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...

Hitch pins

Before stringing the harpsichord, the hitch pins, which are the terminus of the strings, need to be installed.

I'm using 1.8 mm diameter iron hitch pins, which go into 1.7 mm holes drilled through the walnut soundboard moldings into the soundboard liner. The pins are 35 mm long and I want them to project about 5 mm above the molding.

Since the hitch pins are so close to the edge of the case, no normal drill bit can safely drill the holes, because the drill chuck will collide with the case walls well before the hole gets deep enough. The long extension bit shown here keeps the drill clear of the case rim:


The blue tape is a depth indicator for a 32 mm deep hole. A piece of cardboard acts as a shield to protect the case walls from scuffs.

The hitch pin setter shown below has a hole 5 mm deep which leaves each pin exposed by that amount. Once the holes are drilled, the pins are installed by hammering them into their holes with the setter until the tip of the tool contacts the walnut soundboard molding. A scrap of maple veneer protects the case interior as the pins are driven:


I waxed the lower part of each pin a little to avoid excessive friction during installation.

Because the hitch pins block easy access to the lowest part of the case interior, I made sure to apply two coats of my case finish—a gel varnish—to the bentside and tail interiors before driving in the pins. I haven't applied finish to any other part of the case yet, but I decided to do these areas now.

When I string the instrument, I'll bend each hitch pin slightly backwards. This will discourage the string loop that hooks onto each pin from sliding upwards.

Applying shellac to the soundboard

Today, soundboards often receive a few thin coats of shellac as a finish. In past centuries the old makers sometimes applied nothing at all, or they used a wash coat of dilute hide glue. Probably the latter was intended to seal the soundboard surface before painting it, but the brittle quality of dried hide glue is thought to have a positive effect on the soundboard's tone.

I decided to apply shellac because it offers a modicum of protection against humidity, though shellac is not very resistant to liquid water. I don't have experience with hide glue, so perhaps in some future project I'll explore this particular use for it.

After sanding the soundboard, the walnut moldings, the bridge and the nut one last time, I applied a couple of coats of dewaxed blond shellac, sanding very lightly after the first coat to knock down any raised grain. The end result was a more golden appearance for the soundboard and a subtle sheen. The walnut items darkened and received a pleasing gloss.

My soundboard rose is a two-part ornament. The first part was glued to the underside of the soundboard hole a long time ago; the second part is a decorative ring that surrounds the hole from above. Before applying the shellac, I covered the hole perimeter with masking tape to preserve an unfinished gluing surface. After the last coat of shellac dried, I glued down the ring with fish glue. The result is rather nice:

Case moldings: Upper outside edge

The upper outside case molding, glued on along the outer bentside edge:



Lots of clamps were used: the little ones aren't very strong individually, but in quantity they get the job done just fine.

Next, the cheek and nameboard moldings:


Finally, the spine molding:


That's it for this batch. Now the same thing will be applied along the upper inside edges.

Case moldings: Upper edge

I finished the baseboard-level moldings about 10 days ago and have moved on to the moldings that go along the inside and outside edges of the top of the case. These are identical in profile to the baseboard moldings except they aren't as wide. The same molding will be used both along the inside and outside edge, so I ran off two identical batches.

After these are installed, I'll make a cap molding that glues down flat on top of the sandwich made by the inside molding, the case side and the outside molding. This will need to be just bit wider than the combined thickness of all three components that it covers in order to achieve an overlap and a pleasing reveal.

Case moldings: Bentside

Happy New Year to however many people are still reading this blog.

Things got quite busy since my last post, and a large number of concerts descended on me for the last two months of the year. After all that music I felt I needed a holiday, so I'm finally resuming my work on the harpsichord at long last.

At this point I have applied moldings to the cheek, the front and along the spine almost to the tail. The strips from which these moldings are made are a bit shorter than the spine, so a single piece of molding will not suffice to cover the spine all the way from keyboard to tail. Leaving the spine for the time being, I turned my attention to the bentside molding, which I steam-bent to shape. It didn't quite bend far enough to conform perfectly but I was able to muscle it into place using various clamps:


I devised the clamp shown below to help apply heavy pressure where necessary:


By nailing the clamp to the baseboard and screwing down the screw, much more clamping force is applied than I can typically get from my other clamping blocks. The picture directly above shows the clamp in use during an earlier phase; you might be able to see two of them applied along the bentside in places where I needed to bend the molding forcefully.

The tailpiece and the last part of the spine still remain to be done. Then, I start all over again with the moldings along the upper part of the case. Lots more to do still...