HARMONICS. 519 



tuned to the same note, the present D being generally accepted as 

 being most free from false tuning, and less liable for the errors 

 of " temperament." Several of the strings are an octave lower 

 than the others, but the tonic is always the same. 



The instrument is placed in a current of air, generally in a 

 window, with the sash let down upon it, and the air- currents 

 set the strings vibrating in a most wonderful manner. 



There is no need for human fingers to touch them, but they 

 automatically divide themselves into the component parts of the 

 common chord, and produce octaves, fifths, and thirds ad 

 infinitum. 



On the left hand of the same illustration is exhibited a string 

 of the same length and tension, vibrating in two different ways. 

 The upper figure shows it divided into three portions, each 

 of which gives the fifth above the tonic, and all of which, when 

 sounding simultaneously, give a fulness and richness to the 

 tone which could only be attained otherwise by three distinct 

 instruments. All players of stringed instruments know how 

 invaluable are these harmonics, without which many passage? 

 of well-known music could not be played, and which are 

 produced by " damping/' and not pressing the strings. 



So, if the string be lightly touched, or damped at the 

 crossing portion at either end, the result will be that the string 

 divides itself into three portions, and all three resound 

 simultaneously. 



The lower string is vibrating in thirds, having divided itself 

 into four portions. If it were damped in the middle, it would 

 divide itself into two portions, and sound octaves. 



The subject is a most interesting one, but our space is nearly 

 exhausted, and we must pass to another branch of it. 



In all brass instruments furnished with a mouthpiece, and 

 not with a reed, the notes are obtained by vibrations of the 

 enclosed air, caused by the movement of the lips. They are 

 all set to some definite tonic, sometimes C natural, but mostly 

 to a flat tone, such as B flat or E flat. 



Taking the ordinary military trumpet or bugle as an 

 example, we have (when we have learned how to play it), 

 first, the tonic. By alteration of the lips we get the octave 

 above the tonic. Then comes the fifth ; then the third, which 



