640 
Harmonies, more probable to happen than those of $d, and #th; 
Acute. 
but that theory and probability were not against the 
happening, of even more minute vibrating divisions of 
the whole string, as 4th; 4th, ¢th, gth, &c.: and that in 
the use of the trumpet, horn, and other sounding tubes 
or pipes, all these subdivisions of the whole vibrating 
column of air might be made, separated by nodes or 
points in the axis of the tube in a comparative state of 
yest with regard to these inferior or harmonical vibra- 
tions, although moving to and fro with the velocity 
peculiar to the sound of the whole tube: and he in- 
ferred, with great seeming probability, that the parts 
of bells and most other bodies yielding musical sounds, 
were in the same manner capable of subordinate or 
acute-harmonic vibrations, along with those of their 
principal or gravest sound. 
It was probably not until about the year 1765, after 
the very ingenious Mr James Watt of Birmingham had 
contrived his wheel monochord, that the acute harmo- 
mes of a vibrating string were produced in experiment, 
and.some of them actually rendered visible to the eye ; 
as is xelated by the late Dr Robison, who, several years 
after, rade a more extended and complete set of expe- 
riments on the same instrument which Mr Watt had 
before used ; thereby fully confirming all that D. Ber 
noulli had theoretically advanced. 
Some years after this, Mr John Isaac Hawkins of 
London, the ingenious inventor of the piano-forte with 
spirally coiled strings, and of the claviole, or finger- 
keyed viol, contrived an experiment, which seems to 
leave nothing to wish with regard to this very curious 
and interesting subject. A spirally coiled string, many 
feet in length, was prepared by winding a brass piano- 
forte bass wire closely round a steel wire about the size 
of a crow-quill ,and when removed therefrom, pulling 
it out, so that its spirals became considerably more 
open, comparatively, than those of a common cork- 
screw, or the string was nearly in the state of being 
“ cockled,” as tuners call it, at equal distances, through- 
out its whole length. Along the side of a large wains- 
coated room, this spirally coiled string was stretched, 
over two bridges, near its extremities, and brought to 
such a degree of tension, as not to yield a sound, but 
leave its vibrations, when strongly twitched, plainly vi- 
sible to the eye. The space between the bridges had 
previously beep, carefully divided, on the wainscoat, into 
numerous equal parts, and marked 4; 4,25; 4, (2), 3; 
34 45 b (3), (ads (4) & Sees aod He when the 
whole string was vibrating, a slight obstacle was oppo- 
sed to the vibrations of the string, opposite to any one of 
these divisions, like the edge of the feathers of a quill, 
held to touch it very lightly, or even, if a sudden blast 
of air from the mouth were made on the string, oppo- 
site a division, the string instantly assumed all the sub- 
ordinate vibrations proper to the aliquot division 
against which the obstacle or impulse was directed ; 
and the eye and ear too, in many of the instances, could 
be gratified, by seeing these very compound vibrations 
simultaneously carried on by the whole string, and by 
its several aliquot parts, during several minutes, under 
favourable circumstances, many of the vibrations being 
slow enough to be counted, and their number in a gi- 
ven time ascertained and compared, by which eve: 
point of the theory of D. Bernoulli is in the fullest man- 
net confirmed. 
_ Thus an evident explanation is offered, of all the cu- 
rious harmonic effects, of several unison strings on the 
ALoutaNn Harp, (see that article) when agitated by ir- 
HARMONICS. 
regular gusts of wind : acting momentarily on the whole Hai 
string, and on its different nodes, with sufficient force, 
to excite the determinate vibrations, which the elasticity 
of the string, and its parts, dispose them severally to 
take ; but all of which vibratory motions are so vastly 
quicker than the mere motion of the wind, that we can- 
not agree with Dr Matthew Young in thinking, that 
particular tones are excited, or es up, by that means. 
We have calculated the values of all the aliquot 
of astring or pipe(in Farey’s Notation of Intervals) above 
the note of the whole string, viz. 4, $, 2, &c. as far as 
x, and deducted octaves, so as to bring them all within 
e compass of one octave ; and the same when arran- 
ged under their respective finger-key intervals, stand 
as follows, viz. 
4, 4, 4, . ‘] * > 
tit {2 een = 28.11748 5 —2m 
VIL ieee Ss 
mth {r= 4 VIII 4 7th* 4+ 6.124495 + mm 
Xe ap + ss Tth 24,9472 5— im 
VI f=Vl,=VIi 454m 
tip wigs + vie VI 22.58107 5-2 m 
6th 4,-=6th—21>—2m : 
Vv r I I z 
Sth). (5th + 9.46026 = +m 
IV§ *F YIV +4 19.46026 = + 2m 
Lewy vv» 4th $ 97.95171 24 2m 
¥ro z7*-° 
4th 3% = 4th — 13.9472 —m 
IED Sindy Abide 
8d Py we es = Bd — 9.270985 —m 
ies 
Od eae SS — 9.468195 
Fakense ts 2 
Wherein the errors or temperaments of all these acute 
harmonic notes are set down; and hence we perceive 
clearly the reason why a sound is accompanied chief- 
ly by its VIIIth, VIII+Vth, and 2 VIII+I[Ird, and 
rarely by any other of its harnionics, viz. because 3 of 
the string is strengthened, or reinforced by four other 
octaves to it: the XIIth (or V) is re-inforced by 
3 other octaves to it, and the XVIIth (or III) by two 
other octaves to it; and these three are the only con= 
cords to the whole string, that are found among its nu- 
merous harmonics. The II and the VII, each with 
the reinforcement of an octave thereto, should, and 
accordingly are, next heard in the order of acute har« 
monics. The harmonic 6th, being a diatonic interval, 
viz. 6—&, whose ratio is 3%, = 3945 4+ 8f+4 34m, 
may perhaps, under very favourable circumstances, 
be heard as an acute harmonic: but when the very 
discordant nature of all the remaining sounds in one 
table, both with the generator and with all of its other 
harmonics, He MPL are considered, it seems very 
plain why these sounds, although momentarily produ- ~ 
ced by a gust of wind, or other impulse, on the proper 
part of the string, almost immediately’ die away, and 
cannot be maintained, as the VIIIth, XIIth, and 
XVIIth may be, and others, in less degrees. ( ¢) 
HARMONICS, Grave. These are lowsounds, ofsmall 
intensity or loudness, which, if attentively observed by 
an experienced ear, will be heard to accompany every 
accurate or perfect consonance of two sounds, whose ra~ 
tio is expressible in small numbers, whether the same 
may be composed of the Diatonic primes 1, 2, 3, and 
5, or of somewhat “or prime numbers. : 
A grave harmonic of a different species from the above 
* The ratio of this minor seventh being ¢, = 519 E ++ 10f + 45m. 
