Addenda to "Not Only Cones Make It..."

(American Lutherie #101)

 

 

The Geometry of Complex and True Cylindrical Fretboards (PDF) American Lutherie has a general audience, and won't print formula intensive articles unless those formulae are directly applicable to practical lutherie. However, I feel that the paper is incomplete if I don't justify the theory behind the results in it. This document describes the geometry of complex cylinders and then compares them to true cylinders, finding mathematical expressions for the maximum difference between them.

CylCalc If the formulae found in the document above were given to an engineer along with the common dimensions found in guitars, he would start simplifying things and conclude that true and complex cylinders are practically the same thing. They are, and that's one of the key ideas in the article. This calculator won't make any simplifications in those formulae, so you will be able to see by yourself how small the differences are in fact.

ComplexAndTrueSurface (3DM) This is a 3DM file (Rhinoceros) that contains two surfaces, a true and a complex cylinder, so that you can compare both. Of course, the parameters of those surfaces have been magnified to make the differences clearly visible. You may measure some dimensions, input them to the calculator above and check that both agree. Also available in IGS format here.

CylCalc2 Can you tell if a fretboard is a true cylinder just by using a straight edge? This was analyzed at the end of my article in American Lutherie. At first sight, it seems that it could be done by placing it at the nut, following the outer string paths there. Being tangent to the side edge, the "hump" will be amplified, and measuring the distance from the top of the last fret to the straight edge will give us the answer. However, this won't work: true cylinders are great fretboards indeed, even passing this test!

AlternativeStraightEdgeTest (3DM) This is a 3DM file (Rhinoceros) that contains a true cylinder where you can check the results of the calculator above (CylCalc2). Also available in IGS format here.

Contact me if you have any questions or suggestions, thank you!