188 SPECIAL SENSES. 



It is thus seen that musical sounds are excessively com- 

 plex. With single sounds, we have an infinite variety and 

 number of harmonics, or overtones, and in chords, which will 

 be treated of more fully under the head of harmony, we have 

 a series of resultants, which are lower than the primary tones, 

 and a series of additional, or summation tones, which are 

 higher ; but both the resultant and the summation tones bear 

 an exact mathematical relation to the primary tones of the 

 chord. 



Harmony. "We have discussed the overtones, resultant 

 tones, and summation tones of strings rather fully, for the 

 reason that, in the physiology of audition, we shall see that 

 the ear is capable of recognizing single sounds, or successions 

 of single sounds ; but, at the same time, certain combinations 

 of sounds are appreciated, and are even more agreeable than 

 those which are apparently produced by simple vibrations. 

 Combinations of tones which thus produce an agreeable im- 

 pression are called harmonious. They seem to become blended 

 with each other into a complete sound of peculiar quality, .all 

 of the different vibrations entering into their composition 

 being simultaneously appreciated by the ear. From what we 

 have learned of overtones, it is evident that few musical sounds 

 are really simple, and that those which are simple are want- 

 .ing in richness, while they are perfectly pure. The blending 

 of tones which bear to each other a certain mathematical rela- 

 tion is called harmony ; but two or more tones, 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 our knowledge of the rela- 

 tions of overtones, we might infer that the reinforcement of 

 the 5th and 3d by other notes bearing similar relations to the 

 tonic would be agreeable. This is the fact, and it was ascer- 

 tained empirically long before the pleasing impression pro- 



