CHAMBERS'S INFORMATION FOR THE PEOPLE. 



vibrates in two halves ; and from the rapidity of 

 the motion, the eye sees the string in its two 

 extreme positions at one and the same time. The 

 point C is called a node; and the parts AC, BC 

 are called loops, or ventral segments. If we touch 



Fig. 34- 



the string at a third or a fourth of its length, it 

 divides itself into three or four loops. The notes 

 formed by a string vibrating in one, two, three, 

 four, &c. loops, are respectively the primary or 

 fundamental note, its octave, the fifth above the 

 octave, the octave above the octave, &c. ; and the 

 whole series are called the harmonics of the 

 fundamental. 



The actual motion of a vibrating string is not so 

 simple as the motion just described, but added 

 to the primary vibration, there are a number of 

 partial vibrations, of smaller intensity, and corre- 

 sponding to the half, third, fourth, &c. parts of 

 the string, so that a simple note is never heard, 

 unless accompanied by several of its harmonics. 

 The undisciplined ear cannot at first detect the 

 complexity of a musical note, but careful attention 

 will soon prove the fact. The existence of the 

 harmonics may also be demonstrated by partially 

 quenching the fundamental tone. For this pur- 

 pose, after the string has been sounded, if we 

 touch its middle point with a feather lightly for a 

 moment, the fundamental is so much weakened 

 that the octave is clearly heard. But the most 

 satisfactory analysis of musical sounds has been 

 made by Helmholtz, who, for this purpose, con- 

 trived an instrument which he called a resonance 

 globe. This is a globe with two openings, 

 s and t, of which 

 one, J, wide and 

 cylindrical, is turned 

 towards the sound, 

 and the other, /, 

 has an india-rubber 

 tube attached to it, 

 which is applied to 

 the ear. Like the 

 sounding-board, the 

 air in this cavity will respond to a certain note, so 

 that if several other notes be sounded along with 

 this particular one, the resonator will strengthen 

 its own note only, and the ear will hear it dis- 

 tinctly to the exclusion of all the others. Conse- 

 quently, by means of a series of such resonators, 

 each one of which responds to a note of the 

 diatonic scale, and its octaves, a given note can be 

 analysed. And it is found that every note is 

 mingled with many of its harmonics. By means 

 of the same resonators, Helmholtz has succeeded 

 in explaining the timbre or quality of musical 

 notes. He has proved that the difference between 

 the same note sounded on different instruments, 

 say C of the violin and C of the pianoforte, 

 depends solely on the different intensities of 

 the harmonics which accompany the primary 

 note. 



A column of air may be made to vibrate, and 

 emit a musical -sound, by taking a tube, ab, open 

 at both ends, and blowing at one end, a, 



256 



Fig- 35- 



across and a little downwards. When such 

 a tube is made to yield its lowest or 

 fundamental note, the air particles within 

 it vibrate, so that those at a and b are 

 most agitated, their relative distances not 

 being much altered ; while those at the 

 middle point, c, are not displaced at all, 

 the neighbouring particles alternately 

 approaching them, and receding from 

 them. The distance between a point of 

 greatest disturbance and a node, or point 

 of rest, that is, ac on the figure, being 

 quarter of a wave-length, it is clear that 

 the wave-length of the fundamental note is Fig. 36, 

 twice the length of the tube. The number 

 of vibrations in a second is found by dividing the 

 distance which sound travels in a second by the 

 wave-length. Supposing the note C produced by 

 264 vibrations in a second, and the velocity of sound 

 at ordinary temperatures to be 1112 feet, it is easily 

 found that the length of an open pipe, of which C 

 is the fundamental note, is 2-1 feet. By blowing 

 more strongly into the pipe, it is easy to produce 

 a note whose wave-length is half of that of the 

 fundamental note ; and consequently, the new 

 note is the octave above the former one. In this 

 case, there is a node at d half-way between a and c, 

 and another at e, the middle of cb. Again, no 

 note between the fundamental and its octave can 

 be obtained from the pipe, for, as the open ends, a 

 and b, must always be points of greatest dis- 

 turbance, no first node can lie between c and d. 

 The next possible notes are produced when the 

 first node lies at a distance from a of -|, , T V, &c. 

 of the length of the pipe ; and then the wave- 

 lengths of all the notes that can be given by such 

 a pipe are as the numbers I, $, i, 1, &c. or the 

 numbers of vibrations in a given time are as 

 i, 2, 3, 4, &c. Of these notes, which are called the 

 harmonics of the pipe, the first eight are here 

 represented, but the last four of the series are, for 



convenience, written two octaves lower than they 

 should be. As with vibrating strings, so likewise 

 with vibrating columns of air, a pure note is never 

 sounded alone, but each one is always accom- 

 panied by some of its harmonics. 



If the pipe containing the column of air be 

 closed at one end, the conditions which 

 every vibration must fulfil are, that at 

 the open end there must be a point of 

 greatest disturbance and at the closed 

 end, a node. The fundamental note of 

 such a pipe must be one of which the 

 quarter wave-length is that of the pipe, 

 and is, therefore, an octave below the 

 fundamental note of a pipe, of the same 

 length, open at both ends. There can- 

 not be a node in the middle of the 

 closed pipe, for this would require b to 

 be a point of greatest disturbance. There Fig. 37. 

 may be nodes at i, , |, &c. of the 

 length from a, so that all the harmonics are 

 included in the series r, 3, 5, 7, &c. 



