HARMONISTS 



HARMONIUM 



endless range of quality may be conferred upon 

 the fundamental tone. 



For demonstration of harmonics in sounds of all 

 kinds a series of resonators is necessary. When a 

 tuning-fork is vibrated near a hollow vessel of 

 suitable capacity (say a lamp-chimney sunk in 

 water to an adjusted depth ), the air within the 

 hollow vessel vibrates in unison with the fork and 

 emits a loud sound ; similarly, when the capacity 

 of such a resonator corresponds to the pitch of a 

 harmonic tone present in a given sound, the reson- 

 ator sounds out that harmonic. By a series of 

 such observations all the harmonics can thus be 

 severally recognised. The physical basis of har- 

 monic tones is the fact that no vibration of an 

 elastic body is ever accomplished without a more or 

 less well-marked division of the vibrating body 

 into segments which vibrate independently and 

 simultaneously. To realise this, take a long string 

 stretched between two points ; set it in vibration 

 by means of a violin-bow ; the cord will appear to 



vibrate as a whole. Now, by means of the finger- 

 nail or of a stretched thread lightly pressed upon it 

 at the exact mid-point, 'stop 'the mid-point and 

 again bow ; the string will appear to vibrate in 

 two independent halves or loops, with a node or 

 point of rest between them ; the vibrations will be- 

 twice as frequent as at first, and the sound pro- 

 duced will be the octave of that originally heard. 

 Again, stop a point one-third of the length from 

 either end and again set in vibration ; two nodes- 

 and three loops will be formed ; the vibrations will 

 be three times as frequent, and the sound will be 

 the twelfth above the original fundamental. In 

 the same way, any point cutting off one aliquot 

 part of the string may be stopped ; the string will 

 spontaneously form the corresponding number of 

 nodes and loops when set, in any fashion, into 

 vibration. If we suppose the original sound to have 

 been C, on the second ledger line below the bass 

 staff, the various sounds produced by treating the 

 string in this way will respectively be : 



Number of Loops, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 



G c e g ... c' d' e' ... g' 



The unaided ear can distinguish harmonics up to No. 6. 



The notes marked with asterisks are not notes of 

 the natural scale ; 7 and 14 are a flat Bb often to be 

 heard in the sound of chime-bells ; 11 is nearer Fi 

 than Fb ; 13 is nearer to A than it is to Git. Now, 

 in a vibrating string all these vibrations co-exist ; 

 to what degree any one shall be present depends on 

 the way in which, or the point at which, the string 



Notes of the scale of C C 



Notes of any diatonic scale in general... d 

 Ratios 1 



For the modification in these ratios introduced by 

 the system of temperament, see TEMPERAMENT. 

 The standard work on Harmonics is Helmholtz's 

 Sensations of Tone (trans, by Mr Ellis ; 2d ed. 1885). 



Harmonists. See RAPP. 



Harmonium, a musical instrument, for the in- 

 vention of which many claims have been advanced. 

 The arrangement by which the sounds of the 

 harmonium are produced is called the free vibrating 

 reed, supposed to have been a modern discovery, 

 but now ascertained to have been known in China 

 long before it was ever heard of in Europe. Its 

 construction is as follows : A narrow rectangular 

 slit being made in a piece of brass-plate of a quarter 

 of an inch in thickness, a thin elastic spring of the 

 same metal, and of nearly the exact breadth of the 

 slit, is fixed at one end by two small rivets to the 

 surface of the plate, close to one end of the slit, 

 and is so adjusted that it fills the area of the slit, 

 and, when pressed into it at the free end, can 

 pass inwards without touching the end or the sides 

 of the slit, and when left to itself it can return 

 back to its position of covering the slit. The 

 spring at the free end is permanently bent a very 

 little outwards. When a current of air is forced 

 through the slit, the spring is put into vibration, 

 and produces a continuous musical sound, acute or 

 grave, according to the rapidity or slowness of the 

 vibrations. This kind of reed is termed 'free,' in 



is bowed or struck or plucked ; and the quality of 

 the resultant note varies accordingly. From the 

 harmonics the true ratios of the members of the 

 diatonic scale may be found e.g. b' has a fre- 

 quency of vibration 15 times as great as that of 

 Cjj whence Bj has a frequency -V 5 - times as great;: 

 and so for the rest, as follows : 



D E 



G 



A 

 1 



contradistinction to the reed of the organ-pipe, the 

 spring or tongue of which entirely covers an oblong 

 slit, in the side of a brass tube closed at one end, 

 and vibrates against the cheeks or outside of the 

 slit, instead of within it. 



After many attempts, in various countries, to- 

 construct a keyed instrument of really a useful 

 kind with the free reed, Debain of Paris pro- 

 duced his invention (1840) of the harmonium, 

 which became more or less the model of all the 

 others that have followed. The harmonium 

 occupies comparatively little space, being only 

 about 3 feet 3 inches high and 4 feet broad, the 

 depth being according to the number of the stops, 

 usually from 20 to 23 inches. It has a compass 

 of five octaves of keys from C to C, the key -board 

 being placed on the top, immediately below the 

 lid. Under the key-board is the bellows-board, in 

 which are valves for each key ; while above the 

 valves are the different rows of reeds. The sizes 

 of the reeds differ, according to pitch, from about 

 3 inches long to \ inch ; and the quality of sound 

 is affected and modified by the breadth of the 

 vibrating part of the reed, and the shape of the 

 aperture in the bellows-board covered by the valve. 

 The pressure of wind is from a bellows with two 

 feeders, which the player moves alternately with 

 his feet, filling a reservoir, similar to the bellows of 

 a small organ. When a key is pressed down, the 

 valve opens, and the wind, which has access from 



