A blast of air passing over the open end of a tube, as over the reeds in Pan’s pipes; over a hole in one side, as in the flute; or through the aperture called a reed, with a flexible tongue, as in the clarinet, puts the internal column of air into longitudinal vibrations by the alternate condensations and rarefactions of its particles. At the same time the column spontaneously divides itself into nodes, between which the air also vibrates longitudinally, but with a rapidity inversely proportional to the length of the divisions, giving the fundamental note or one of its harmonics. The nodes are produced on the principle of interferences by the reflection of the longitudinal undulations of the air at the ends of the pipe, as in the musical string, only that in one case the undulations are longitudinal, and in the other transverse. A pipe, either open or shut at both ends, when sounded, vibrates entire, or divides itself spontaneously into two, three, four, &c., segments separated by nodes. The whole column gives the fundamental note by waves or vibrations of the same length with the pipe. The first harmonic is produced by waves half as long as the tube, the second harmonic by waves a third as long, and so on. The harmonic segments in an open and shut pipe are the same in number, but differently placed. In a shut pipe the two ends are nodes, but in an open pipe there is half a segment at each extremity, because the air at these points is neither rarefied nor condensed, being in contact with that which is external. If one of the ends of the open pipe be closed, its fundamental note will be an octave lower: the air will now divide itself into three, five, seven, &c., segments; and the wave producing its fundamental note will be twice as long as the pipe, so that it will be doubled back (N. 182). All these notes may be produced separately by varying the intensity of the blast. Blowing steadily and gently, the fundamental note will sound; when the force of the blast is increased the note will all at once start up an octave; when the intensity of the wind is augmented the twelfth will be heard; and, by continuing to increase the force of the blast, the other harmonics may be obtained, but no force of wind will produce a note intermediate between these. The harmonics of a flute may be obtained in this manner, from the lowest C or D upwards, without altering the fingering, merely by increasing the intensity of the blast and altering the form of the lips. Pipes of the same dimensions, whether of lead, glass, or wood, give the same tone as to pitch under the same circumstances, which shows that the air alone produces the sound.