This is explanation is a good start but it is incomplete because it did not name the fundamental principle behind the design. The main term is "mechanical advantage." I suppose if you wanted to analyze the force distribution, you could define a "mechanical moment" as the force analog of a moment of a mass (or charge) distribution. The main idea here, as you know, is to decrese the force pulling the pegbox toward the bridge.
The mechanical advantage is the ratio of the force that performs useful work of a machine to the force that is applied to the machine. The mechanical advantage that the angle offers is similar to the mechanical advantage of a pulley or a lever. The nut acts as the pivot point or fulcrum. Maybe a luthier can tell us the exact formula. However, I suspect that the formula for the force reduction is not linear but depends on the sine of the angle. The tension holding the nut in place is convenient because it allows a quick change of different nuts without having to bother about glue. Cases are made to fit instruments. Instruments are not ordinarily made with the idea that they will fit into existing cases. In the case of swan neck lutes over time, the strings will pull the pegs toward the nut particular on the burdons. You will see an unven distribution of string heights above the rose. I don't know about other instruments but I would not doubt that something similar happens to them as well. The advantage of the angular peg box is that you avoid the uneven string height. The disadvantage is, as has been mentioned before, you have to put up with the strings getting caught on the nut and consequently, the non-linear tuning feature, which is actually the worst thing about the peg box design. Cheers, Marion -----Original Message----- From: Ed Durbrow <[EMAIL PROTECTED]> Sent: Mar 11, 2005 10:52 PM To: timothy motz <[EMAIL PROTECTED]>, lute list <lute@cs.dartmouth.edu> Subject: Peg box bent: was: Pegs, revisited - ebony > >Jon, >In addition to reducing the mechanical moment (I haven't used that >phrase since high school physics class), the angled peg head makes it >easier for the peg head to bear the tension of the strings. If the >peg head was straight out, as in a guitar, there would be tremendous >pull from the strings that would tend to flip the peg head up. By >angling it back and locking it in place with the angled cut on the >back of the neck (almost like one half of a dovetail), most of the >tension serves to hold the nut in place (useful), and less is >transmitted to the peghead/neck joint. That's the best explanation I've heard yet as to why the peg box of a lute bends back. When asked why the peg box is bent back, I usually reply so that it will fit in the lute case. Of course one then wants to ask what about theorbos, swan necks and archlutes? I still don't have one of those instruments but I would answer that theorbos are single strung and that there is mounting evidence of fairly low tension on Baroque instruments. Archlutes? You tell me. cheers, -- Ed Durbrow Saitama, Japan http://www9.plala.or.jp/edurbrow/ To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
