HAR 
or hinciteds and every addition of them -in pairs isthe fame 
as 3d + lt = ¥ = fifth + 4th = 6th, the minor 
fixth; and Ill + ile the 
Haxsonic Date he ancien 
to the mar conmonly ftyled the Enharmonic Ginus. 
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ocean, &c. ae 
ber ¥ fhort oda a woo the fame breadth and thick. 
nefs, but of different i a fliding eafily fide by fide in a 
ry a thumb-fcrew at 
tice eee ae peers 
undulating aioe like the figure of fines almoft. num- 
ber of folid pieces of wood are wrought on the top into 
planes, having fimilar undulating curves ? 
« the phe- 
™M 
bie'ea i in Mr. Farey’s Notation to 50.4 
t+f+4 but a trifle lefs than the half-tone o "the 
equal oR feale, and therefore as ill adapted to re- 
ts eee gave this ot 
See 
HAR 
‘In its more proper and Bios desley harmonical compofi- 
tion is reftrained to that of h Jn which fentfe it 
may be defined, the art of dilpoling eid concerting feveral 
fingle parts Lopetnet, in fuch manner as to make one agrec- 
a < whole, 
The art 4 harmony has been long known under the name 
of counterpoint. 
At the time when parts were firft introduced, mufic ey 
then very rip Dee were no ener notes of time ; a 
the parts were very note made c 
This they Sec coe fi imple, or oF ies counterpoint, to 
eye ps it from another kind; then introduced, wherein 
notes of different value were ed IR and difcords brought 
etween the parts. 
This they called figurative counterpoint. 
ARMONICAL Curve, a curve, the nature of which will be 
underitood from its conftruction. et late 1X. Ana- 
, lyfis, Sg: 4.) be the common centre of any two circles zs 
EG; and CDE, CFG, any two femidiameters, and of 
either of Pa eluded arcs, as D e the fine, i in 
which, produced both ways, let the lines HI and X be 
a equal to the other are 4 ; then, while iad femi- 
diameter G moves round the i with 
it the line IF HK, ae to itfelf, and contantly equal 
to twice the arc E the Pare I | deferibe ‘ 
curve, whofe vertex is 'D and axis DC, da ote. bafe 
ACB is equal to the pis caluletei nce of the circle E G. 
5: 
Cor..t.—Drawin ( fig. §-) perpendicular to the bafe 
ACL,a re é P, EECA bs to the curve at K, 
parallel to E 
For dewig K KNp Rerpeataues tos to the ley let the radius. 
CFG go forwards a little into the plac f gy -and. carr 
the line K H FI into the place afi cutting K N in 
and FLinr. Then fincee HK = y the déhaition, 
and alfo. 44 = we 
Eg, their difference vy D = Gg. No 
by the fimilar triangles CLT and Fr Le crs 
CGzg, OKéan eeeee we have CL: CF :x 
eT 6 Be ae Gog, and ex aqua CL :C 
: (Fr: Gg >: :O8: :) NP:NK; Siikebettlp 
‘ise right-angled Wan sles CLE, NP K are equian . 
and the perpendicu PMis parallel to. the line 
Cor. ¥ ar any pokes K the radius of curvature K M: 2 
ie: : KN x CE. 
FL,. atic line : M, perpendicular 
be parallel to E/ (by Cor. a} $ uently, if the arc 
K£ be infinitely diminifhed, e Sot ‘the coinciding per- 
culars K M, 4 M will be sis radias of the curvature at 
prefent an imperfeét wni/on, as the figure alluded to is to convey 
ith aN or, indeed, that of any other confo- veal LEs and KMé4, CEL or CE/ and « 
3 e€ are Caz what furprifed,that Mr. John Gough, ultimately Soe yee Now KN or FL: LC: fr: 
a fo ge wel 2 and fuccefsfully combated the doctor’s theory, 7 rF or KO, an 2 #5, 5 : 1 E::PN: PK: KO: Ké; 
hich this is a branch, in this and the preceding volume of and, ex equa, N: LE:: fr: Kd. on ny a L. ts 
Me Nichofon Sean did not animadvert on io hatte ex- a : i lor if % OL componendo, :LE 
of the har s(sL: 
ers. aurea ce aed Cor. 3.—Hence if the fatio of the se Kv cE EG,, thd 
ear ICAL, b toh harmonical be very great, the curvature “ “34 point K will be extremely 
divifions of onrcar c - ford, harmonica ; acigice Tae sia “fmall, Eas its radius KM: CE::CE:KN very. nearly ; 
cal becaufe the lines L FE. and - Et will be very nearly equal. 
canon, &c. 
Mises. Mivhnetic, is se much of the theory 
4o&rine of numbers as relates to making the ie ss mer 
reductions, &c. of mufical sepa which are exprefled by 
Bumbers, in order to, our og Sei ores utual relations, com- 
Harmonicat, C. sila.” in its fenfe, includes 
the compofition both of h and melody ; 
$ i. e. of mulic, 
w ngs both in ingle part and inf parts, 
- Dos he rd. 9 Agi fuppofition the very {mall curva-. 
K are very ag Ne the ratio.of their 
ot bse og 
e curvature at K, being 
sails cds 1 Nn is rel as = KN (by Cor. 3+) 
mA 5.— While the g ti re aay 
fler be diminithed, an corel 
or 
aie water Ri ri of the fame pecs d every ordinate 
