The vibrating lengths of the strings of the polygonal virginal and of
the Ridolfi harpsichord can be roughly determined from the drawings. For
purposes of comparison, a tabulation of the vibrating lengths (in
inches) of the _C_ strings on both instruments follows:
_Polygonal _Harpsichord_
virginal_
c´´´ 6-5/8 5-1/16
c´´ (pitch C) 12-15/16 10
c´ (middle C) 25-9/16 20-1/2
c 43-5/16 42-1/16
C/E 50-5/6 61-1/4
The lengths shown for the harpsichord represent the shorter of the two
strings with which each key is provided.
In order to produce a uniform tone color throughout the compass of a
stringed instrument, it is necessary, among other things, to have the
tension of all the strings reasonably uniform. In the treble this is
accomplished by varying the string lengths. Since the length of a
vibrating string is inversely proportional to its frequency, each string
is made about half as long as the string an octave below, two thirds as
long as the string a fifth below, etc. This principle cannot be carried
all the way into the bass since the lowest strings would be
inconveniently long, so somewhere below middle _C_ the strings are
gradually shortened and the diameters of the wires are increased in
compensation.
As the above comparison shows, the string lengths are approximately
doubled at each descending octave down to _c´_ on the virginal and _c_
on the harpsichord. The shape of the case allows the harpsichord to have
longer bass strings than the virginal; between _c´_ and _c_ the string
length is doubled in the harpsichord. However, in the virginal the _c_
string is considerably less than twice as long as the string an octave
above. In fact, the bass strings of the virginal are shortened to such
an extent that the lowest string of the harpsichord is much longer than
the lowest string of the virginal, although in the treble the virginal
has longer strings than the harpsichord.
If the length of one treble string of an instrument of this sort is
known, the lengths of all but the bass strings can be readily inferred;
we can approximately describe the lengths of two-thirds to three-fourths
of the strings of either of the above instruments by giving the length
of one string. It has become customary to use _c´´_ for this purpose,
and to refer to it in such cases as pitch _C_.
In examining a number of Italian harpsichords and virginals dating from
1540 to 1694, lengths for pitch _C_ ranging from 8" to 13-3/4" have been
found. This seems to be a great discrepancy for instruments that are
otherwise so standardized. Since a uniform standard of pitch did not yet
exist in the 16th and 17th centuries, we would expect the string lengths
employed to be varied somewhat in order to accommodate the instruments
to higher or lower tunings. Also, a preference for the sound of thinner,
longer wires or shorter, thicker ones may have caused some builders to
increase or decrease the string lengths on their instruments in
proportion to the string diameters chosen. We have no precise evidence
concerning the original wire gauges of the strings of Italian
harpsichords and virginals. Although the variety of pitch _C_ lengths
encountered on the instruments studied can partially be accounted for by
these two factors, a third and more important cause existed.
Among the 33 instruments about which information has been secured, a
correlation is discernible between the apparent manual compass and the
pitch _C_ string lengths. Sixteen of the instruments ascend to _f´´´_.
For these, the length of the pitch _C_ string varies from 10-1/4" to
13-3/4". The remaining instruments, with either _a´´_ or _c´´´_ as the
highest notes, have pitch _C_ strings ranging from 8" to 11-3/8" in
length. If the average tension and wire diameter of the two groups are
assumed to have been about equal, the difference in string lengths would
suggest a corresponding difference in pitch, the instruments having the
compass extended to _f´´´_ sounding somewhat lower than the others.
[Illustration: Figure 11.--ACTION OF HARPSICHORD. A, bottom; B, belly
rail; C, soundboard; D, wrest plank; E, key frame; F, rack; G, key; H,
jack; I, jack rail. Scale, 1:2.]
There is some historical evidence that this actually was the case. In
his _Theatrum Instrumentorum_ Michael Praetorius[1] pictures a polygonal
virginal, which appears to be very much like the many Italian examples
that survive today, and a rectangular virginal that seems to be Flemish.
