ate depending on the rate of
the vibrations it sets up in the air column, this rate varying according
to the length of the column as determined by opening the lateral holes
and keys. A cylindrical tube played by means of a reed has the acoustic
properties of a stopped pipe, i.e. the fundamental tone produced by the
tube is an octave lower than the corresponding tone of an open pipe of
the same length, and overblows a twelfth; whereas tubes having a conical
bore like the oboe, and played by means of a reed, speak as open pipes
and overblow an octave. This forms the fundamental difference between
the instruments of the oboe and clarinet families. Wind instruments
depending upon lateral holes for the production of their scale must
either have as many holes pierced in the bore as they require notes, or
make use of the property possessed by the air-column of dividing into
harmonics or partials of the fundamental tones. Twenty to twenty-two
holes is the number generally accepted as the practical limit for the
clarinet; beyond that number the fingering and mechanism become too
complicated. The compass of the clarinet is therefore extended through
the medium of the harmonic overtones. In stopped pipes a node is formed
near the mouthpiece, and they are therefore only able to produce the
uneven harmonics, such as the 1st, 3rd, 5th, 7th, &c, corresponding to
the fundamental, and the diatonic intervals of the 5th one octave above,
and of the 3rd and 7th two octaves above the fundamental. By pressing
the reed with the lip near the base where it is thicker and stiffer, and
increasing the pressure of the breath, the air-column is forced to
divide and to sound the harmonics, a principle well understood by the
ancient Greeks and Romans in playing upon the aulos and tibia.[3] This
is easier to accomplish with the double reed than with the beating reed;
in fact with a tube of wide diameter, such as that of the modern
clarinet, it would not be possible by this means alone to do justice to
the tone of the instrument or to the music now written for it. The bore
of the aulos was very much narrower than that of the clarinet.

In order to facilitate the production of the harmonic notes on the
clarinet, a small hole, closed by means of a key and called the
"speaker," is bored near the mouthpiece. By means of this small hole the
air-column is placed in communication with the external atmosphere, a
ventral segment is formed, and the air-column divi