therefore, vary not only with the distance of the sounding body, but also with the amount of vibration in the sounding body.
- The pitch of a note depends simply upon the number of vibrations per second, that is, the frequency of the body which produces it.
- 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.:
- 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.
- 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.
| 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 | 98 | 109 | 1615 | 98 | 109 | 98 | 1615 | |||||||||
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).
Acre (ä-ker or ā-ker), a seaport of Syria. Its harbor is the best on the neighboring coast. It is very old, and famous for the attacks and sieges it has sustained, particularly the assault of Richard Cœur de Lion in 1191, and the sixty days’ siege of Napoleon in 1799. Population, 10,000.
Ac′tinism (Gr. aktin, a ray), the chemical property of light, solar or other radiant energy, as the sun’s rays in photography, and by which chemical changes are produced. The sun-recording instrument which measures and records the quantity of actinism present is called the actinograph; while the actinometer is the instrument or apparatus for measuring the chemical effects of radiation from any source, as in measuring the intensity of the rays on a photographic plate, or piece of sensitized paper, when exposed to the sunlight.
Ac′tinomor′phic (ak′tĭn-o-môr′fĭk) Flowers. Those whose parts are repeated uniformly about a center, like the parts of a radiate animal. Such flowers are often called “regular.” Although the name applies to all parts of the flower it is most commonly used in connection with the petals. When the petals are all about alike and equally spaced about the center, as in the buttercup and the rose, the flower is actinomorphic. The contrasting phrase is “zygomorphic flowers.” The noun form of the word is “actinomorphy.”
Actium (ak′shĭ-ŭm), in Acarnania, the scene of the naval battle in which Octavius, afterward called Augustus Cæsar, conquered Mark Antony and Cleopatra and became, in consequence, emperor of Rome. The number of ships on each side was about the same, but the battle was lost by the cowardice of Cleopatra, who fled with her triremes (ships propelled by oars) as soon as attacked, followed by Antony, who would not be separated from her even to win an empire. The Actian games, occurring every four years, were established here by Augustus in honor of his victory.
Ad′am, the first man, the father of the human race. His sons were Cain, Abel and Seth. He lived to be 930 years old, and through his son Seth was the direct ancestor of the Hebrew nation.
