850 OF THE VOICE AND SPEECH. 



produce being elevated by increased tension. This resemblance disappears, 

 however, on more accurate comparison ; for it may be easily ascertained by 

 experiment, that no string so short as the vocal ligaments could give a clear 

 tone at all to be compared in depth with that of the lowest notes of the hu- 

 man voice ; and also, that the scale of changes produced by increased tension 

 is fundamentally different. When strings of the same length but of different 

 tensions are made the subject of comparison, it is found that the number of 

 vibrations is in proportion to the square roots of the extending forces. Thus, 

 if a string extended by a given weight produce a certain note, a string ex- 

 tended by four times that weight will give a note in which the vibrations 

 are twice as rapid ; and this will be the octave of the other. If nine times 

 the original weight be employed, the vibrations will be three times as rapid 

 as those of the fundamental note, producing the twelfth above it. Now by 

 fixing the larynx in such a manner that the vocal ligaments can be extended 

 by a known weight, Miiller has ascertained that the sounds produced by a 

 variation of the extending force do not follow the same ratio ; and therefore 

 the condition of these ligaments cannot be simply that of vibrating cords. 

 Further, although a cord of a certain length, which is adapted to give out 

 a clear and distinct note equal in depth to the lowest of the human voice, 

 may be made by increased tension to produce all the superior notes (which, 

 in stringed instruments, are ordinarily obtained by shortening the strings), 

 it does not follow that a short string, which, with moderate tension, nat- 

 urally produces a high note, should be able, by a diminution of the tension, 

 to give out a deep one ; for, although this might be theoretically possible, 

 yet it cannot be accomplished in practice; since the vibrations become 

 irregular on account of the diminished elasticity. 1 These considerations are 

 in themselves sufficient to destroy the supposed analogy ; and to prove that 

 the Chord* Vocales cannot be reduced to the same category with vibrating 

 strings. 



695. The next kind of instrument with which some analogy might be 

 suspected, is the flnte-pipe, in which the sound is produced by the vibration 

 of an elastic column of air contained in the tube ; and the pitch of the note 

 is determined almost entirely by the length of the column, although slightly 

 modified by its diameter, and 'by the nature of the embouchure or mouth 

 from which it issues. This is exemplified in the German Flute, and in the 

 English Flute or Flageolet ; in both of which instruments the acting length 

 of the pipe is determined by the interval between the embouchure and the 

 nearest of the side apertures; by opening or closing which, therefore, a 

 modification of the tone is produced. In the Organ, of which the greater 

 number of pipes are constructed upon this plan, there is a distinct pipe for 

 every note ; and their length increases in a regular scale. It is, in fact, with 

 flute'-pipes as with strings, that a diminution in length causes an increase 

 in the number of vibrations, in a simply inverse proportion ; so that of two 

 pipes, one being half the length of the other, the shorter will give a tone 

 which is the octave above the other, the vibrations of its column of air being 

 twice as rapid. Now there is nothing in the form or dimensions of the column 

 of air between the larynx and the mouth, which can be conceived to render 

 it at all capable of such vibrations as are required to produce the tones of 

 the Human voice ; though there is some doubt whether it be not the agent 

 in the musical tones of certain Birds. The length that would be required 

 in an open pipe to give the lowest G of the ordinary bass voice, is nearly six 



i Thus it would be impossible to produce good Buss notes on the strings of a Violin, 

 by diminishing their tension ; the length afforded by the Violoncello or Double Bass 

 is requisite. 



