The case, stringing and fretting design of the 1543 Venetian clavichord by Dominicus Pisaurensis

an article published in  De Clavicordio, Proceedings of the V International Clavichord Symposium/Atti del V congresso internazionale sul clavicordo.  Magnano, 5-5 September 2001, edited by Bernard Brauchli, Alberto Galazzo and Ivan Moody, (Musica antica a Magnano, Magnano, 2002), 91-107

by Grant O'Brien

 

 

String-scaling design

            Recent work that I have done on the use of the local unit of measurement to design and build historical keyboard instruments suggests that the use of simple units of the local unit of measurement was as fundamental to the design of the string scalings as it was to the design and construction of the case[1].  For example, instruments made in different centres throughout Italy and designed for yellow brass stringing and tuned to normal reference pitch R would have treble scalings based on a length for c2 given in the following table[2]:

 

 

 

10 soldi = 1 palmo = ½ braccio = 275.6mm (in Florence 1 soldo = 27.56mm)

once =272.0mm (in Milan 1 oncia = 36.265mm)

13 once = 283.9mm (in Naples 1 oncia = 21.835mm)

15 once = 279.3mm (in Rome 1 oncia = 18.619mm)

10 once = 289.8mm (in Venice  1 oncia = 28.98mm)

Table 3 - Common c2-equivalent scalings of brass-strung harpsichords and virginals

 

Indeed it is likely that the local variation in pitch from one centre to another in Italy and elsewhere arose because the design and construction of instruments, and especially of organs, was based on the different local units of measurement.  Brass-strung harpsichords, virginals and clavichords designed using each of these local units of measurement would, however, all sound well at roughly the same pitch.  This suggests that instruments using other stringing materials like iron and red brass were also designed using scalings based on a simple number of the local units of measurement.

 

            Hence it would seem to be worthwhile to look at normal iron, yellow brass and red brass string scalings and to compare them with simple numbers of Venetian once when considering a clavichord like the one made and designed by Pisaurensis.  This is done in Table 4 below.

 

 

 

                                                                         At a ‘normal’ pitch R                           At a pitch of R + 5

                          Taskin's      Ruckers'        c-based scalings    g-based scalings                   c-based scalings

   Material           scalings       scalings            once      mm           once      mm                         once      mm

      Iron             364.0mm      355.0mm            12      347.8           8       231.8                         8       231.8

Yellow brass       292.6mm     289.5mm            10       289.8          6     193.2                        6    193.2

  Red brass          231.4mm     211.2mm             8       231.8          5     154.6                        5     154.6

Table 4 – Typical French and Flemish scalings compared with some simple Venetian measurements

 

            From Table 4 it is clear that the normal seventeenth and eighteenth-century scalings found in North-European instruments are close to c2 scalings based on 12, 10 and 8 Venetian once for iron, yellow brass and red brass stringing respectively.  For the note g2 a fifth higher than c2, the corresponding scalings would just be  those of c2 and these are shown near the middle of Table 4  Thus for an instrument pitched a fifth higher than reference pitch at R + 5, iron, yellow brass and red brass stringing would correspond to c2–equivalent scalings of 8, 6 and 5 Venetian once respectively (shown on the right-hand side of Table 4).

 

            Let us look therefore at the scalings of the Pisaurensis clavichord to see whether or not any aspect of the stringing of this instrument fits into this pattern.  The string lengths for each note with the bridges in their present positions are given in Table 5 below.

 

                                                   c3        117½

                                                   b2          126

                                                   bb2         132

                                                    a2          141

                                                   g#2        150½

                                                   g2           159

                                                   f#2        168½

                                                    f2          178

                                                    e2        188½

                                                   eb2        198½

                                                    d2          210

                                                   c#2        224½

                                                    c2         234½

                                                    b1         246½

                                                   bb1         259

                                                    a1         274½

                                                   g#1        287½

                                                    g1          302

                                                   f#1          321

                                                    f1           335

                                                    e1          347½

                                                   eb1         361½

                                                    d1           386

                                                   c#1          398

                                                    c1            418

                                                     b           450½

                                                     bb          466½

                                                     a            476½

                                                    g#            510

                                                     g            534½

                                                    f#            545

                                                    f              570

                                                    e              581

                                                   eb             601½

                                                    d              733

                                                   c#             745

                                                    c              756

                                                    B             766

                                                   Bb            779

                                                   A              869

                                                   G              894

                                                   F              919

                                                   E              880

                                                   D              904

                                                   C              933

Table 5 – String scalings as measured with the bridges in their present positions

Dominicus Pisaurensis clavichord, Venice, 1543

Leipzig Musikinstrumentenmuseum der Universität, Clavichorde Cat. No. 1

 

            These scalings are plotted in the graph shown in Figure 2 below.  This graph shows the pitches of the played notes at the bottom of the graph and, assuming that the instrument was designed to sound at a pitch of R + 5, with the actual sounded pitch given at the top of the graph.  In all of the discussions below unless otherwise stated the notes referred to are the played notes, not the sounded notes.

