] Here, anticipating the results found below, the string scalings and other measurements have been expressed in units of the Florentine soldo = 27.52mm (see footnote 38).

[30] This instrument bears the Yale University of Musical Instruments catalogue number 4889.72.  My thanks to Richard Rephann, curator of the Collection, for his kind help and co-operation in my examination of this instrument.

[31] Although it seems unusual that the instrument should be signed twice, both signatures are similar to those on other Bolcioni instruments.  The one in Roman capitals is similar to that on the Russell Collection harpsichord, and the one in cursive script is similar to the signatures on the virginals by Bolcioni in Leipzig (see footnotes 39 and 41), Munich (see Hubert Henkel, Besaitete Tasteninstrumenten, (Erwin Bochinsky, Frankfurt-am-Main, 1994) Catalogue Number 1907-9231, p. 106-8), and in Rome (see Louisa Maria Cervelli, ‘Per un catalogo degli strumenti a tastiera del Museo degli Antichi Strumenti Musicali’, Accademie e Biblioteche d’Italia, 44, Nº 4-5 (1976) Inv. No. 1764, p. 318-9 and La Galleria Armonica (Istituto Poligrafico e Zecca dello Stato, Rome, 1994) 218.  I can see no reason to doubt that both of the signatures on the Yale harpsichord were made by anyone other than Bolcioni.

[32] The reason for this unique arrangement is almost certainly that, by making the strings diverge as they leave the two nuts, more space can be given between the pins in the near nut and the scalloped cut-outs for the strings of the second nut further from the player.  Otherwise the pins on the near nut would have had to have been placed in a weak position right on the edge of the scalloped cut-outs.

[33] Here, anticipating the results found below, the string scalings and other measurements have been expressed in units of the Florentine soldo = 27.52mm (see footnote 38).

[34] It will be shown below from the size of the unit of measurement that Florence is the centre in which the instrument was built.  The Florentine braccio was divided into 20 soldi, and not into once as found in some other centres.

[35] Johann Georg Krüniß, Öconomische Encyklopädie oder allgemeines System der Staats-, Stadt-, und Landwirtschaft, in alphabetischer Ordnung, 15 (Joseph Georg Traßler, Brünn, 1788) p. 519-22.  These are given as 1440-th parts of the Paris pouce, and were converted into millimetres by me using the millimetre length of the pouce given by Colonel Cotty, Aide-Mémoire, p. 896 (see footnotes 10 and 38).  My thanks to John Koster for pointing out this source to me.

[36] The plural form of braccio is irregular in Italian and changes gender so that il braccio in the singular becomes le braccia in the plural.

[37] See: Angelo Martini,, Manuale di metrologia, (E. Loescher, Turin, 1883; reprint Editrice Edizioni Romane d’Arte, Rome, 1976) 206.  Martini is one of the few authors to give the length of the braccio and soldo before the standard of length in Florence was re-defined by legislation passed on 2 July, 1782.

[38] Colonel Cotty, Aide-Mémoire a l’usage des officiers d’artillerie de France, 2 (Paris, 1819) 896-7gives the length for the Florentine braccio da terra divided into 20 soldi as 550.3671mm.

Go to my home page