HAR 



HAR 



ahd the other notes of the octave' with Hie 

 seven prismatic colours ; so that glasses 

 of the same colour (the white excepted) 

 are always octaves to each other.' When 

 the glasses are tuned, they are to be fixed 

 on a round spindle of hard iron, an inch 

 in diameter at the thickest end, and ta- 

 pering to n quarter of an inch at the small- 

 est. For this purpose the neck of each 

 glass is fitted with a cork, projecting a lit- 

 tle without the neck : these corks are per- 

 fbraied with holes of different diameters, 

 according to the dimension of the spindle 

 in that part of it where they are to be fix- 

 ed. The glasses are all placed within one 

 another; the* largest on the biggest, end 

 of the spindle, with the neck outwards ; 

 the next in size is put into the other, leav- 

 ing about an inch of its brim above the 

 brim of the first; and the others are put 

 on in the same order. From these ex- 

 posed parts of each glass the tone is 

 drawn, by laying a finger upon one of 

 them as the spindle and glasses turn 

 round. The spindle, thus prepared, is fix- 

 ed horizontally in the middle of a box, 

 and made to turn on brass gudgeons at 

 each end. A square shank comes from 

 its thickest end through the box, on which 

 shank a wheel is fixed by a screw : this 

 will serve, like a fly, to make the motion 

 equable, when the spindle is turned by 

 the foot like a spinning- wheel. The wheel 

 is eighteen inches in diameter, and con- 

 ceals near its circumference about twen- 

 ty-five pounds of lead, and may be made 

 of mahogany. An ivory pin is fixed in the 

 face of the wheel, about four inches from 

 the axis ; over which is put the loop of 

 the string that comes up from the move- 

 able step to give it motion. The box is 

 about three feet long, eleven inches wide 

 at the biggest end, and five inches at the 

 smallest end ; it is made with a lid, which 

 opens at the middle of its height, and 

 turns up by back-hinges. The instrument, 

 thus completed, stands on a neat frame 

 with four legs. This instrument is played 

 upon by sitting before it, as before the 

 kevsofa harpsichord, turning the spin- 

 dle with the foot, and wetting the glasses, 

 now and then, with a sponge and clean 

 water. The fingers should be first soak- 

 ed in water; and rubbed occasionally 

 with fine chalk, to make them catch the 

 glass, and bring out the tone more rea- 

 dily. Different parts may be played to- 

 gether by using both hands; and the 

 tones are best drawn out when the glasses 

 turn from the ends of the fingers, not 

 when they turn to them. The advantages 

 of this instrument, says Dr. Franklin, are, 

 that its tones are incomparably sweet be- 



yond those of any other ; and that they 

 may be swelled and softened at pleasure 

 by stronger or weaker pressures of the 

 finger ; and continued to any length : and, 

 when it is once well tuned, it never again 

 wants tuning. Franklin's Letters, &c. 



HARMONICAS arithmetic, that part of 

 arithmetic which considers musical inter- 

 vals, expressed by numbers, in order to 

 our finding their mutual relations, com- 

 positions, and resolutions. 



HAR.HONICAL composition, in a general 

 sense, includes both harmony and melody. 

 i. e. of music or songs, both in a single 

 part, and in several parts. In its more 

 proper and limited sense, harmonical 

 composition is restrained to that of har- 

 mony ; and may be defined the art of 

 disposing and concerting several single 

 parts together, so as to make one agree- 

 able whole. 



HARMOMCAL interval, in music, denotes 

 the difference of two sounds, which is 

 agreeable to the ear, whether in conso- 

 nance or succession ; and are, therefore, 

 the same with concord. 



HARMONICAL proportion or musical pro- 

 portion,is that in which the first term is to 

 the third, as the difference of the first 

 and second is to the difference of the se- 

 cond and third; or when the first, the 

 third, and the said two differences, are in 

 geometrical proportion. Or, four terms 

 are in harmonical proportion, when the 

 first is. to the fourth as the difference of 

 the first and second is to the difference of 

 the third and fourth. Thus 2, 3, 6, are in 

 harmonical proportion, because 2 : 6 :: 1 : 

 3. And the four terms, 9, 12, 16, 24, 

 are in harmonical proportion, because 9 

 24:: 3: 8. If the proportional terms be 

 continued in the former case, they will 

 form an harmonical progression, or series. 

 1. The reciprocals of an arithmetical 

 progression are in harmonical progres- 

 sion : and, conversely, the reciprocals of 

 harmonicals are arithmeticals. Thus, the 

 reciprocals of the harmonicals 2, 3, 6, are 



-, ^, , which are arithmeticals ; for - 



^,=g,and - g = - also : and the reci- 

 procals of the arithmeticals 1, 2, 3, 4, &c. 

 are - , g'J'T* &c - which are harmonicals ; 

 f 1 1 1 11 1 



1 : 3 " I "~ 2 : 2 ~~ 3' S n * ' 



in general, the reciprocals of the arith- 

 meticals a, a-4-d, a+2 d, a-4-3 d, &c. viz. 



& c - are harmom- 



cals ; et e contra. 2. If three or four nunr- 



