The only thing essential for the production of a musical sound is that the waves which reach the ear shall be rapid and regular; it is immaterial how these waves are produced.  If a toothed wheel is mounted and slowly rotated, and a stiff card is held against the teeth of the wheel, a distinct tap is heard every time the card strikes the wheel.  But if the wheel is rotated rapidly, the ear ceases to hear the various taps and recognizes a deep continuous musical tone.  The blending of the individual taps, occurring at regular intervals, has produced a sustained musical tone.  A similar result is obtained if a card is drawn slowly and then rapidly over the teeth of a comb.

[Illustration:  FIG. 176.—­A rotating disk.]

That musical tones are due to a succession of regularly timed impulses is shown most clearly by means of a rotating disk on which are cut two sets of holes, the outer set equally spaced, and the inner set unequally spaced (Fig. 176).

If, while the disk is rotating rapidly, a tube is held over the outside row and air is blown through the tube, a sustained musical tone will be heard.  If, however, the tube is held, during the rotation of the disk, over the inner row of unequally spaced holes, the musical tone disappears, and a series of noises take its place.  In the first case, the separate puffs of air followed each other regularly and blended into one tone; in the second case, the separate puffs of air followed each other at uncertain and irregular intervals and the result was noise.

Sound possesses a musical quality only when the waves or pulses follow each other at absolutely regular intervals.

262.  The Effect of the Rapidity of Motion on the Musical Tone Produced.  If the disk is rotated so slowly that less than about 16 puffs are produced in one second, only separate puffs are heard, and a musical tone is lacking; if, on the other hand, the disk is rotated in such a way that 16 puffs or more are produced in one second, the separate puffs will blend together to produce a continuous musical note of very low pitch.  If the speed of the disk is increased so that the puffs become more frequent, the pitch of the resulting note rises; and at very high speeds the notes produced become so shrill and piercing as to be disagreeable to the ear.  If the speed of the disk is lessened, the pitch falls correspondingly; and if the speed again becomes so low that less than 16 puffs are formed per second, the sustained sound disappears and a series of intermittent noises is produced.

263.  The Pitch of a Note.  By means of an apparatus called the siren, it is possible to calculate the number of vibrations producing any given musical note, such, for example, as middle C on the piano.  If air is forced continuously against the disk as it rotates, a series of puffs will be heard (Fig. 177).

If the disk turns fast enough, the puffs blend into a musical sound, whose pitch rises higher and higher as the disk moves faster and faster, and produces more and more puffs each second.