Jack bodies, part 1

Now for a very critical part of the instrument: the jacks.

Last autumn I resawed some walnut I bought back on my very first lumber buying expedition in August 2007. The walnut was planed to a 4.9 mm thickness, with a projected final jack thickness of about 4.6 mm. After resawing and planing, I stickered everything in layers, under bricks to keep it all flat:


The top item is a sheet of holly 3 mm thick, from which the jack tongues will be made. The sheets of walnut are underneath.

Having sat around for about a year, all this material is quite stable, which is an essential basis for producing jacks that are to be well-behaved.

The first order of business was to slice the walnut sheets up into long strips slightly wider than the finished jacks:


These were stacked together on edge, a dozen at a time, taped together on the underside, and planed to establish the final width of the jacks (13.4 mm):


The jack slots in the register are a bit over 14 mm wide, so there is a clearance of about 0.6 mm. This is fine; in fact it could be a little more and still be OK: Skowroneck's book suggests that even 1 mm of clearance isn't problematic.

These bundles, still taped together, were cut down into individual jack lengths on the bandsaw. I'm aiming for a final length of 9.7 cm, so I cut to 9.8 cm to give me a little room to sand the ends and eliminate the roughness left by the bandsaw. The required jack length is actually 10.4 cm: the extra length will be provided by an end screw that will allow the jack height to be adjusted. I know that historical harpsichords didn't have this little convenience; it's the one place where I feel a modern screw could possibly be useful. A generation ago, horrible modern jacks were made that had far too many screws all over the place: see this web page for photos.

Here's a box full of jack blanks:


The most critical part of the jack body is its thickness; the clearance in this dimension is about 0.2 mm at most. Too little and the jacks might rub in the register slots during the dry winter months; too much and the plucking of the strings will be inconsistent as the jacks wobble around.

I suppose one could thickness jacks by machine until the required dimension is reached, as I did with the edges. However, a machine-planed surface isn't completely smooth; under raking light a washboard-like series of ripples can easily be seen. It's best to hand-plane the jack faces, since the hand plane gives a completely smooth surface without ripples. An alternative might be to thickness-sand instead, but sanding tears wood fibres and mats them down instead of cutting them cleanly like the plane does, and these fibres might decide to stand up again sometime later, compromising the smooth surface. Since the jacks have a more generous clearance in the direction of their width, I don't think there will be any trouble leaving the edges machine-planed. They feel smooth, even if they aren't on a microscopic level.

Here's the setup for hand-planing jacks to a controlled final thickness:


Two hardwood rails are screwed to a plywood board. Each rail has a groove with its base exactly 5.0 mm above the plywood. The hand plane seen at left slides in these grooves. A jack is held in place between the rails as shown below:


Scrap wood pieces keep the jack from shifting sideways or backward as the plane rides over it. These scraps must obviously be thinner than the finished jack so as not to interfere with the plane. Note the white paper shims inserted under the jack: these are used to raise the blank up each time the plane cuts away the top surface.

The hand plane is a Veritas low-angle smooth plane with a 38-degree bevel-up blade. The blade is bedded at 12 degrees, yielding a cutting angle of 50 degrees (York pitch, for the plane experts out there). This yields a smoother surface than the usual 45 degree cutting angle, at the expense of more physical effort to push the plane.

A well-adjusted plane should be able to take off a shaving just one thousandth of an inch thick:


To thickness a jack with this setup, a jack blank is put in place and is planed until no more shavings come off. Then a paper shim 0.07 mm thick is put underneath and the jack is planed again. Next, the jack is turned end-over-end to keep the grain angle at the surface consistent, and the other face is planed and shimmed a few times until the correct thickness is reached:


The final jack thickness is about 4.6 mm. The register slots are about 4.76 mm, and the wiggle of the planed jacks within the registers seems right to me: there's just a little bit of play.

Two registers full of jacks:

Chipping up to pitch

Chipping refers to a rough tuning designed to get strings up to pitch without worrying about complete accuracy. Now that the instrument is strung and the nut is pinned, it can be tuned for the first time.

There's no completed action as of yet, so the instrument can't be played in the customary manner, but the strings can still be tuned to an electronic tuner by plucking them with a toothpick.

