INTRODUCTION TO PNEUMATICS. Ixxiii 



trumpet used by deaf persons acts on the same principle ; the rays, in 

 this case, being collected into a focus near the smaller end of the trumpet 

 which is applied to the ear. The trumpets used as musical instruments 

 are also constructed on this principle, so far as their form tends to 

 increase the sound ; but, as a musical instrument, the trumpet becomes 

 itself the sonorous body, which is made to vibrate by blowing into it, and 

 communicates its vibrations to the air. 



If a sonorous body be struck in such a manner that its vibrations are all 

 performed in equal times, the vibrations of the air will correspond with 

 them, and be equal also; and thus, striking uniformly on the drum of the 

 ear, they produce an uniform sensation on the auditory nerve, and excite 

 the same uniform idea in the mind ; or, in other words, we shall hear one 

 musical tone. But if the vibrations of the sonorous body be irregular, 

 there will necessarily follow a confusion of aerial vibrations ; for a second 

 vibration may commence before the first is finished, meet it half way on its 

 return, and interrupt it in its course. The quicker a sonorous body 

 vibrates, the more acute or sharp is the sound produced. The duration 

 of the vibrations of strings or chords depends upon their length, the 

 thickness or weight, and their degree of tension : thus the low, bass notes 

 of a harp or piano are produced by long, thick, loose strings ; and the 

 high, treble notes, by those which are short, small, and tightly strung : so 

 that the different length and size of the strings serves to vary the duration 

 of the vibrations, and, consequently, the acuteness or gravity of the notes. 



Among the variety of tones, there are some which, sounded together, 

 please the ear, producing what we call harmony, or concord. This is 

 thought to arise from the agreement of the vibrations of the two sonorous 

 bodies ; so that some of the vibrations of each strike upon the ear at the 

 same time. Thus, if the vibrations of two strings are performed in equal 

 times, the same tone is produced by both, and they are said to be in 

 unison. If a violin is to be tuned in unison with another, the strings 

 must be drawn tighter if too low, or loosened if at too high a pitch, in 

 order to bring them to vibrate in equal times with the strings of the 

 other instrument. 



But concord is not confined to unison, for two different tones har- 

 monize in a variety of cases. If one string (or any sonorous body 

 whatever) vibrate in double the time of another, the second vibration of 

 the latter will strike upon the ear at the same instant as the first vibration 

 of the former ; and this is the concord of an octave. If the vibrations of 

 two strings are as two to three, the third vibration of the first corresponds 

 with the fourth vibration of the latter, producing the harmony called a 

 fifth : so that when the key-note is struck with its fifth, you hear every 

 third vibration of one, and every fourth of the other at the same time. 

 The key-note struck with the fourth is likewise a concord, and the vibra- 

 tions are as three to four. The vibrations of a major third with the key- 

 note are as four to five ; and those of a minor third, as five to six. 



There are other tones which, though they cannot be struck together 

 without producing discord, if struck successively, give us the pleasure 

 which is called melody. 



