192 SPECIAL SENSES. 



low ; still we have dissonance, less disagreeable, but no beats. 

 Passing down, an octave at a time, as the numbers of vibra- 

 tions become smaller, the difference between them is less, and 

 there are fewer beats in a second, until they are readily ap- 

 preciated as beats and can even be counted. 



Beats, then, are due to interference of sound-waves, and 

 the number in a second is equal to the difference in the rate 

 of vibrations. When these are too rapid to be appreciated as 

 beats, we have simply a sensation of discord. There is no in- 

 terference of the waves of tones in unison, provided the 

 waves start at the same instant ; the intensity of the sound 

 being increased by reenf orcement. The differences between 

 the 1st and 8th, the 1st and 5th, the 1st and 3d, and other 

 harmonious combinations, is so great that we have no beats 

 and no discord, the more rapid waves reenforcing the har- 

 monics of the primary sound. It is important to remember, 

 in this connection, that resultant tones are equal to the differ- 

 ence in the rates of vibration of two harmonious tones. If 

 we take a note of 240 vibrations, and its 5th, with 360 vibra- 

 tions, these two have a difference of 120, which is the lower 

 octave of the 1st and is an harmonious tone. 



It is evident that the laws which we have thus stated are 

 equally applicable to overtones, resultant tones, and addi- 

 tional tones, which have their beats and dissonances, as well 

 as the primary tones. 



Tones ~by Influence (Consonance). The term consonance 

 is generally applied to the harmonious combinations of two 

 or more sounds, and is synonymous with accord, as it is used 

 in music. In this sense, it is opposed to dissonance, or dis- 

 cord. By some writers, however, consonance is used to de- 

 note sounds produced in sonorous bodies by the influence 

 of sounds in unison. If, for example, we have a bell tuned 

 to a certain note, and bring near its opening a tuning-fork 

 vibrating in unison with this note, the bell will sound vigor- 

 ously in unison, though it is influenced only by the vibra- 



