174 SPECIAL SENSES. 



range of sounds that can be legitimately employed in music, 

 those of from 40 to 4,000 vibrations in a second, embracing 

 about seven octaves. In an orchestra, the double bass gives 

 the lowest note, which has 40'25 vibrations in a second, and 

 the highest note, given by the small flute, has 4,752 vibra- 

 tions. In grand organs, there is a pipe which gives a note of 

 16*5 vibrations, and the deepest note of modern pianos has 

 27*5 vibrations ; but delicate shades of pitch in these low 

 tones are not appreciable to most persons. 1 Sounds above 

 the limits just indicated are painfully sharp, and their pitch 

 cannot be exactly appreciated by the ear. The physiological 

 interest connected with these facts is, that the limits of the 

 appreciation of musical sounds are probably due to the ana- 

 tomical arrangement of the auditory apparatus, as we have a 

 limit to the acuteness of vision, which can be explained by 

 the structure of the eye. This fact is the basis of the ac- 

 cepted theories of the appreciation of musical sounds. 



The Siren. As the ear is capable of distinguishing mu- 

 sical sounds in unison, if we can construct an apparatus by 

 which we are able, not only to produce different tones, but 

 to calculate accurately the number of vibrations of each, we 

 can make an absolute demonstration of the facts just stated. 

 Such an instrument is the siren, the tones of which can be 

 compared by the ear with those produced by other instru- 

 ments. It is not essential to our purpose to describe mi- 

 nutely the mechanism of the siren, as all that we desire is 

 to understand, in general terms, the principle of its action. 



The principle of the siren depends upon the fact that 

 puffs of air, produced at regular intervals, will give rise to 

 musical tones, the pitch of which is high in proportion to the 

 rapidity of the puffs, each of which forms a sound-wave. In 

 the siren, we have a fixed disk of metal, perforated with sev- 

 eral series of orifices, which may be closed or opened at will. 

 Of these, the outer series of openings presents usually sixteen 



1 HELMIIOLTZ, Theorie physiologique de la musique, Paris, 1868, p. 24. 



