String Lengths and Pitch Standards

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
virginal		Harpsichord
c´´´6-5⁄85-1⁄16
c´´ (pitch C)12-15⁄1610
c´ (middle C)25-9⁄1620-1⁄2
c43-5⁄1642-1⁄16
C/E50-5⁄661-1⁄4

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.

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.

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.

DATA ON THE 33 INSTRUMENTS STUDIED

DatePitch C length
(in inches)		Apparent
compass		TypeRegistersMakerPresent Location
Transposing Instruments
154011-11⁄16C/E-f´´´Polygonal virginal8´Vi ... iesMetropolitan Museum of Art
156913-1⁄4C/E-f´´´Polygonal virginal8´Annibale RossiJuilliard School of Music
160213-1⁄4C/E-f´´´Rectangular virginal8´Ioannes Baptista BononienSmithsonian Institution
161013-1⁄2C/E-f´´´´Polygonal virginal8´Pasquino QuerciHarding Museum, Chicago
161311-1⁄2C/E-f´´´Harpsichord8´8´Pasquino QuerciSmithsonian Insitution
161713-3⁄4C/E-f´´´Polygonal virginal8´Giovanni Battista BoniYale University, New Haven, Conn.
162013-9⁄16C/E-f´´´Polygonal virginal8´Francesco PoggioRhode Island School of Design, Providence
11-15⁄16C/E-f´´´Polygonal virginal8´AnonymousSkinner Collection, Holyoke, Mass.
12-15⁄16C/E-f´´´Polygonal virginal8´AnonymousSmithsonian Institution
13"C/E-f´´´Polygonal virginal8´AnonymousBoston Museum of Fine Arts
11-1⁄2C-f´´´Polygonal virginal8´AnonymousFolger Library, Washington, D.C.
12-3⁄4C/E-f´´´Polygonal virginal8´AnonymousCincinnati Art Museum
13-5⁄8C/E-f´´´Polygonal virginal8´AnonymousSmithsonian Institution
Nontransposing Instruments
154811C/E-c´´´Polygonal virginal8´Domenicus PesaurensisMetropolitan Museum of Art
1554[[a]]10-1⁄2C/E-c´´´Harpsichord8´8´Padre StoppacioVassar College, Poughkeepsie, New York
1585[]11-1⁄2C/E-a´´Ottavina4´Franciscus BonafinisMetropolitan Museum of Art
160210-1⁄2C/E-c´´´Harpsichord......Christoforus RiguniniStearns Collection, Ann Arbor, Mich.
1615[]9-3⁄4C/E-a´´Ottavina4´Pasquino QuerciMetropolitan Museum of Art
162510-1⁄8C/E-c´´´Harpsichord8´Valerius PeresSkinner Collection, Holyoke, Mass.
163311-3⁄8C/E-c´´´Harpsichord8´8´Horatius AlbanaSmithsonian Instituion
164511C/E-c´´´Harpsichord8´8´Horatius AlbanaVizcaya, Miami, Fla.
165410-1⁄4C/E-f´´´Harpsichord8´8´AnonymousSmithsonian Institution
165811-1⁄8C-f´´´Harpsichord8´8´Hieronymus de ZentisMetropolitan Museum of Art
166510C/E-c´´´Harpsichord8´8´Giacomo RidolfiSmithsonian Institution
166610-15⁄16A1-f´´´Harpsichord8´8´Hieronymus de ZentisMetropolitan Museum of Art
168210-7⁄8C/E-c´´´Harpsichord8´8´Giacomo RidolfiRhode Island School of Design, Providence
16838C/E-c´´´Polygonal virginal8´B. ObiciHarding Museum, Chicago
169010-13⁄16C/E-c´´´Harpsichord8´Giovanni Andrea MenegoniSmithsonian Institution
169310-5⁄16G1-c´´´Harpsichord8´8´AnonymousSmithsonian Institution
16949-7⁄8C-c´´´ (minus C#)Harpsichord8´8´4´Nicolaus de QuocoSmithsonian Institution
9-3⁄4C/E-a´´Clavicytherium8´8´AnonymousSmithsonian Institution
[]10-3⁄8C/E-c´´´Clavicytherium (Ottavina)4´AnonymousBoston Museum of Fine Arts
11C/E-c´´´Polygonal virginal8´AnonymousSmithsonian Institution

a This length is approximate. It is double the length of the shortest string on the instrument.

bIn order to arrive at a meaningful average value for the string lengths of the nontransposing group, it was necessary to double the measured lengths of the pitch C strings of the three instruments tuned an octave higher.

FigureNegative
Number		Catalog
Number
156322326,905
246792303,544
349355A303,544
449355B303,544
549356A303,544
649356303,544
749356D332,173
849356D332,173
949357A332,173
1049357332,173
1149355C332,173
1246795303,545

GPO: 1970 O—380-228

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington 25, D.C. Price 25 cents.