Many, many tunings will be required to stabilize the harpsichord at pitch. The wire stretches out a great deal in the beginning, which affects the tuning stability at first. Brass wire takes several weeks to develop its proper sound: at first it sounds quite dull, but eventually it acquires a kind of high-frequency sizzle that, to me, is the hallmark of a good-sounding string.

Nothing broke during the first tuning! So far so good...

Pinning the nut

At least one register pair needs to be in place to pin the nut. I've installed one and wedged it place so it doesn't shift from side to side:



Here are the tools needed to pin the nut:


From top left: 1.2 mm bridge/nut pins, Dremel Stylus with #57 drill bit installed, marking awl made from a nut pin installed into a dowel, and a marking jack with two pencil lines showing the proper string spacing for the wide string pairs (10.75 mm).

With the exception of the marking jack, the exact same tools were used to pin the bridge.

Pinning the nut starts by installing the first nut pin a known distance from the case edge. When pinning the bridge, I put the lowest bridge pin 37 mm rightward of the spine, so the first nut pin must match that position. Here it is:


The leftmost string is now in the correct position.

Next, the marking jack is dropped into the leftmost register slot and the wedge is adjusted until the side-to-side position of the register brings the left pencil line on the jack into alignment with the leftmost string. Now the register position and marking jack together will ensure the correct spacing of the remainder of the string band. Since the spacing of the register slots is 13.75 mm, and the pencil lines on the marking jack are 10.75 mm apart, the narrow string pairs end up 3 mm apart, as desired.

Each register slot can be used to pin two strings by matching them with the left and right pencil line positions, respectively. Pinning is as simple as catching the string with the marking awl and pushing it leftward until it matches up with the appropriate line, as shown in the next two photos:



When the string position is satisfactory, the awl is used to make a dimple in the nut:


Since the awl uses an actual nut pin, the thickness of the pin is automatically taken into account.

Next, a hole is drilled at the dimpled location and a nut pin is installed with the same pushing tool used when pinning the bridge. The tool automatically leaves a few millimetres exposed:


All that's left is to lift the string over the nut pin. Obviously the strings are pretty loose at this point to make them easy to manipulate: they've been tightened just enough to eliminate any visible slack.

Here is an overhead view of the process. Correctly pinned strings are to the left, unpinned strings and mess from drilling lots of holes are to the right:


Not only do the strings end up spaced correctly, but the string band is now parallel to the spine. Previously the strings all sloped slightly to the right as they reached the tuning pins. This was done to ensure they would gain some sidebearing once the nut was pinned.

A method such as this, done purely by eye, will yield some very slight inconsistencies in the string spacing, but this is accounted for when the plectra are cut to length and voiced.

When the nut pinning was complete, the position of the two gap spacers was rechecked. In order to keep out of the way of the jacks, each spacer must lie exactly below a close pair of strings. I moved one of them a little bit; the other appears to be correct. The spacers were made 3 mm wide to match the close pair string spacing.

Finishing the registers

The four registers need to be cut down in length and assembled together in pairs. Each pair is held together with spacer posts, which have a profile designed to fit into the grooved underside of the upper register:


These posts go not into the register slots, which are for the jacks, but in between them.

First, the registers are stacked in pairs, and to make sure the slots are vertically aligned between the two, blocks sized to fit snugly in a register slot are slipped through slots at opposite ends:


Spacer posts are installed into the bottom register at 5 places, and the entire assembly is drilled at these locations with a #54 drill bit. The hole depth is controlled so that the bit passes through both registers and makes a small dimple in the post. It is not possible to drill much further because the drill bit is pretty short.

Next, the assembly is taken apart. The dimple mark is used to align the bit correctly and drill the spacer posts vertically all the way through. The holes in the registers are then enlarged with a 5/64" bit.

This process creates holes for #2-56 machine screws in the spacer posts that are accurately aligned with clearance holes in both registers. The spacer posts are tapped with the appropriate tap from both ends, and all the components are temporarily screwed together with 3/4" brass machine screws to check the configuration.

