746 SPECIAL SENSES. 



the pleasing impression produced by such combinations was explained mathe- 

 matically. 



It is a law in music that the more simple the ratio between the number 

 of vibrations in two sounds, the more perfect is the harmony. The simplest 

 relation, of course, is 1 : 1, when the two sounds are said to be in unison. The 

 next in order is 1 : 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 is therefore continuous. The next in order is 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 indefinitely, 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 1st, 

 3d, 5th and 8th form the common major chord ; and the waves of each tone 

 blend with each other at such short intervals of time that the ear experiences 

 a continuous impression, and no discord is appreciated. This explanation of 

 the common major chord illustrates the law that the smaller the ratio of vi- 

 bration between different tones, the more perfect is their harmony. Sounded 

 with the 1st, the 4th is more harmonious than the 3d ; but its want of har- 

 mony with the 5th excludes it from the common chord. The 1st, 4th and 

 8th are harmonious, but to make a complete chord the 6th must be added. 



Discords. A knowledge of the mechanism of simple accords leads natu- 

 rally to a comprehension of the rationale of discords. The fact that certain 

 combinations of musical notes produce a disagreeable impression was ascer- 

 tained empirically, with no knowledge of the exact cause of the dissonance ; 

 but the mechanism of discord may now be regarded as settled. 



The sounds produced by two tuning-forks giving, precisely the same num- 

 ber of vibrations in a second are in perfect unison. If one of the forks be 

 loaded with a bit of wax, so that its vibrations are slightly reduced, and if 

 both be put in vibration at the same instant, there is discord. Taking the 

 illustration given by Tyndall, it may be assumed that one fork has 256, and 

 the other, 255 vibrations in a second. While these two forks are vibrating, 

 one is gradually gaining upon the other; but at the end of half a second, one 

 will have made 128 vibrations, while the other will have made 127|-. At this 

 point the two waves are moving in exactly opposite directions ; and as a con- 

 sequence, the sounds neutralize each other, and there is an instant of silence. 

 The perfect sounds, as the two forks continue to vibrate, are thus alternately 

 re-enforced and diminished, and this produces what is known in music as beats. 

 As the difference in the number of vibrations in a second is one, the instants 

 of silence occur once in a second ; and in this illustration the beats occur 

 once a second. Unison takes place when two sounds can follow each other 

 indefinitely, their waves blending perfectly; and dissonance is marked by 

 successive beats, or pulses. If the forks be loaded so that one will vibrate 

 240 times in a second, and the other 234, there will be six times in a second 



