408 THE BODY AT WORK 



is a pause. The compound sound produced by the two forks 

 reaches the ear in throbs. If the forks were vibrating at the 

 rates of 101 and 99, there would be two pauses and two beats in 

 every second ; if at the rate of 202 and 198, four. The number 

 of beats per second equals the difference in frequency of 

 vibration of the tones. A pianoforte tuner does his work best 

 if he has a musical ear, yet he may discharge his duties with 

 competence without one. Having struck a note, he sounds 

 its octave, holding both keys down, and listens for the beat. 

 If the first note gave no beat with his tuning-fork, the second 

 is in tune when it likewise gives no beat with the first. We 

 have met a tuner who did his work in this way ; but it must be 

 admitted that his tempering of the intervals of the octave 

 with which he commenced, and consequently of the other 

 octaves above and below it, left something to be desired. The 

 result might have been satisfactory had he been provided with 

 twelve tuning-forks. 



The question as to whether beats, when sufficiently rapid, 

 blend into a tone has been much discussed, without a decision. 

 Probably they do not. The complementary question as to 

 the cause of dissonance is also not completely closed. Two 

 notes harmonize, as we have seen, when the ratio of their 

 frequencies is a simple fraction. Musicians are not quite 

 agreed as to the level of numerical complexity at which a 

 compound tone first produces a feeling of discomfort. A good 

 deal depends upon its position in the scale and the instruments 

 which are combining to produce it. A minor third () is on 

 the safe side. This is the first chord in our list of intervals in 

 which a beat can be detected. Slow beats, however, do not 

 distress us. It is the rapid beats of conflicting overtones 

 which give a harsh, rough character to a compound note. The 

 level at which a line is drawn between harmony and dissonance 

 seems to depend to a considerable extent upon musical educa- 

 tion, using the term in its widest sense. In primitive music 

 Hungarian, Scotch, Welsh intricate minor chords predomi- 

 nate. The minute subdivision of the octave in Indian music 

 is quite incomprehensible to a European ear. Musical cultiva- 

 tion tends to eliminate complex fractions. It is, however, to 

 be noted that the history of Western music also shows the 

 influence of an opposite tendency. Later generations have 