Each register pair hangs from a pair of gap spacers which span the gap between the wrestplank and upper belly rail:


In other harpsichord designs, these little struts keep the gap from closing up due to the tension of the strings. Italian harpsichord designs don't need this kind of help; if they do, the design is fatally flawed. I'm using them just to hold up my registers. The upper register lies on top of the gap spacers and the remainder simply hangs down inside the gap, like this:


Each register pair is installed by screwing the spacer posts to the lower register and pushing it up into the gap from the back of the keywell. Then the upper register is slid sideways into the instrument through the spine window, pressed down onto the spacer posts, and screwed in place.

One final detail is this walnut cover plate for the spine window:

Stringing technique

And now for some actual hands-on stringing.

First, a generous amount of string is uncoiled and a hitch pin loop is made at the free end. The loop is a set of double helix twists, in which two strands of wire wind around an imaginary central axis and not one around the other (think of DNA to get an idea of what I mean). After a dozen or so twists are made, the free end of the wire is wrapped around the base of the emerging loop with a couple of straight turns.

There are numerous ways to make these twists. Professionals do so by hand. For fun, I've been using this gadget that fishing tackle makers use to make double helix twists on wire leaders. In the fishing equipment world, this loop is called the "haywire twist".

Whatever the method, the result looks like this:


The loop is slipped over a hitch pin and the free end of the wire is guided around the appropriate bridge pin and pulled towards the wrestplank. Since the wire is kind of springy, it wants to coil back up again and make a nuisance of itself. To keep it from slipping off the bridge pin, a hemostat acts as a handy little clamp:


Note that the hemostat isn't actually clamping the wire to the bridge pin: that would cause the wire to break once it is put under tension. Instead, the hemostat presses the wire down against the bridge, acting like an extra set of helping hands.

Next, the wire is drawn about 4 inches past its final position in the wrestplank and cut free from the coil. The free end is inserted into a little hole in the tuning pin shaft, and the pin is rolled forward to make the wire wind itself on. When the tuning pin is over the correct hole in the wrestplank, the pin is hammered down into the hole with a hammer and a tuning pin setter (basically like a glorified nail set, except the notch in the bottom end is as wide as the tip of a tuning pin).

The wire, as it leaves the tuning pin and heads out towards the soundboard, must be on the right-hand side of the pin. In addition, care must be taken to ensure the wire doesn't angle downwards too severely as it leaves the nut and approaches the pin. This downbearing, if excessive, will exert an upward force on the tuning pin and try to unseat it from the wrestplank. Ideally, the wire will meet the tuning pin at right angles to the pin, which means it exerts only a forward force. The tuning pin holes were drilled leaning back at about 5 degrees to provide some resistance to this forward pull.

The best way to control the downbearing is to ensure there isn't too much excess wire to wind onto the tuning pin. The wire coils on the pin can then be spaced widely or narrowly, as needed, to control how much downbearing there will be. If there are any problems when the pin is hammered into the wrestplank, the coil spacing can be adjusted with a screwdriver tip before the pin is twisted clockwise to put the wire under tension, which freezes the coils in place.

Here are all the tuning pins with their wire coils:


Notice that there is comparatively little wire wound on the pins. The wide spiral between the upper and lower sets of coils allows me to adjust the downbearing.

Here is a view of the instrument fully strung. Note the change in sidebearing for the lowest couple of strings:


Some hitch pin loops, up close:


The hitch pins lean back a bit to resist the pull of the wire. I did this by tapping each pin with a hammer and a short piece of dowel.

With stringing completed, I examined the spacing of the string pairs at the bridge. It should be identical to that of the register slots (13.75 mm). I found a few visible discrepancies in the spacing, which also affected the sidebearing when the strings came off the bridge and headed for the hitch pins. I don't think this has anything other than a cosmetic impact, but for the sake of consistency I figured out which bridge pins were wrongly placed by using a caliper set to 13.75 mm and checking successive pairs of strings to see which one was out. Then I pulled out each wrong pin with a small vise grip, redrilled the hole correctly and installed a new bridge pin.

Stringing practice

After all the verbiage in the previous post, the question still begs to be answered: how does one actually string a harpsichord?

The old makers often used a system of numerical progression. For Italian harpsichords with a scale of about c''=280 mm, they used a simple rule of thumb like this, starting from the top down:

10 wires of #10 gauge
9 of #9
8 of #8
...

and so on.

