194 THE HUMAN BODY 



sound. The pitch of a note depends on the length of the waves, 

 that is, the distance from one point of greatest condensation to the 

 next, or (what amounts to the same thing) on the number of waves 

 reaching the ear in given time, say a second. The shorter the 

 waves the more rapidly they follow one another, and the higher the 

 pitch of the note. When audible 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 v 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", 

 (27 J), 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 vibrational 

 amplitude of its physical antecedent, and its pitch on the vibra- 

 tional 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 



