504 STUDIES IN ADVANCED PHYSIOLOGY. 



definite rhythms, and when these rhythms are easily per- 

 ceived; that is, are mathematically simple, we become con- 

 scious of this pleasure. 



Something of this rhythm appeals to the eye. Soldiers 

 that march in unison present a pleasing appearance. A 

 company of soldiers composed of a column of adults and a 

 column of boys marching in such a way that the boys would 

 take two steps while the adult soldiers took one step would 

 be very pleasing to the eye. The interval between the two 

 columns of soldiers would really be an octave. We can 

 imagine the pleasing effect of two columns marching with 

 such regularity that for every two steps of one column the 

 other should take three, so that at every third step of the 

 second column all of the soldiers would step together. 

 This would be the interval of 2 to 3, or the perfect fifth. 

 If, finally, all mathematical ratio should be lost, or at least 

 become very complex, we would no longer be able to per- 

 ceive any rhythm in the march, and the column now would 

 present nothing but an ordinary crowd rushing in confusion 

 down the street. This, in terms of sound, is mere noise. 



In the building of a musical instrument, therefore, such, 

 for instance, as the piano, which has only a certain number 

 of keys, the point is to pick out those notes which bear 

 these simple ratios and omit those of complex ratios. In 

 this way there is produced what is commonly called the 

 scale, consisting of eight sounds. The vibrations determin- 

 ing these notes are in the proportion of the numbers as here 

 given : 



CDEFGABC 

 1, 9 /s, 5 A> 4 /3, 3 / 2 , 5 /3, 15 /s, 2. 



Cleared of fractions these proportions may be expressed 

 by the numbers, 



CDEFGABC 



24, 27, 30, 32, 36, 40, 45, 48. 



Thus for every 24 vibrations of C, D will have 27, A 40, 

 and the upper C 48, etc. 



