224 THE HUMAN BODY 



vibrations bear the ratio 1 :2 to one another, we hear the musical 

 interval called an octave. The middle C of the musical scale is 

 due to 256 vibrations per second. Its octave has 512 vibrations. 



Sound vibrations may be too rapid or too slow in succession to 

 produce sonorous sensations. The highest-pitched audible note 

 answers to about 38,000 vibrations in a second, but it differs in 

 individuals; many persons cannot hear the cry of a bat nor the 

 chirp of a cricket, which lie near this upper audible limit. On the 

 other hand, sounds of vibrational rate about 40 per second are not 

 well heard, and a little below this become inaudible. The highest 

 note used in orchestras is the d v of the fifth accented octave, pro- 

 duced by the piccolo flute, due to 4,752 vibrations in a second; 

 and the lowest-pitched is the E\, of the contra octave, produced 

 by the double bass. Modern grand pianos and organs go down to 

 C, in the contra octave (33 vibrations per second) or even A", 

 (271), but the musical quality of such notes is imperfect; they pro- 

 duce rather a "hum" than a true tone sensation, and are only used 

 along with notes of higher octaves to which they give a character 

 of greater depth. 



Timbre. Since the loudness of a tone depends on the vibra- 

 tional amplitude of its physical antecedent, and its pitch on the 

 vibrational rate, we have still to seek the cause of timbre; the 

 quality by which we recognize the human voice, the violin, the 

 piano, and the flute, even when all sound the same note and of 

 the same loudness. Helmholtz showed that the quality of any 

 tone is determined by the particular overtones or harmonic partials 

 that are combined in it with the fundamental tone. Most vibrating 

 bodies are able to vibrate both as a whole and in sections. Since 

 the sections are smaller than the whole body their vibrations are 

 more rapid than those of the body as a whole. The vibrating 

 sections may be halves, thirds, fourths, or any other fraction of 

 the whole body. Also one and the same body may be vibrating 

 at once in halves, quarters, and several other smaller divisions. 

 These vibrations in parts are the sources of overtones, the pitch 

 of the tone being determined by its vibration as a whole, the so- 

 called fundamental vibration. 



The air waves set in motion by a body vibrating in such com- 

 plex fashion must necessarily be themselves very complex. Since 

 they are periodic, however, they produce audible notes, if rapid 



