Ii6 ELEMENTS OF SCIENCE 



of our perceptions of musical sounds is analogously 

 limited. There are some persons who can hear the 

 very shrill cry of the bat, but to many it is quite 

 inaudible. 



When one musical note is said to be an octave above 

 another, this means that, to reveal it to us, there must 

 be twice as many vibrations as in the case of the lower 

 note. In notes emitted from the vibrations of strings, 

 the longer the string the deeper the note, and to produce 

 a note an octave higher than that produced by a string 

 of any given length, the string must be shortened one 

 half. 



There are what are called reed instruments (e.g., the 

 clarionet), and in them the air blown by the player 

 strikes deeply on a little blade placed in the mouthpiece 

 of the instrument and causes it to vibrate, so eliciting 

 various sound?. In a cornet-a-piston there is no arti- 

 ficial reed, but the player's lips are made to vibrate as 

 if they were two reeds one on either side of the orifice 

 of the instrument. The vibrations of the lips are 

 transmitted to the air within the cornet which then 

 emits very intensified sounds. 



Sounds may be intensified in various ways. They 

 will be so if sonorous vibrations be transmitted to the 

 walls of an empty box, and such is the action of the 

 wooden case of the violin, without which the musical 

 sounds of the strings would be greatly enfeebled. 



The waves of air which occasion musical notes, differ 

 greatly in length as well as in rapidity. Waves which 

 occasion very low notes may be sixty-four feet long, 

 whereas high ones may be less than an inch. 



Differences of timbre are due to the relations which 

 may exist between the main series of vibrations and 

 secondary ones. If these secondary vibrations are 



