Planimetric layout

When the plane-geometric model (2D) was completed with its mirror-image layout on the longitudinal centre line, it became clear to me that there was also an obvious "planimetric basis" to the instrument: that the starting point for the construction pattern was a square. Dimensions and properties between the length (6/8 of the square size) of the instrument and its smallest width, as predicted by this model, corresponded precisely with the structure of a the instrument. The relationship between the "upper" and "lower" parts of the instrument is found when definite symmentrical rotations of the main triangles, which decides the form of the baseline, one clockwise and the other counter clockwise, are carried out as shown in the step by step drawings. The rotations are also found to determine the exact location and the customary size of the F-holes, the location of the bridge, as well as the length of the strings and the proportion of the neck to the body. The apparently irrational location of the bass-bar and the dimension of the fingerboard are also found to bear a curious relationship to the intersections of the baseline with the equilateral triangles. The location of the corners is found lying on a circular arc through the intersection points of the arcs of the base line. If the intersections of baseline and triangles are regarded as chords, it is found that their congruent extensions to the centerline after rotation define a point shared by extentions of the sides of the fingerboard. This point also appears to determine the position of the bass-bar where it touches the upper edge of the F-hole. Step by step drawings explain the 2D and 3D geometric development.

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