596 Original Articles. [Oct., 



tones must be looked upon from a musical point of view as a major 

 chord in which the key-note is the most powerful. These upper 

 tones may be either harmonic or inharmonic, harmonic if their 

 vibrations are simple multiples of those of the fundamental, inhar- 

 monic when no such simple relation exists. There is scarcely any 

 musical instrument which is free from these upper tones ; the tuning- 

 fork is nearly so, and those which are produced when the fork is first 

 struck lie so far from the fundamental, that they speedily disappear 

 and leave a perfectly simple sound as the characteristic of this 

 instrument. 



When a stream of air is directed across a wide tube, closed at the 

 bottom and provided with a narrow opening at the top (such as a 

 bottle), a tone is produced which is also free from upper tones. Again, 

 by applying the handle of a tuning-fork to the end of a string so 

 stretched as to be in perfect unison with it, the string takes up a pure 

 pendulum-like vibration free from nodes, and gives also a simple sound. 

 As might be expected from what has been said, these sounds, produced 

 in three different ways and perfectly alike, are undistinguishable the 

 one from the other. It is strictly true that could we eliminate altogether 

 the upper tones of the various instruments used for musical purposes, 

 they would all give nothing but the dull soft sound characteristic of 

 the tuning-fork. 



So long as the upper tones are harmonic to the fundamental they 

 give it a peculiar rich quality by supporting it. As their vibrations 

 are simple multiples of those of the fundamental, it is obvious that at 

 certain regularly recurring intervals their vibration must be identical 

 with that of the fundamental, so that like impulses applied at the proper 

 moment to a swinging pendulum the action is increased and main- 

 tained. When the upper tones are inharmonic they give a peculiar 

 piercing metallic character to the sounds, which is characteristic of 

 instruments so situated. 



The only cases in which the upper tones are strictly harmonic to 

 the principal tone are vibrating strings and vibrating columns of air, 

 and hence we find that musical instruments depend almost exclusively 

 on these two means of producing sound. 



Sounds produced in other ways are always accompanied by secon- 

 dary inharmonic tones, and are only used by the musician when the 

 fundamental is far more powerful than the secondary tones, in military 

 and dance music, to mark the time or on account of their piercing 

 quality. The tuning-fork itself is an instrument producing inharmonic 

 upper tones, which are, however, so high and lie so far apart, and, 

 moreover, are after a few moments so weak, that the principal tone is 

 almost the only one which is appreciable. Vibrating bars of metal or 

 other material are sometimes used in another form, either suspended 

 perfectly free as in the triangle, or supported at the nodes of their 

 principal tone as in the glass harmonicon. 



Here the material of the bar has only just so much influence on 

 the sound as depends upon its mass or elasticity. The high inharmonic 

 tones will last longer in bodies of considerable mass and great elas- 

 ticity, such as steel and certain alloys of copper ; and on this account 



