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

**
** Table 6
above also reveals that Pisaurensis used the Venetian oncia to set out
the position of the tangents not only for the lowest notes of each of the
fretted groups on the top bridge, but also for all of the lowest
notes on each of the bottom bridges. If one compares the corrected lengths with
my proposed design lengths in *once* for the strings on the two lowest
bridges, then it is clear that each of these string lengths must have been
designed by Pisaurensis to be a simple number and fraction of Venetian *once*.
This result had not been expected when moving the bridges to give the critical
lengths, but provides convincing evidence about how Pisaurensis designed the
fretting of this instrument:

1.
he used the Venetian *oncia* in the design of
the string lengths of his instrument,

2. the bridges were positioned in those locations given by the critical lengths for each bridge,

3.
the strings lengths of each of the lowest notes of
the fretted groups on the top bridge were also designed in terms of a simple
number and fraction of Venetian *once* and

4.
the string lengths and tangent positions for **
all** of the notes on the lowest two bridges were also designed to be a
simple number and fraction of Venetian

As is well known
the position of the tangents on the ends of the keylevers in any fretted
clavichord gives an indication of the size of the semitone for each of the
fretted pairs producing the semitones[1].
The sizes of these semitones in cents have been calculated and are given in the
last two columns of Table 6.
Here it is clear that a number of different sizes of semitones is produced by
the fretting of this instrument, and that there is a clear division into
chromatic and diatonic semitones in the usual places with the enharmonic
equivalent note g^{T}/a^{I}
being tuned to g^{T}
giving a small chromatic semitone g-g^{T}.
The sizes of these semitones have been transferred to Table 7
where the sizes of each of the semitones can be compared in each of the three
top octaves (the strings of the notes from c to d of the lowest octave are
placed on the middle bridge and are unfretted).

Octave c-c^{T}
c^{T}-d d-e^{I}
e^{I}-e
e-f f-f^{T}
f^{T}-g g-g^{T}
g^{T}-a a-b^{I}
b^{I}-b b-c

Top (c^{2}-c^{3}): 77 117
91 101 96 97
115 82 124

Middle (c^{1}-c^{2}): 85 v 114v
69 75 v 107 86 102
87

Bottom (c-c^{1}):
- - - - - - 62
78 82 118 61 130

Average: 81 117 114 74 101 83 107 88 117 102 77 127

Table 7 – The sizes in cents of each of the semitones produced by the top bridge fretting patterns

**Leipzig Musikinstrumentenmuseum der
Universität, Clavichorde Cat. No. 1**

There is a number of unusual and inconsistent features among these results. It
is possible to imagine a tuning system in which there are different sizes of
either or both the chromatic and diatonic semitones[2].
However, in order for the octaves to be in tune, any fretting system where there
are combinations of treble and quadruple fretting across different notes in
separated octaves should have the same size of semitone in each octave. If the
corresponding semitones are not of the same size then it is impossible for the
octaves played on the top and bottom notes of the semitone pair to be in tune.
Generally the diatonic semitones are fretted only once in each of the top 3
octaves and so there is not a problem of tuning the octaves for any of these
notes. Where the same diatonic semitones are fretted more than once these
semitones (g^{T}-a
and b-c) occur in separated octaves so no problem of octave tuning would occur.
However for the chromatic semitones there are serious octave tuning problems for
the intervals e^{I}-e
, f-f^{T} and b^{I}-b
where the varying sizes of the semitones themselves would give rise to octaves
that are badly out of tune by 22 cents, 21 cents and 26 cents, respectively.
Other smaller problems would also occur for some of the other chromatic
semitones. Some of the apparent error may be the result of simple measurement
inaccuracy, especially for the treble part of the compass where an error in the
measured position of only one millimetre would make a difference of about 10
cents in the size of the calculated interval.

A
related inconsistency in the tuning and temperament produced by the fretting
pattern of this instrument involves the sizes of the major seconds formed by the
triple and quadruple fretting groups. The last column in Table 6
gives the size of each of the major seconds formed by these fretting groups.
These can be calculated either directly from the corrected lengths of the
strings or simply by adding together the sizes of the chromatic and diatonic
semitones which comprise the major second (here and there a slight rounding-off
error occurs in the final decimal place of the two). As can be seen the major
seconds vary in size from 181 cents to 212 cents (an equally-tempered major
second is 200 cents wide and a ¼-comma meantone major second is 193.2 cents).
In the top octave the major second b^{I2}-c^{3}
has a size of 206 cents and in the bottom octave of fretted notes b^{I}-c^{1}
has a size of 191 cents. This is a difference of 15 cents, an amount not
accounted for by the error in measurement, and an amount that would be clearly
audible. This makes a nonsense of using the fretting patterns to tune the
instrument in octaves using the diatonic notes as described above.

Nonetheless there seems to be a deliberate attempt on the part of Pisaurensis to
use his fretting system to produce different sizes of chromatic semitones, and
seemingly also different sizes of major seconds. It seems equally clear,
however, that the fretting pattern designed by Pisaurensis produces a
temperament that is musically unviable: namely **it produces octaves that are
not in tune**. No solution has so far been found to this predicament.

From Table 7
it can be seen that the average sizes of the individual chromatic semitones vary
from 74 cents to 88 cents and have an average size of 80.5 cents (r.m.s.
deviation from ¼-comma meantone = 4.8 cents). The diatonic semitones vary from
101 cents to 127 cents and have an average size of 114.2 cents (r.m.s. deviation
from ¼-comma meantone = 7.9 cents). Quarter-comma meantone tuning is a kind of
equal temperament in those keys that are playable since each of the intervals
are of exactly the same size regardless of the tonality. Hence in ¼-comma
meantone all chromatic semitones are of the same size and all diatonic semitones
are different from this but also all of the same size as one another. Although
apparently not designed with equal sizes of either kind of semitone in mind, the
correct position of the tangents for ¼-comma meantone tuning have been
calculated for this instrument for the fretted notes on the top bridge and these
are the lengths given in the design-length column of Table 6
for each fretting group. Comparison of these with the actual lengths given in
the columns of the corrected lengths expressed either in millimetres or in *
once* shows that, although some groups are very similar, there is a small but
significant difference between them for other groups.

At the moment the Leipzig Musikinstrumentenmuseum is temporarily closed and the Pisaurensis clavichord is not accessible. Without first-hand access to the instrument to enable the tangent positions to be re-measured it seems that the question of the exact temperament produced by the various fretting patterns of this instrument cannot be resolved[3].

[1]
See John Barnes, *Restoration of German Fretted Clavichord c.1700*,
(unpublished restoration report held by the Russell Collection of Early
Keyboard Instruments at the University of Edinburgh, Edinburgh, 1967),
Edwin M Ripin, ‘A reassessment of the fretted clavichord’, *The Galpin
Society Journal*, 23 (1970) 40-8, Herbert Henkel (see footnote 1) and
Peter Bavington and Miles Hellon, ‘Evidence of historical temperament
from fretted clavichords’, FOMRHI Quarterly, 64 (July, 1991) 55-7.

[2]
Denzil Wraight, for example, suggests that this
instrument and the so-called ‘Onesto Tosi’ clavichord in the Boston
Museum of Fine Arts, were both designed to produce third-comma meantone
which introduces unequal sizes of chromatic semitones. However, his
calculations use the present un-corrected scalings which are basically
unrelated to the original makers’ design, and he does not confront the
problematic octave mis-tunings. See Denzil Wraight, ‘The tuning of two
16^{th}-century Italian clavichords;, *Clavichord
International*, 1, no 2 (November, 1997) 49-53.

[3] What is required, of course, is to measure accurately the positions of the tangents not at their top end but where they enter the keylever’s top surface, this being the point marked out and designed by the maker to give the lengths he wanted.