Twined Strings for Clavichords
The bass strings of clavichords are foreshortened, meaning that they are shorter in proportion to their pitch than the treble strings. This is unavoidable, even in very large clavichords, but small ones are particularly affected; the result is that solid wire strings, whatever gauge you fit, sound muddy, weak and unfocused. One solution is to fit overwound strings, with a winding of soft copper or silver wrapped round a core of brass or iron, usually in an open spiral. Overwound strings sound better than solid wire because the core wire can be tensioned much as it would be if used in the treble, whilst the added mass of the winding lowers the mass per unit length of the string (the linear density) so that it produces the desired note. The design and manufacture of overwound strings was described in an article by John Barnes, published in the FoMRHI Quarterly in 1981 (Comm 325); this is still the best summary of the subject that I know of.
The earliest mention of overwound strings seems to be in the 1664 edition of Playford’s Introduction to the Skill of Musick :There is a late invention of Strings for the Basses of Viols and Violins, or Lutes, which sound much better and lowder that the common Gut strings ... It is a Small Wire twisted or gimpd upon a gut string or upon Silk ...
I do not know when the idea was adopted on wire-strung instruments such as clavichords, but it can hardly have been earlier than the 1660s and might have been a good deal later, since it is not immediately obvious that a wire winding can be made to adhere to a wire core as effectively as to a core of softer material like gut.
In any case, clavichords with foreshortened basses existed long before this. John Koster has shown that the principle of foreshortening was known in the fifteenth century, and there are surviving clavichords with foreshortened basses from the sixteenth. The C/E short-octave keyboard, a feature of nearly all sixteenth- and early seventeenth-century clavichords, inevitably involves foreshortening, because (for example) the sounding lengths of the strings for note C can be only slightly longer than those for note F, so that even if F is fully scaled (rarely the case), C will unavoidably be quite severely foreshortened. Similarly, notes D and E are even more problematic, since in most designs their sounding lengths are actually shorter than those of note F.
Did clavichord players at this period accept the poor sound and unstable tuning of solid wire strings on these bass notes, or was there an alternative to overwinding that solved the problem?
The answer can be found in Marin Mersenne’s Harmonie Universelle (1636). In volume 3,Livre Troisiesme, des Instrumens à chordes, Proposition IV (pp. 114–116) he describes a manichordion or clavichord, with a full-page illustration of an instrument of the old type with several straight bridges arranged at right angles to the long sides. Referring to these bridges (chevalets), he says:Quant au cheualets, le premier porte six rangs de chordes, cest à dire 12. Le second en a 9. rangs ou 18. dont les 8. premiers sont redoublées & retorces, de sorte quil y a 20 chordes en double.
(As for the bridges, the first bears six courses of strings, that is 12. The second has nine courses or 18 strings, of which the first eight are doubled and twisted, so that there are 20 strings). [note]
What are these doubled and twisted strings? Mersenne gives a clearer description near the end of his account of the wire-strung cittern, where he writes:... la plus grosse chorde du 3, & du 4. rang est tortillée, & faites d’vne chorde redoublée & pliée en deux, afin de faire des sons plus remplis, & plus nourris.I was therefore wrong to say, in a previous version of this article, that there was no hard evidence of the use of these twisted or twined strings on clavichords.
(the thickest strings, nos. 3 and 4, are twisted, and made of a single string doubled and folded in half, in order to produce fuller and richer sounds.)
Some of my fellow clavichord makers began using them on the smaller, earlier types of clavichord several years ago, and the results were so convincing that I began using them myself. They are normally made from yellow or red brass wire. There is a technique to making them effectively. Whatever method you use starts, of course, with a double-length wire folded in half: the half-way point conveniently serves as the hitch-pin loop. You could, of course, simply anchor the two loose ends and twist the wires together with a revolving hook at the folded end. However, this has the disadvantage that the two wires would themselves be excessively twisted: they would be work-hardened, and might even break before you achieved the required closeness of spiral. They would certainly be weakened, and probably somewhat less flexible, and there would be a tendency for them to unwind before you could get the string safely on to the instrument.
So I looked for an alternative which would wrap the two wires closely around each other without twisting them (thats why I prefer to say twined rather than twisted strings). After I had made some failed attempts, Darryl Martin explained to me the following method, which he had been using: I am most grateful to him for his help. It is very effective and does not need much in the way of special equipment (see diagram below).
You need to fix a rotating hook, somewhere near the ceiling of the workshop: I use an electric drill on the slowest possible setting, fixed to a beam. To start and stop it, I use a push-button switch on a longish lead. You hang the fold in the middle of the wire on the hook, then attach equal, and fairly modest, weights to the free ends (mine are 500g each). To produce the twined string, you need a spreader in the form of a piece of wood about 10 inches (250 mm) long with grooves in each end, which holds the two wires a fixed distance apart as they hang. I also fixed a guide in the form of a rod pointing up vertically from the middle of it, and a handle opposite the guide to hold the thing by. Before you start the hook rotating, move the guide up close to the hook: if the guide is half the length of the spreader, the two wires will make an angle of 90° at the hook. Now start the hook rotating, and as the two wires wrap round each other move the spreader down, keeping the top of the guide close to the point where the two wires meet so that the angle between them is constant all the way down.