There is a certain numerological elegance to this system, and possibly that was part of its appeal. From a practical standpoint, as one descends the compass, the string gauges change more frequently. This makes sense because the sounding length of the strings changes rapidly as the bridge curvature straightens out, which the progressive stringing system takes into account.

Gauge numbers are sometimes found inked or stamped onto the wrestplanks of old harpsichords, showing which gauges were used and where they changed. The numbers in German and Italian harpsichords correspond to the old Nürnburg gauge system, which had at least 10 different diameters. Based on measurements of surviving wire fragments, the closest modern equivalent diameters are:

#10 = 0.008" = 0.20 mm
#9 = 0.009" = 0.23 mm
#8 = 0.010" = 0.25 mm
#7 = 0.011" = 0.27 mm
#6 = 0.012" = 0.30 mm
#5 = 0.013" = 0.33 mm
#4 = 0.014" = 0.36 mm
#3 = 0.016" = 0.40 mm
#2 = 0.018" = 0.46 mm
#1 = 0.020" = 0.52 mm

Note that the U.S. and metric units are not exact conversions of each other (for example, 0.020"=0.508 mm, not 0.52 mm). The chart is, as stated, a list of the closest available modern diameters.

Our knowledge of the Nürnberg gauges is complicated by the fact that exacting measurements of surviving wire are skewed by centuries of corrosion. Another significant issue is the gradual increase over time in the diameter of historical wire as the holes in the draw plates wore out and got larger. Draw plates were extremely valuable—literally worth their weight in silver—and wire makers were not anxious to dispose of them just because the wire was getting a tiny bit thicker. So, at best, the old gauge system represents a range of diameters instead of a single precise number.

I decided to use this system of numerical progression in stringing my own harpsichord, with one caveat. Several modern makers report that better results are obtained by stringing one gauge heavier, which means 10 wires of #9 and so on. I've adopted this modification as well.

Given the 50-note range of my keyboard, it should be clear that the stringing will end in the bass without having employed all 10 gauges shown above. An instrument with exactly 4 octaves will use 7 gauges. I'll need one more because of my extra low note. The extra pair of strings at the top (which provide c''' at A=440 Hz) are strung with #9 gauge but are not counted as part of my overall tally.

If you look at my tension chart in the previous post, you'll see two columns off to the right where I mapped out gauges by numerical progression, one column starting with #10 gauge, the other with #9. The equivalent gauge numbers are also listed horizontally just below each metric diameter along the top.

The very last wire for the note GG/BB needs a little extra thought. Since it is a third lower than the keyboard key assigned to it, I'm going to try stringing it in 0.56 mm/0.022" red brass. This is pretty thick stuff, but I have a German harpsichord here at home that has a similar GG string length, and it's strung that way. I'll find out whether that's a good idea once the instrument is up to pitch.

Stringing theory

The project has now reached an important milestone: it's time to string the instrument.

Choosing the appropriate string diameters (gauges, to use the technical term) will have a significant impact on the sound of the resulting instrument. If one looks at the wide range of available gauges and string materials, the question immediately arises: how do you know which string material to use, and which gauge to choose for each note?

The first question is a little easier to deal with. Historically, harpsichords have been strung with iron, yellow brass and red brass. Some of earliest Italian harpsichords appear to have been strung with iron: a practically zero-carbon iron, high in phosphorus, which produces a strong yet flexible wire. If true, this choice of string material would have yielded an overall pitch level about a fourth lower than brass-strung instruments. Iron strings need a longer scale than the short scale typical of Italian instruments, so if they are used on an Italian harpsichord, the effect is as if the notes on the keyboard have all shifted leftward to longer strings. As musical requirements changed, it appears that the early instruments were converted to brass stringing, which also brought them more or less into the range of pitches familiar to modern players of Baroque music.

Yellow brass (a 70%-30% copper-zinc alloy) is the most suitable material for this harpsichord project. Red brass (a 90%-10% copper-zinc alloy) is scarcely used in Italian harpsichords, though some modern makers find it useful on a few of the very lowest notes.

