The amateur performer on the banjo, if he be of a mechanical turn, is
often tempted to exercise his skill by making an instrument for
himself; and the temptation is the greater because he can confine
himself to the essentials. The excellence of a banjo in respect to
power and tone depends mainly upon the rim and the neck, that is,
supposing the parchment head to be of proper quality; but then the
preparation of the heads is a business of itself, and the amateur is
no more expected to make the head than to make the strings. So again,
all the minor accessories, such as pegs and tail pieces, brackets and
bridges, are kept in stock for his benefit, and he may justly claim
all the credit if his efforts in connection with the two principal
parts first mentioned result in the production of a superior
instrument. Among these ready-made items is a "fret wire" of peculiar
section, furnished with a flange ready for insertion into fine saw
cuts across the neck, which much facilitates his work.
Of course, the correctness of the notes depends entirely upon the
accuracy with which the frets are spaced, and the accompanying diagram
exhibits a convenient method of determining the spaces by graphic
means.
[Illustration: SPACING FOR BANJO FRETS]
It is to be understood that when the distance from the "nut," N, to
the bridge, B, has been determined, the first fret is to be placed at
1/18 of that distance from the nut, the distance from the first to the
second is to be 1/18 of the remainder, and so on. To determine these
distances by computation, then, is a simple enough arithmetical
exercise; but it is exceedingly tedious, since the denominators of the
fractions involved increase with great rapidity; being successive
powers of the comparatively large number 18, they soon become
enormous.
In the large diagram, the distance, A C, on the horizontal line
corresponds to the distance, N B, on the instrument. At A erect a
vertical line, and mark upon it a point B such that B C shall be
exactly eighteen times any convenient unit, B I. In the illustration B
C is 26 inches, and B I is 11/2 inches, so that B C is 27 inches in
length. About C as a center describe the arcs, B L, I K, and through I
draw a vertical line, cutting B L in D; draw the radius D C, cutting
the inner arc, I K, in J, through J draw another vertical, cutting B L
in E, and so on.
In the triangles, A B C, 1 D C, 2 E C, we have B I = D J = E F = 1/18
of the hypotenuse in each case, therefore the bases, A C, 1 C, 2 C,
are divided in the same proportion, as required, at the points 1, 2,
3. And we might extend the arcs, B L, I K, and repeat the above
operation until all the frets were located. But should that be done,
the diagram might become inconveniently large, and some of the
intersections might not be reliably determined. In order to avoid
this, the spacing of the outer arc may be stopped at any convenient
division, as L. The vertical by which that point is determined cuts B
C at B', and through B' a new arc, B' L', is described. Through the
points in which this arc cuts the radial lines already drawn, a new
series of verticals is passed, which will divide another portion of A
C as required, and by repeating this process the spacing of the whole
neck may be effected by a diagram of reasonable size.
* * * * *