Page:Elementary Text-book of Physics (Anthony, 1897).djvu/181

§142] vibrations reduced to its lowest terms become smaller, until they are no longer distinguishable as separate beats, but appear as an unpleasant roughness in the sound. If the terms of the ratio become smaller still, the roughness diminishes, and when the ratio is $$\tfrac{6}{5}$$ the effect is no longer unpleasant. This, and ratios expressed by smaller numbers, as $$\tfrac{5}{4}, \tfrac{5}{3}, \tfrac{4}{3}, \tfrac{3}{2}, \tfrac{2}{1}$$, represent concordant combinations.

140. Major and Minor Triads.—Three tones of which the vibration numbers are as 4:5:6 form a concordant combination called the major triad. The ratio 10:12:15 represents another concordant combination called the minor triad. Fig. 53 shows the resultant curves for the two triads.

141. Intervals.—The interval between two tones is expressed by the ratio of their vibration numbers, using the larger as the numerator. Certain intervals have received names derived from the relative positions of the two tones in the musical scale, as described below. The interval $$\tfrac{2}{1}$$ is called an octave; $$\tfrac{3}{2}$$, a fifth; $$\tfrac{4}{3}$$, a fourth; $$\tfrac{5}{4}$$, a major third; $$\tfrac{6}{5}$$, a minor third.

142. Musical Scales.—A musical scale is a series of tones which have been chosen to meet the demands of musical composition. There are at present two principal scales in use, each consisting of seven notes, with their octaves, chosen with reference to their fitness to produce pleasing effects when used in combination. In one, called the major scale, the first, third, and fifth, the fourth, sixth, and eighth, and the fifth, seventh, and ninth tones, form major triads. In the other, called the minor scale, the same tones form minor triads. Prom this it is easy to deduce the following relations: