Man's physical universe




altered by the musician's pressing down on the strings at various


The strings in stringed instruments lose their tension by use and by

changes in temperature and, therefore, have to be "tuned" frequently.

The laws of vibrating strings may be summarized as follows: the

pitch is

1. Inversely proportional to the length.

2. Directly proportional to the square root of the tension.

3. Inversely proportional to the square root of the linear density.

Another way of expressing these laws is as follows

Long, loose, large (thick and dense) strings produce low pitch.

Short, stretched, small (thin and not dense) strings produce high


Wind Instruments.

There are two kinds of instruments which are

operated by wind. In the first type only the air vibrates, while those

of the second type require a mechanical vibrator such as a reed or the

player's lips. All wind instruments contain air columns which amplify

by means of resonance. Such resonators can emit only their fundamentals

or one or more of their harmonic overtones. Bugles produce

different pitch by changing the position of the lips and changing the

force of blowing, much as whistling with the lips is accomplished.

Different notes in other wind instruments are obtained by changing

the length of the resonator. This may be accomplished by opening

side holes, as in the flute and clarinet, by use of valves which insert

additional lengths of tubing, as in the cornet, or by sliding tubes as

in the trombone.

It is interesting to note that the tones produced by wind instruments

depend somewhat on the nature of the materials from which the

instruments are made.

The clarinet generates sound by means of a single reed which vibrates

against the opening in the mouthpiece, while the oboe has a mouthpiece

consisting of two reeds which vibrate against each other.

The slender conical tube of the horn may sometimes be more than

eighteen feet long. Very long, straight horns are used by the Chinese,

but the majority of horns are made spiral-shaped in order to increase

the ease of handling. Cones in wind instruments provide the overtones

that help to determine the quality of the tones produced. The lips

of the musician serve as the generator in the horn, the bugle, the trombone,

and other similar instruments.

Harmonicas and accordions produce their

thin metal reeds to vibrate with a column of air.

tones by causing many

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