730 



SPECIAL SENSES 



notes are richer when the strings are attacked at this point, is that 

 the harmonious overtones are full and perfect, and certain of the dis- 

 cordant overtones are suppressed. 



When two harmonious notes are produced under favorable condi- 

 tions, one can hear, in addition to the two sounds, a sound differing 

 from both and much lower than the lower of the two. This sound is 

 too low for an harmonic, and it has been called a resultant tone. The 

 formation of a new sound by combining two sounds of different pitch 

 is analogous to the blending of colors in optics, except that the primary 

 sounds are not lost. The laws of the production of these resultant 

 sounds are very simple. When two notes in harmony are sounded, the 

 resultant tone is equal to the difference between the two primaries. 

 For example, C, with 48 vibrations, and its 5th, with 72 vibrations in a 

 second, give a resultant tone equal to the difference, which is 24 vibra- 

 tions, and it is consequently the octave below C. These resultant tones 

 are feeble as compared with the primary tones, and they can be heard 

 under only the most favorable experimental conditions. In addition to 

 these sounds, Helmholtz has discovered sounds, even more feeble, which 

 he calls additional, or summation-tones. The value of these is equal to 

 the sum of vibrations of the primary tones. For example, C (48) and 

 its 5th (72) would give a summation-tone of 120 vibrations, or the octave 

 of the 3d ; and C (48) with its 3d (60) would give 108 vibrations, the 

 octave of the 2d. These tones can be distinguished by means of 

 resonators. 



It is thus seen that musical sounds are complex. With single 

 notes there are many different harmonics, or overtones, and in chords 

 there are series of resultants, that are lower than the primary notes, and 

 series of additional, or summation-tones, that are higher ; but both the 

 resultant and the summation-tones bear exact mathematical relations to 

 the primary notes. 



Harmony. Overtones, resultant tones and summation-tones of 

 strings have been discussed rather fully, for the reason that in studying 

 the physiology of audition, it will be seen 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 apparently are produced by simple 

 vibrations. Combinations of notes which thus produce an agreeable 

 impression are called harmonious. They seem to become blended with 

 each other into a complete sound of peculiar quality, all the different 

 vibrations entering into their composition being simultaneously appre- 

 ciated by the ear. The blending of notes which bear to each other 

 certain mathematical relations is called harmony; but two or more 



