64 0]^ THE PHYSIOLOGICAL CAUSES OF 



in the same time are as 2 to 3, the two tones form a fifth ; 

 if they are as 4 to 5, the two tones form a major third. 



If you observe that the numbers of the vibrations which 

 generate the tones of the major chord C E Gr c are in the 

 ratio of the numbers 4:5:6:8, you can deduce from 

 these all other relations of musical tones, by imagining 

 a new major chord, having the same relations of the num- 

 bers of vibrations, to be formed upon each of the above- 

 named tones. The numbers of vibrations within the 

 limits of audible tones which would be obtained by 

 executing the calculation thus indicated, are extraordi- 

 narily different. Since the octave above any tone has 

 twice as many vibrations as the tone itself, the second 

 octave above will have four times, the third has eight 

 times as many. Our modem pianofortes have seven 

 octaves. Their highest tones, therefore, perform 128 

 vibrations in the time that their lowest tone makes one 

 single vibration. 



The deepest C, which our pianos usually possess, answers 

 to the sixteen-foot open pipe of the organ — musicians call 

 it the ' contra-C ' — and makes thirty-three vibrations in 

 one second of time. This is very nearly the limit of audi- 

 bility. You will have observed that these tones have a 

 dull, bad quality of sound on the piano, and that it is 

 difficult to determine their pitch and the accuracy of their 

 tuning. On the organ the contra-C is somewhat more 

 powerful than on the piano, but even here some uncer- 

 tainty is felt in judging of its pitch. On larger organs 

 there is a whole octave of tones below the contra-C, 

 reaching to the next lower C, with 16^ vibrations in a 

 second. But the ear can scarcely separate these tones 

 from an obscure drone ; and the deeper they are the more 

 plainly can it distinguish the separate impulses of the air 

 to which they are due. Hence they are used solely in con- 

 junction with the next higher octaves, to strengthen their 

 notes, and produce an impression of greater depth. 