Any consideration of a stringing plan needs to remember the following points, which entered into the picture back in the design phase:

1. The string scale cannot be too short because then, at the chosen pitch level, the strings will be too slack and will sound strange.
2. On the other hand, if the string scale is too long, the strings will break as they are tuned up to the chosen pitch level.

In striking an effective balance between these two factors, the harpsichord maker sets the operating tension of the string band. If the string scale is well designed, the chosen pitch level will require that all the strings be tuned to within a few semitones of their breaking point. The instrument will sound good and the problems above will be avoided.

A handy thing to do, early in the design process, is to calculate the tension of each string to see if there will be any problems with the chosen scale. The tension is calculated from the string diameter, length, pitch, and density of the string material as follows:

T=(ρπ/g)(fld)²

T=tension, in kg

ρ=density of the string material, in kg/m³

g=the gravitational constant, 9.8 m/s²

f=pitch frequency, in Hz

l=string length, in m

d=string diameter, in m

For yellow brass, the wire makers give ρ=8536 kg/m³. The string length comes from a Pythagorean scale based on c''=273 mm (except below c, where the strings foreshorten). The frequency of each note also follows a Pythagorean scale, meaning that neighbouring notes differ by 1/12 octave. Diameters depend on what the wire makers produce; most of them make (in inches) 0.008, 0.009, 0.010, 0.011, 0.012, 0.013, 0.014, 0.016, 0.018, 0.020, 0.022 and so on.

With this information, I created a spreadsheet that shows the tension on any note of the compass for any chosen diameter of wire. Note that wire gauges in this chart are in millimetres, not inches:


The orange line identifies the point at which the Pythagorean scaling stops, so the top portion of the chart does not accurately represent the bass string lengths, which are actually shorter than Pythagorean. Therefore the real string tension in this region is smaller than what is shown.

Upon reading the chart, an interesting phenomenon quickly becomes apparent: wires of the same gauge actually have the same tension, irrespective of pitch or length, provided they fall within the Pythagorean part of the scale below the orange line. This is no coincidence: in the equation above, the frequency increases by the same factor that the string length decreases, as one goes from left to right across the instrument, so the changes effectively cancel each other out.

The breaking point of the wire has to be known to determine if any of the tensions are excessive. The wire maker provides this information in the form of a tensile strength figure: the stress (tension/unit area) at which the material breaks, in PSI or MPa. Centuries ago, the old makers would have determined this empirically using a monochord. They set a specific length for the wire and cranked it up to a chosen pitch, noting whether it broke before it got there.

However, the breaking stress is not directly useful. A harpsichord wire is subject to additional stresses and friction as it passes around bridge pins, nut pins and tuning pins. As the wire bends, it is subject to compression on the inside of the curve and tension on the outside, experiencing a level of stress some 15-20% higher than in the straight sections. So a wire cannot safely be tuned just a little below its mathematical breaking point, because it will encounter stresses greater than the breaking point in several places. On top of that, an additional safety factor of about 20% must be included to guard against swings in humidity or clumsy tuning, both of which can increase the overall tension. The maximum "safe stress" is therefore about 1.4 times less (2 × 20%) than the breaking stress, which corresponds to a decrease of several semitones in the highest pitch the string can safely sustain.

Moreover, although it is true that thicker wire is capable of bearing a greater tension, one cannot solve the problem of an excessively long scale by putting on "stronger" (i.e. thicker) wire. A thicker wire will require increased tension to reach the same level of pitch as a thinner wire, and that extra tension will cancel out the greater strength of the thicker wire. In fact, the rule of thumb is that wires of various gauges will basically break at the same pitch level, regardless of their diameter, as long as they are of the same metallurgy.

After all this discussion, the question still remains: which gauges are used? The tension chart only shows that the wires won't break at the chosen pitch level. One could actually draw the odd conclusion that the entire harpsichord could be strung with a single gauge of wire. Of course, this is nonsensical. Most people appreciate the fact that a thin wire naturally produces a higher pitch and a thick one a lower pitch, and on any stringed instrument the diameters certainly increase as one descends the compass. The truth is that, as the great pioneering harpsichord maker Frank Hubbard said, "One strings by ear, not by physics". The wire must be chosen to produce a good overall sound and balance the tonal qualities of the various regions of the instrument's compass. And how to do that is the subject of the very next post...