 

 

Figure 2 – Measured scalings with the bridges in their present positions

Dominicus Pisaurensis clavichord, Venice, 1543

Leipzig Musikinstrumentenmuseum der Universität, Clavichorde Cat. No. 1

 

            The graph shown in Figure 2 is plotted on semi-logarithmic graph paper.  This is used because it makes Pythagorean scalings, which double and halve with each octave drop and rise in pitch, plot as straight lines.  Indeed Pythagorean scalings for c2-equivalent scalings given by 8, 6 and 5 Venetian once have been drawn on this graph, and all of these correspond to straight lines.

 

            Comparing the theoretical thin lines for Pythagorean c2 scalings of 8, 6 and 5 Venetian once with the measured scaling in the treble it is clear that the line formed by the measured points is close to the theoretical line for iron scalings (c2 = 8 once at a pitch of R + 5) but deviates gradually more and more for the notes at the extreme treble end of the compass.  The measured length of c2 itself is 234½mm, about 2.7 mm longer than 8 Venetian once = 231.84mm.  The measured lengths in the extreme treble are also about 2.7mm too long when compared to the theoretical line, and this suggests that the whole treble bridge is now about 2.7 mm too far away from the tangents.

 

            On the other hand the measured length of tenor c is somewhat short of the theoretical line for yellow brass stringing based on c2 = 6 Venetian once.  At a pitch of tenor c two octaves lower than c2 the equivalent of c2 = 6 once is  once = 26 once = 772.8mm.  The measured length of tenor c is 756mm which is about 16.8mm less than this value.  Therefore moving the middle bridge away from the tangents by this amount would bring it into agreement with the theoretical value for yellow brass stringing above this note.  In a parallel way the third bridge would also have to be moved away from the tangents by 8.4mm at the note F in order to position it at a distance of 4x8 once = 32 once = 927.36mm.  Instead of giving an F scaling of 919mm as it does in its present position it would then be in a position where it would correspond to a red brass f2-equivalent scaling of exactly 8 once (ie a c2 scaling of 5 once transposed).[3]

            The lengths c2 = 8 once, c = 26 once, and F = 32 once could be considered to be the critical design scalings for this clavichord corresponding to notes critically stressed just at their breaking points for the materials iron, yellow brass and red brass respectively.  It is also, in my view, these lengths that determine the correct positions of each of the three moveable bridges.  This has been shown diagramatically below in Figure 3 where a plan view of the instrument is shown along with the fret positions and the string pairs for each of the critical design notes.  The green lines show the new positions of the bridges which would have to be moved from their old positions in order to achieve these critical design scalings.

 

Figure 3 – Critical design scalings, the proposed bridge positions (in green), and the fret positions

Dominicus Pisaurensis clavichord, Venice, 1543

Leipzig Musikinstrumentenmuseum der Universität, Clavichorde Cat. No. 1

  

A numeric analysis of all of the string lengths is given below in Table 6

 

Played note

Sounded note

Measured length

Corrected length

Design length

Corrected length in once

Design length in once

Size of chromatic semitones

Size of diatonic semitones

Size of major second

c3

g3

117½

114.8

116.6

3.96

4.02

 

 

 

b2

fT3

126

123.3

124.8

4.25

4.31

 

124

 

bI2

f3

132

129.3

130.4

4.46

4.50

82

 

206

a2

e3

141

138.3

138.2

4.77

4.77

 

 

 

gT2

eI3

150½

147.8

147.9

5.10

5.10

 

115

 

g2

d3

159

156.3

154.6

5.39

5.33

97

 

212

fT2

cT3

168½

165.8

167.4

5.72

5.78

 

 

 

f2

c3

178

175.3

175.0

6.05

6.04

96

 

 

e2

b2

188½

185.8

187.2

6.41

6.46

 

101

197

eI2

bI2

198½

195.8

195.6

6.76

6.75

91

 

191

d2

a2

210

207.3

207.4

7.15

7.16

 

 

 

cT2

gT2

224½

221.8

221.9

7.65

7.66

 

117

 

c2

g2

234½

231.8

231.8

8.00

8.00

77

 

193

b1

fT2

246½

243.8

241.9

8.41

8.35

 

 

 

bI1

f2

259

256.3

252.8

8.84

8.72

87

 

 

a1

e2

274½

271.8

270.5

9.38

9.33

 

102

188

gT1

eI2

287½

284.8

285.3

9.83

9.84

 

 

 

g1

d2

302

299.3

298.1

10.33

10.29

86

 

 

fT1

cT2

321

318.3

318.9

10.98

11.01

 

107

193

f1

c2

335

332.3

333.3

11.47

11.50

75

 

181

e1

b1

347½

344.8

343.4

11.90

11.85

 

 

 

eI1

bI1

361½

358.8

358.9

12.38

12.38

69

 

 

d1

a1

386

383.3

384.0

13.23

13.25

 

114

183

cT1

gT1

398

395.3

396.9

13.64

13.70

 

