Strähle construction

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Strähle's construction is a geometric means of approximating the placement of lute, viol, and guitar frets.

It was proposed by Daniel Strähle in the 1743 Proceedings of the Swedish Academy. Academy secretary and founding member, economist, and geometer Jacob Faggot appended an analysis which showed the error to be about five times what was musically acceptable. So Strähle's construction was ignored until 1957 when J. M. Barbour of Michigan State University showed Faggot's error was about 10× the truth. (By that time readily-obtained precision scales made the method unnecessary.)

The method: Draw AB roughly the intended neck length. Construct an isosceles triangle ABC with AC=BC=2AB. Divide AB into 12 equal parts. Place D on AC so that AD=7 if AB=12. Extend BD to E so that BD=DE. The guitar must be sized so that the nut is at B and the bridge at E. A fret is placed where each division-point of AB then projects through BD to C .

Image:Strahle-construction.png

The method places the top 12 frets. Further frets are placed by bisecting from those.