In introducing the subject of hearing we shall have to say a few words about that which is heard, namely sound. Any object that has any degree of elasticity at all is apt, if struck or rubbed or otherwise set suddenly in motion, to start vibrating back and forth; the vibrations will nearly always be regular, and will occur at a rate that is the same for that particular object whenever it vibrates. The rate depends on the size, the character, and the degree of stretch of the object. Air is to all intents and purposes perfectly elastic; it is set vibrating by any object that is vibrating in it, but since it has no particular size nor degree of stretch it takes the vibration rate of the object that started it going in the first place. The vibrations once started in air spread in all directions, just as waves spread from a stone thrown into a pond, and when these air waves strike upon another object that is free to vibrate they will set it going at the same rate. The human hearing apparatus is a device which is set in vibration by air waves, and the result is called sound. The ear is limited in its ability to respond to vibrations; they must be neither too fast nor too slow; if slower than 16 a second, most people will fail to hear them, and the same is true if they are more rapid than about 40,000 a second. Between these limits vibrations that strike upon the ear are heard as sounds. Differences in vibration rate between one sound and another can be recognized by the ear; the difference is a matter of pitch. By the pitch of a tone we mean the vibration rate which it has. More rapid vibrations give tones of higher pitch; a slow rate means a low pitch. Middle C on the piano has a rate of either 256 or 261 a second according to the system used by the tuner. The human voice has an extreme range starting with the lowest note that the bass voice can compass with a rate of about 80 vibrations a second, to the highest note that famous sopranos can attain at about 1,400 a second. There is a record of a singer who could achieve a tone with a rate of 2,100 a second, but this has not been duplicated so far as is known. Of course no single voice can cover more than a fraction of this range. Most men produce all their tones at rates of between 90 and 500 a second, and women between 200 and 800 a second. Not every different vibration rate is heard as a tone of different pitch; the ear is not sensitive enough for that. The interval between one note and the next includes several vibrations, more the higher one goes in the scale. A perfectly true tone has exactly the rate called for; a departure of one or two vibrations a second may not be noticed, but if the error is greater the singer is sharping or flatting his tone, according as he is above or below the true rate. A note that has just double the rate of another one is said to be its octave. For convenience the interval of the octave has been split up into twelve