 

 

c1

g1

418

415.3

414.7

14.33

14.31

85

 

 

b

fT1

450½

447.8

443.8

15.45

15.31

 

130

216

bI

f1

466½

463.8

463.7

16.00

16.00

61

 

191

a

e1

476½

473.8

475.2

16.35

16.40

 

 

 

gT

eI1

510

507.3

508.5

17.51

17.55

 

118

 

g

d1

534½

531.8

531.3

18.35

18.33

82

 

200

fT

cT1

545

542.3

540.8

18.71

18.66

 

 

 

f

c1

570

567.3

565.1

19.58

19.50

78

 

 

e

b

581

577.7

573.2

19.93

19.78

 

 

 

eI

bI

601½

598.8

598.9

20.66

20.67

62

 

 

d

a

733

749.8

748.7

25.87

25.83

 

 

 

cT

gT

745

761.8

760.7

26.29

26.25

 

 

 

c

g

756

772.8

772.8

26.67

26.67

 

 

 

B

fT

766

782.8

782.5

27.01

27.00

 

 

 

BI

f

779

795.8

797.0

27.46

27.50

 

 

 

A

e

869

877.4

876.6

30.28

30.25

 

 

 

G

d

894

902.4

903.2

31.14

31.17

 

 

 

F

c

919

927.4

927.4

32.00

32.00

 

 

 

E

B

880

888.4

888.7

30.66

30.67

 

 

 

D

A

904

912.4

912.9

31.48

31.50

 

 

 

C

G

933

941.4

941.9

32.48

32.50

 

 

 

                                                                                                                   Total:        1127           1028      2352

                                                                           Average measured size of interval:          80             114      196.6

                                                                        Size of ¼-comma meantone interval:        76.05         117.11    193.16

Table 6 – Theoretical string lengths and fretting with the bridges in their proposed positions

Dominicus Pisaurensis clavichord, Venice, 1543

Leipzig Musikinstrumentenmuseum der Universität, Clavichorde Cat. No. 1

 

            In Table 6 the played notes on each of the three bridges are indicated by the colours green, peach and violet in column 1.  The grouping of the fretted notes of the 11 pairs of strings on the top bridge has also been indicated in columns 1, 5 and 7 where it can be seen that there is double-, triple-, and quadruple-fretting.  It should be noted that, unlike most eighteenth-century fretting system, there are no fretting groups which are repeated from octave to octave.  For example bI is fretted [bI2, b2, c3] in the top octave, [a1, bI1, b1] an octave lower, and [bI, b, c1, cT1] an octave lower still.  At first this seems somewhat unusual and arbitrary.  However, when examined in detail the system used here has one enormous advantage when it comes to tuning the instrument.  If any one of the diatonic notes is chosen for tuning and its pitch is fixed relative to a tuning standard, then the rest of the instrument can be tuned by tuning octaves either up or down from this chosen note.  This can be seen by beginning on any diatonic note on the top bridge and noting that, by tuning up or down an octave, this also tunes a major second higher or lower than the chosen note.  If this is done repeatedly the result is to tune all of the 11 top strings without the necessity of having to temper any of the intervals involved:  it is all done by the fretting design.  Once the notes on the top bridge have been tuned, then the notes on the two lowest bridges can also be tuned in octaves in the usual way.

 

The critical design lengths in Venetian once have been indicated by dark blue shading of column 6 in Table 6.  The measured length in column 3 is the uncorrected length of the strings with the bridges in their present positions.  The corrected lengths in the next column are the lengths of the strings that would result from a movement of the top bridge (notes shaded in green) by 2.7mm toward the tangents, of the middle bridge by 16.8mm away from the tangents and a movement of 8.4mm away from the tangents for the bottom bridge.  These can be compared with the design lengths, which are the lengths that I feel were used by Pisaurensis when building and designing this instrument.  Remember that the bridges were moved to give exactly the desired lengths for the critical notes in the columns giving the corrected and design lengths in columns 6 and 7. 

 

However fixing the lengths of the critical notes by moving the bridges naturally also affects the lengths of the other notes on the bridges.  The lengths of the longest string in each of the fretted groups is indicated in the design length column with light blue shading.  It is clear that, having moved the bridges by the necessary amounts to give the desired critical lengths, this then gives lengths for the lowest note of each of the fretted groups which are close to a simple number or fraction of Venetian once

 

Go to the next chapter

 


[1] A book on historical stringing practice illustrating the traditions in various centres in Italy is currently in preparation by me.  In the work that I have done so far preparing this book I have been able to show how the local unit of measurement relates to the string scaling design and to the use of the most common stringing materials of iron, yellow brass and red brass.

[2] See footnote 6.

[3] Karin Richter, who has made a copy of this instrument, has pointed out to me that the two bass bridges are slightly too high in their present positions so that the strings are not all in the same plane.  Moving the two bass bridges away from the tangents and down the right-hand sloping soundboard section as suggested here would have the result of bringing all of the strings closely to the same level for all three bridges.