There is some stress to the two wires, but essentially they remain untwisted and wrap very closely round each other with a very small pitch. The weights revolve, eventually at the same speed as the hook, proving that the two constituent wires are not themselves being unduly twisted. The finished string shows absolutely no tendency to unwind; it displays a close and even pitch along its length.
It seems to be important that the two wires are twined extremely closely around each other: the pitch must be barely more than the diameter of the wire. I found that wires twined at 90° worked very well, and in the end added a block incorporating a 90° angle to the top of the guide rod, which also helps ensure a smooth and even twining. It would be possible to experiment with greater or lesser angles by making the guide rod longer or shorter.
The acoustic results of strings made this way are quite extraordinarily good: by which I mean that the sound they produce has a clear and definite pitch, with a good blend of partials and without marked inharmonicity, and with satisfactory volume and sustain. Moreover the twined strings are easier to tune and more stable in pitch.
It is not immediately obvious why they perform so much better than solid wires. Naively, I reasoned that since each constituent wire bears half the tension of the combined string, the relationship between cross-sectional area and tension – the stress on the wire – would be no different from that of a solid wire of equivalent cross-section, and one would not expect any improvement.
In order to understand what was going on, I ran a number of experiments on twined strings. As it seemed that twined strings were more stretchy than the constituent wires, in the first experiment I attempted to measure their effective elastic modulus, so that it could be compared with that of solid wires. Sample twined strings were stretched between a hitch-point and an ordinary wrestpin mounted in a block. A spring balance was fitted at the hitched end so that tension could be measured. Two markers made of tiny gummed paper slips were attached roughly a metre apart on each sample, and the precise distance between them was measured as carefully as possible with a plastic rule. The tension on each sample was increased, and tension readings taken for each 1 mm increase in length. From the readings of force and length it was possible to calculate the elastic modulus of each sample string, and by dividing this by the cross-sectional area (assumed to be twice the cross-sectional area of the constituent wire) a value for the effective Youngs modulus could be calculated, which could be compared with published data for the material from which the sample was made. The surprising result is that the effective Youngs modulus of a twined string is considerably lower than that of the individual wires from which it is made; typically about 0.65 times the Youngs modulus of the solid wire (though this varies with the composition of individual strings). This is why they work so well in practice: it is as if we were able to fit a super-dense, super-stretchy kind of wire for these low notes. One result of this is that whereas with solid wires it is next to impossible to tune the notes because a tiny movement of the tuning pin causes a large change in pitch, with the twined strings the notes can be tuned very much as for fully-scaled wires or overwound strings.
In the second experiment, I attempted to measure the effective linear density of twined strings. Two bridges were placed 1000 mm apart on an improvised monochord, and sample twined strings were stretched across them from a hitch-point at one end to a tuning pin at the other. Tension was applied by turning the tuning pin, and measured by means of a spring balance as before. Each sample was tuned to various pitches, measured using an ordinary tuning meter. From the resulting values for pitch (i.e. frequency), tension and sounding length it was possible to calculate a series of values for the linear density: these produced reasonably consistent results for each sample (somewhat to my relief). To express the results in a convenient practical form, I calculated the equivalent solid wire diameter for each sample, i.e. the solid wire that would produce the same tension when tuned to the same pitch. Eventually I derived the following working rule-of-thumb for wires twined at 90°:
Material Equivalent solid wire
= constituent wire diameter
70/30 yellow brass 1.40 85/15 red brass 1.48 90/10 red brass 1.50
If the linear density of the twined string were simply twice that of the constituent wire, the factor in the second column of the table would be 1.414 (the square root of 2). The larger values for red brass reflect the increased mass resulting from the way the wires are coiled round each other rather than stretched out straight; it seems that for yellow brass, the added mass is negligible.
These conclusions are based on a limited amount of data: weeks of experimenting would probably produce more reliable figures (would anyone with suitable laboratory facilities care to undertake this?). In the meantime, I would encourage makers interested in the smaller, earlier fretted types of clavichord to consider this type of string. At present, several European makers are using them, but they do not seem to have crossed the Atlantic.[note] Maria Boxall has argued, I think very convincingly, that the words dont les 8. premiers sont redoublées & retorces, de sorte quil y a 20 chordes en double refer to the first bridge, bearing the strings for the lowest notes, which would indeed then have 20 strings if one counts the twined strings as two. See Maria Boxall: The Clavichord in Mersennes Harmonie Universelle, Appendix II to her article The Origins and Evolution of Diatonic Fretting in Clavichords in the Galpin Society Journal LIV (May 2001). [return]
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