AUDITORY SENSATIONS 563 



sticks of different lengths and strike them in succession, it will be 

 noticed that the sound produced by each stick corresponds to a dis- 

 tinct note, and tunes may be played on such a collection of sticks. 

 On the other hand, the tone of a musical instrument maybe so harsh 

 that there is very little difference between it and a noise. 



In a musical tone we can distinguish various characters or qualities : 



(1) The loudness of a tone is determined by the amplitude of the 

 vibrations of which it is composed. If a violin string be bowed 

 forcibly the excursion of its string at each vibration is greater than when 

 it is bowed gently, and the amplitude of the corresponding alternating 

 waves of sound varies in proportion to that of the vibrating body by 

 which they are started. By attaching a pointed slip of paper to the 

 end of a tuning-fork and so recording its vibrations on a blackened 

 surface, it is easy to see the connection which exists between the 

 amplitude of vibrations and the loudness of the sound produced by 

 the vibrating fork. 



(2) The pitch of a musical tone depends on the rapidity of the 

 vibrations of which it is composed. By means of a siren we can 

 determine the number of vibrations corresponding to each note. 

 As the speed of revolution of the siren is increased, and therefore the 

 number of interruptions per second of the stream of air passing through 

 the holes in its disc, the note appears to us to rise continuously. If 

 we take two tuning-forks, one vibrating at 100 times per second and 

 the other vibrating 200 times per second, the pitch of the latter is 

 observed to be considerably higher than that of the former. In fact 

 it forms the octave. If the number of vibrations is less than about 

 thirty per second no musical tone is produced, the individual vibrations 

 being perceived as a series of pulses in the surrounding air, and it is 

 only when we increase the number to about forty per second that we are 

 able to appreciate the pitch of the note produced. As the number 

 of vibrations per second is increased the note rises steadily without 

 break till we arrive at 40,000 to 50,000 vibrations per second. Above 

 this number of vibrations the human ear is incapable of perceiving any 

 note at all, though it is probable that small animals can perceive notes 

 still higher in the scale. In music neither the lowest nor the highest 

 tones are used. The lowest tones of the large organs, that of the 

 sixty-four foot pipe, is 16 vibrations per second, and one can hardly 

 speak of its effect as that of a musical tone. The highest notes 

 employed in music are 4 and c5 with 3520 and 4224 vibrations per 

 second on the piano, and d with 4752 vibrations on the piccolo flute. 

 In music therefore we only employ between 40 and 4700 vibrations 

 per second, i.e. about seven octaves. The manner of construction of 

 the musical scale will be dealt with later. 



(3) Timbre or quality of musical sounds. 