He specifies that both are _so recht Chor-Thon_ (at regular choir
pitch). Praetorius also shows a harpsichord[2] that looks like a
typical Italian instrument except for the presence of a set of strings
tuned an octave above unison pitch, a rare feature on Italian
harpsichords. This harpsichord is described as _so eine Quart tieffer
alss Chor-Thon_ (a fourth lower than choir pitch), clearly indicating
that single manual keyboard instruments a fourth apart in pitch were in
existence. Since no reason is given for the harpsichord being tuned a
fourth lower than the two virginals, we may assume that the author
considered the matter commonplace enough as to demand no further
elaboration and that instruments a fourth apart in pitch were not rare.
Praetorius does not state that the harpsichord in his illustration was
tuned to a low pitch standard, which was actually used for certain
purposes or in particular localities. He discussed the numerous pitches
in use before and during his time, but the only one that he mentioned as
being a fourth below choir pitch he considered obsolete and suitable
only for plainsong. If the harpsichord was not intended to be tuned to
this standard and used for this purpose, it must have been tuned to
choir pitch and treated as a transposing instrument.
Querinus van Blankenburg,[3] writing in 1739, states:
At that time [the beginning of the 17th century], men had so little
experience in transposition that in order to be able to transpose a
piece a fourth downwards they made a special second keyboard in the
harpsichord for this purpose. This seems incredible, but the very
remarkable proof is the fact that the famous Ruckers from the
beginning of the last century for a period of more than thirty
years made harpsichords only in this way.[4]
That the second manual of the two-manual harpsichord originated as a
device for transposition is well known. In an article titled
"Transposing Keyboards on Extant Flemish Harpsichords," Sibyl Marcuse[5]
discusses surviving examples that show how the second keyboard was
arranged. The upper keyboard was the principal one, with the lower
keyboard sounding a fourth below. The strings acted upon by a _c_ key on
the upper manual were sounded by an _f_ key on the lower; so, in
changing from the upper manual to the lower, the player would have to
move his hands to the left the distance of a perfect fourth in order to
strike the same keys, thus producing the downward transposition. The
compass of the upper manual was _E/C_ to _c´´´_. Since the lower
keyboard was shifted to the left, space was provided for five additional
keys at its treble end. The apparent treble range of the lower keyboard
was therefore extended to _f´´´_, although the lower _f´´´_ and upper
_c´´´_ keys worked on the same strings and produced the same pitch. Room
was also made for five extra bass keys at the lower end of the upper
manual. However, since short octave tuning was employed and it was
desirable to be able to use the same fingering in the bass on both
manuals, the tails of the _C/E_, _D/F#_ and _E/G#_ keys of the upper
manual had to be bent to the left in order to work on the strings played
by the _F_, _G_, and _A_ keys respectively of the lower manual. The
vacant space to the left of the upper manual _C/E_ was filled by a block
of wood. Hence the five extra bass strings not used by the upper manual
were those played by the _C/E_, _D/F#_, _E/G#_, _B_, and _c#_ keys of
the lower keyboard.
Of the 16 Italian harpsichords and virginals studied that ascend in the
treble to _f´´´_, 13 range to _C/E_ in the bass, thus having exactly the
same compass as the lower (transposing) keyboard of the Flemish
two-manual instruments. Twelve of the 14 Italian examples having _c´´´_
as the highest key stop on _C/E_ in the bass and are identical in
apparent compass to the Ruckers upper manual.
The correlation of compass and string length of the Italian instruments,
the statements of Praetorius, and the similarity of the Italian keyboard
ranges to those of the Ruckers transposing harpsichords have been
considered. A plausible conclusion is that the Italian instruments
extending to _f´´´_ were transposing instruments sounding a perfect
fourth lower than the prevailing pitch standard. Adopting the
terminology used for orchestral wind instruments, these could be
referred to as harpsichords in _G_.
