of such instrument makers as Carl Almenraeder in
Germany, Triebert and Jancourt in France, Sax in Belgium, Cornelius Ward
and Morton in England, to introduce improvements based upon acoustic
principles, it is necessary to understand what these general principles
are, and why they have been disregarded in the bassoon. In all tubes the
note given by the vibrating air column is influenced directly by the length
of the tube, but very little, if at all, by the diameter of the bore. The
pitch, however, is greatly affected by the diameter of the opening, whether
lateral or at the bell, through which the vibrating column of air is again
brought into communication with the outer air. The tube only sounds the
normal note in proportion to its length, when the diameter of the lateral
opening is equal to the internal diameter of the tube at the opening. As in
most of our early wood-wind instruments the holes would in that case have
been too large to be stopped by the fingers, and key-mechanism was still
primitive, instrument-makers resorted to the expedient of substituting a
hole of smaller diameter nearer the mouthpiece for one of greater diameter
in the position the hole should theoretically occupy. This important
principle was well understood by the Romans, and perhaps even by the
ancient Greeks, as is proved by existing specimens of the aulos (_q.v._)
and by certain passages from the classics.[2]

Another curious acoustic phenomenon bears upon the construction of wind
instruments, and especially upon the bassoon. When the diameter of the
lateral opening or bell is smaller than that of the bore, the portion of
the tube below the hole, which should theoretically be as though
non-existent, asserts itself, lowering the pitch of the note produced at
the hole and damping the tone; this is peculiarly noticeable in the A of
the bassoon [Notation: A2.] whose hole is much too high and too small in
diameter.[3] To cite an example of the scope of Carl Almenraeder's
improvements in the bassoon, he readjusted the position of the A hole,
stopped by the third finger of the right hand, boring lower down the tube,
not one large hole, but two of medium diameter, covered by an open key to
be closed by the same finger from the accustomed position; one of these A
holes communicates with the narrower bore in the butt joint, and the other
with the wider bore. The effect is a perfectly clear, full and accurate
tone. Almenraeder's other alterations were ma