Musical Instruments
By musical sounds, are meant sounds that are pleasant to hear, and their combination in such a way that their effect is agreeable produces music. Any instrument, therefore, that is capable of producing pleasing sounds may be called a musical instrument, and music is sometimes produced by very odd devices; but by musical instruments we ordinarily mean instruments that are especially designed to produce musical sounds. The number of such instruments that have been invented is enormous, but all of them may be divided into comparatively few classes, only two of which are of much importance. The two classes, only two of which are of much importance. The two classes referred to are stringed instruments and wind instruments.
WHAT PITCH IS IN MUSIC
Stringed musical instruments are those in which the sounds are produced by the vibration of a number of strings, and are generally reinforced by a sounding board. The strings are arranged in the instruments in such a way that the pitch of the sound produced by each string shall bear relation to the pitch of those obtained from the other strings. As long as this relation exists, the instrument is said to be in tune, and when the relation is destroyed, the instrument is out of tune, and the music produced by it is apt to contain what we call discords.
The conditions that determine the pitch of sounds produced by strings can be very easily discovered by experiment. Thus, by taking two pieces of the same wire, one twice as long as the other, and stretching them equally, you will observe on striking them that the shorter one yields the higher note. If their vibration frequencies are measured it will be found that the shorter string has a vibration frequency just twice as great as that of the longer string. From this we conclude that when two strings of the same size (and material) are stretched equally taut, their vibration frequencies are inversely proportional to their lengths.
By now taking two pieces of wire, of the same size and length, and stretching them so that the tension of one is four times as great as that of the other, we shall find that the vibration frequency of the tighter string is just twice as great as that of the looser. Thus, we see that the vibration frequency depends upon the tension applied to a string, and, that in strings of the same size and length, the vibration frequencies are proportional to the square roots of their tensions.
Now taking two strings of the same length, but with the diameter of one twice as great as that of the other, and stretching them equally, we shall find that the vibration frequency of the smaller string is twice that of the larger; which shows that when the lengths and tensions of two strings are equal, their vibration frequencies are inversely proportional to their diameters.
In constructing stringed instruments, advantage is taken of each of these conditions that affect the vibration of strings, and the requisite pitch is secured in a string by choosing one of convenient length and diameter, and by stretching it to just the right tension.
When a string is plucked in the middle, it vibrates as a whole, and its rate of vibration, or vibration frequency, is determined by the three conditions that have just been discussed; but if a finger is laid on the string, in the middle, and the string is plucked between the middle and the end, the string will vibrate in halves, and the middle point will remain at rest. If the string had been touched at a point one-fourth of the length from the end it would have vibrated in fourths, and there would have been three stationary points.
When vibrations are set up in a string, with nothing to prevent the free vibration of the whole string, it first vibrates as a whole, and the sound produced is known as the fundamental tone of the string; but very soon smaller vibrations of segments of the string begin, first of halves of the string, then of thirds, and then of fourths. These smaller vibrations produce sound waves that blend with the fundamental tone and are known as overtones. The combined sound of the fundamental tone and the overtones is called a note. The overtones present in notes that have the same fundamental tone are not the same when the notes are produced by different instruments, and, consequently, the sound of notes of the same pitch is not the same on different instruments. This difference in notes of the same pitch has already been mentioned, but the way in which overtones are produced was not explained in connection with it.
In wind instruments the sounds are produced by the vibrations of columns of air in pipes. In the organ, which is probably the best example of a wind instrument, the vibrations are usually produced by causing a current of air to strike a sharp edge, just above the opening of the pipe, as is done in a common whistle. A portion of the air current is deflected into the organ pipe, and it sets up vibrations in the air within the pipe.
The pitch of the sound produced by an organ pipe is determined by the length of the pipe. A pipe that is open at both ends, called an open pipe, produces a sound that has a wave length twice as great as the length of the pipe; and if the pipe is open at one end only, a closed pipe, the sound produced has a wave length twice the length of the open pipe. Hence it will be seen that a closed pipe produces a sound that has the same pitch as that produced by an open pipe that is twice as long.