The bridge curvature is a function of the Trasuntino's scaling parameters. In my version of the design, the majority of the instrument follows a true Pythagorean scale with c''=273 mm. This scale is accurate from the top down to c, an octave below middle c'. From that point downwards the strings shorten somewhat to keep the instrument from being inordinately long.
I made up a chart of Pythagorean string lengths derived from this scale, and, working from the treble downwards, I used a long wooden T-square with a tape measure to measure out each string length. I lined the square up successively with the tick marks made along the nut, and at the far end I put a little cross on the soundboard to mark the string length.
Back in September, when I was determining the curvature of the bentside, I mostly used Pythagorean C and F# string lengths to derive the curve and I did not make definitive conclusions about the bass string lengths. The time had come to be more precise, so, starting from c (below middle c'), I experimented with some foreshortened string lengths to see what the far end of the bridge curve would look like. Based on some foreshortening ratios from the original design, I found that the bridge would straighten out and also move leftwards well away from the bentside. I felt I didn't like this look so much. After looking through emails from my friendly harpsichord maker, I was reminded that Italian bridges were often made pretty much parallel to the bentside. In testing out this shape, the appearance was nicer and a side effect was that the bass strings were slightly lengthened, something which my contact had suggested to me could be beneficial to the overall design. The flip side was that the bass hook (the little straight section of bridge going off to the left) would now be longer and would carry about 10 strings instead of 4. This didn't seem to be a problem. I decided to put the hook as far in from the tail as the bridge was spaced from the bentside.
After finishing all this, I realized that I probably could just have set a compass to a fixed spacing and simply traced the whole bridge curve out without all these measurements. It really is quite consistently placed with respect to the bentside curve: no surprise, since the shape was derived from the same data. I have read that Italian bridges were often located by purely cosmetic means, with any ramifications to the scaling apparently secondary to a pleasing appearance. Live and learn, I guess.
I went over the space between each cross in pencil to make a solid curved line showing the bridge position. My plan was to then determine the hitch pin positions along the tail and bentside by going off the straight line of the string at a 12 degree angle and putting a cross right at the edge of the soundboard for the hitch pin.
But, in looking over my T-square, I grew concerned that perhaps it was flexing a bit, particularly at the far end when I was marking down string lengths of some 1800 mm. Any flexing might cause a lateral shift of the bridge pin positions, and my hitch pin positions would only be accurate if the bridge pins were well located. So I decided to double-check the bridge pin positions using the same register that had originally placed the tick marks along the front edge of the soundboard.
I made this jig to hold the register, with a stout oak board to keep the register from flexing and a guide to slide the whole thing along the edge of the spine. The register is clamped so that the edge of the first slot is 37 mm from the left edge, just as it was when the first markings were made.
All I had to do was slide the jig along and see if my original bridge pin marks were aligned with the edge of each slot, like this:
It turned out that most of pin positions were good; a few corrections were needed only in the bass region.
In the photo above you can see that I am working on the second register's pin positions. I only needed to clamp the register slightly to the right to align with the first right-facing string, and then I could mark off all the bridge pins for the second register, which would be spaced 3 mm to the left of the first register's strings (as seen from the nut).
Once the bridge is glued on it will obscure all my pencil marks, so I will actually have to mark out all the bridge pins a second time. I'll slide the same jig along the bridge, marking positions with a little awl, then drill each dimple with a small drill bit and push each bridge pin home.
Hitch pin positions are to follow.
No comments:
Post a Comment