The New Student's Reference Work/Acoustics

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Acoustics (a-kōōs′tĭks). Those phenomena which one detects by the ear are generally studied together under the head of acoustics. But whenever any sound is heard we find that somewhere in the neighborhood there is what we call a
  1. The pitch of a note depends simply upon the number of vibrations per second, that is, the frequency of the body which produces it.
  2. But even when notes have the same loudness and the same pitch they may be quite different, as, for instance, the difference between middle C on the guitar and on the piano. Two notes of this kind are said to differ in quality. And quality has been shown to depend upon the presence of other notes, called overtones, along with the note under consideration.

THE MUSICAL SCALE

When we consider one tone in relation to other tones we are led to a study of the musical scale. Two definitions are necessary to any understanding of the musical scale, viz.:

  1. A musical interval between any two notes is defined as the ratio of their frequencies. Two notes which have the same frequency are said to be in unison. But if the ratio be 2:1 then the interval is said to be an octave.
  2. The Major Triad. — It is a very remarkable fact that the ears of all western nations consider any three notes whose frequencies are in the ratio 4:5:6 as harmonious. Such a combination is called the major triad, and is always pleasing to the ear.

The interval between any note and its octave is divided by musicians into a series of seven smaller intervals, called tones and semitones. These tones are called by letters of the alphabet, and together form what is known as the musical scale.

THE MAJOR SCALE.
Name of Note. C D E F G A B 2C
Name of Note in
Vocal Music
do re mi fa so la si do
Interval 9/8 10/9 16/15 9/8 10/9 9/8 16/15

From inspection of this table it will be readily seen that the entire Major Scale, as it is called, is made up of the three following major triads:

C : E : G = 4 : 5 : 6
F : A : 2C = 4 : 5 : 6
G : B : 2D = 4 : 5 : 6
For an excellent experimental discussion of acoustics, see Tyndall’s Lectures on Sound (Appleton), and Blaserna’s Theory of Sound (Int. Sci. Series). The great masterpiece in the literature of acoustics is, however, Helmholtz’s Sensations of Tone, trans. by Ellis (Longmans).