HARMONY AND DISCORDS 731 



notes, though each one be musical, are not necessarily harmonious. 

 The most prominent overtone, except the octave, is the 5th, with its 

 octaves, and this is called the dominant. The next is the 3d, with its 

 octaves. The other overtones are comparatively feeble. Reasoning, 

 now, from a knowledge of the relations of overtones, it might be in- 

 ferred that the reenforcement of the 5th and 3d by other notes bearing 

 similar relations to the tonic would be agreeable. This is the fact ; and 

 it was ascertained empirically long before the pleasing impression pro- 

 duced by such combinations was explained mathematically. 



It is a law in music that the simpler the ratio between the number 

 of vibrations in two sounds, the better the harmony. The simplest 

 relation, of course, is I : I, when the two sounds are said to be in unison. 

 The next in order is I : 2. In sounding C and its 8th, for example, 

 there are 48 vibrations of one to 96 of the other. These sounds can 

 produce no discord, because the waves never interfere with each other, 

 and the two sounds can be prolonged indefinitely, always maintaining 

 the same relations. The combined impression, therefore, is continuous. 

 The next in order are the 1st and 5th, their relations being 2:3. In 

 other words, with the 1st and 5th, for two waves of the 1st there are 

 three waves of the 5th. The two sounds may thus progress indefi- 

 nitely, for the waves coincide for every second wave of the 1st and 

 every third wave of the 5th. The next in order is the 3d. The 3d 

 of C has the 8th of C for its 5th, and the 5th of C for its minor 3d. 

 The ist, 3d, 5th and 8th form the common major chord; and the waves 

 of each note blend with each other at such short intervals of time that 

 the ear experiences a continuous impression, and no discord is heard. 

 This explanation of the common major chord illustrates the law that 

 the smaller the ratio of vibration between different tones, the better is 

 their harmony. Sounded with the ist, the 4th is more harmonious 

 than the 3d ; but its want of harmony with the 5th excludes it from the 

 common chord. The ist, 4th and 8th are harmonious, but to make a 

 complete chord the 6th must be added. 



Discords and Dissonance. A knowledge of the mechanism of sim- 

 ple accords leads naturally to a comprehension of the rationale of dis- 

 cords and dissonance. Two inharmonious notes that can not be resolved 

 into harmony by the addition of another note or other notes produce 

 discord. When the inharmonious sound is resolved into a harmony, 

 the notes first sounded produce what is called dissonance. The fact 

 that certain combinations of musical notes produce a disagreeable im- 

 pression was first ascertained empirically, with no knowledge of the 

 exact cause ; but the mechanism of discord is now regarded by most 

 physicists as settled. 