The evidence of the correlation between string length and compass
becomes much more convincing if we assume that the Italian builders
abandoned the practice of making transposing harpsichords about the same
time that the Ruckers family stopped employing the transposing lower
manual. In the quotation previously given, Querinus van Blankenburg
tells us that the Ruckers did not make transposing instruments later
than the 1630's. Of the 10 dated Italian instruments with the keyboard
extended to _f´´´_, only three were made after the third decade of the
17th century. Each of these has a shorter pitch _C_ string than any of
the seven earlier instruments. These three harpsichords, dated 1654,
1658, and 1666, are accordingly considered nontransposing instruments,
with the extra treble keys representing an actual extension of the
upward range. The six undated instruments with _f´´´_ in the treble are
classified as transposing instruments because of their pitch _C_ lengths
and are accordingly believed to have been made before about 1635.
[Illustration: Figure 12.--TYPICAL DECORATIVE DEVICE, known as rose,
that appeared in soundboards of virginals and harpsichords.]
The 33 instruments on which this study is based are classified in the
list on page 107. They are grouped according to whether the highest key
is _f´´´_ or _c´´´_, with the exceptions of the three harpsichords
mentioned in the preceding paragraph and three instruments that go only
to _a´´_. That the three instruments ending on _a´´_ belong with the
nontransposing group is indicated by their string lengths.
The listing gives additional information about each example. String
lengths of instruments having two registers are for the shorter of the
two pitch _C_ strings.
Information has been secured on two Italian virginals which were not
included in the tabulation. Their measurements are completely at
variance with the pattern consistently set by the other 33 examples
studied. One, made by Giovanni Domenico in 1556, is in the Skinner
collection; it has a pitch _C_ string 14-1/16" in length and an apparent
compass of _C/E_ to _c´´´_. The other, with the same apparent compass
and a 7-1/2" pitch _C_ string, is at Yale University. Whether these
instruments are exceptional in terms of the pitch to which they were
tuned, the tension which was applied to the strings, or the thickness
and weight of the strings themselves, has not been determined.
The average of the pitch _C_ lengths of the transposing instruments in
the list is 12.78"; that of the nontransposing group is 10.45". This
suggests a separation between the two groups of about a major third
since the first average is roughly 5/4 of the second. However, the fact
that the separation of the two averages is not great enough to
positively indicate a perfect fourth--the first average would have to
be 4/3 of the second to do so--does not disprove the theory of
transposition by a fourth. In the first place, a considerable variety of
pitches is no doubt represented in both groups since a universal pitch
standard did not exist in the 16th and 17th centuries. Also, a margin of
error of only a semitone is as good as could be expected considering the
small number of examples on which the averages are based.
A further possible justification for the relationship of the two
averages is found in Praetorius' discussion of the pitch standards with
which he was familiar.[6] He states that choir pitch was a major second
lower than chamber pitch and that _tertiam minorem_ was a minor third
lower than chamber pitch. Praetorius says of _tertiam minorem_:[7]
But in Italy and in various Catholic choirs in Germany, the said
lower pitch is much in use. For some Italians, not unjustly, take
no pleasure in high singing, and maintain it is not beautiful, and
the words cannot be properly understood, and it sounds like
crowing, yelling, singing at the top of one's voice....
Possibly some of the nontransposing instruments were tuned to choir
pitch and others to _tertiam minorem_, while the transposing instruments
were set a fourth lower than choir pitch.
Three of the instruments listed are ottavinas, small instruments tuned
an octave higher than usual. Ottavinas correspond to a four-foot
register. Mersenne[8] mentions that they existed in two sizes, one a
fifth above the usual pitch and the other an octave above. The three
ottavinas included in the table are considered to be of the size
sounding an octave above the usual pitch because they have _C/E_ to
_c´´´_ ranges and pitch _C_ string lengths about half the average length
of the other instruments in the nontransposing group. Although no
examples were found for inclusion in this study, it is probable that
some ottavinas a fifth above the usual pitch--and therefore an octave
higher than the transposing instruments in our listing--survive. Such
instruments would be expected to have apparent ranges of _C/E_ to _f´´´_
and pitch _C_ strings between 5-3/4" and 6-3/4" in length.