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upon it with a diamond, they are to be 
tuned by diminishing the thickness of those 
that are too sharp, which is done by grind- 
ing them round from the neck towards the 
brim ; comparing, by means of a well- 
timed harpsichord, the tone drawn from the 
glass by your finger with the note you want, 
as sounded by the corresponding string 
of the harpsichord. The largest glass in 
the instrument is G, a little below the reach 
ef a common voice, and the highest G, in- 
cluding three complete octaves ; and they 
are distinguished by painting the apparent 
parts of the glasses within side, every semi- 
tone white, and the other notes of the oc- 
tave with the 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 a quarter of an inch at the small- 
est. For this purpose the neck of each 
glass is fitted with a cork, projecting a little 
without the neck : these corks are perfora- 
ted with holes of different diameters, ac- 
cording to the dimension of the spindle in 
that part of it where they are to be fixed. 
The glasses are all placed within one an- 
other; the largest on the biggest end of 
the spindle, with the neck outwards ; the 
next in size is put into the other, leaving 
about an inch of its brim above the brim 
of the first; and the others are put on in the 
same order. From these exposed 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 fixed horizontally in the middle of a box, 
and made to turn on brass gudgeons at each 
end. A square shank comes from its thick- 
est 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 eigh- 
teen inches in diameter, and conceals near 
its circumference about twenty-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 moveable step to give 
it motion. The box is about three feet 
long, eleven inches wide at the Jfiggest 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 
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a neat frame with four legs. This instru- 
ment is played upon by sitting before it, as 
before the keys of a harpsichord, turning the 
spindle with the foot, and wetting the glasses, 
now and then, with a sponge and clean 
water. The fingers should be first soaked 
in water ; and rubbed occasionally with 
fine chalk, to make them catch the glass, 
and bring out the tone more readily. Dif- 
ferent parts may be played together 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 beyond 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. Frank- 
lin’s Letters, &c. 
Harmonical arithmetic, that part of 
arithmetic which considers musical inter- 
vals, expressed by numbers, in order to our 
finding their mutual relations, compositions, 
and resolutions. 
Harmonical composition, in a general 
sense, includes both harmony and melody, 
1. 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 harmony ; and may- 
be defined the art of disposing and concert- 
ing several single parts together, so as to 
make one agreeable whole. 
Harmonical interval, in music, denotes 
the difference of two sounds, which is agree- 
able to the ear, whether in consonance 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 second 
and third ; or when the first, the third, and 
the said two differences, are in geometrical 
proportion. Or, four terms are in harmoni- 
cal 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, be- 
cause 2 : 6 :: 1 : 3. And the four terms 9, 
12, 16, 24 are in harmonical proportion, be- 
cause 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 arithme- 
tical progression are in harmonical progres 
