HAR 
- © Panmonicat Interval. See INTERVAL. 
’ ‘Harmonicat Proportion. See Harmonical Proportion. 
HARMONICAL Series, is a {eries of many numbers in con- 
tinual harmonical proportion. 
_ Jf there be four or more numbers, whereof every three 
immediate terms are harmonical, the whole makes an har- 
monical feries, of continual harmonical proportionals ; as, 30: 
20:15: 12310. . 
Or if every four immediately next each other are harmoni- 
cal, it is alfo a continual harmonical feries, but of another 
fpecies ; a8, 3, 4, 6 
» 9» 18, 36, &e. 
Harmonica Sounds, or Sons Harmonigues. See Son 
and Sounp. - : 
HARMONICS. All the concomitant or acceflary 
founds, which, on the principle of refonance, accompany 
every fingle found, and render it perceptible, are thus called. 
thus all the aliquot parts of a ftring produce harmo 
nics. This fubftantive is mafculine when found is under- 
ftood; and feminine when the word chord, or ftring, is in 
in. See Nore-Fiutee. The 
effects of different tunings, beats of unifons and octaves on 
the violin, all the itrings itruck at once on. the guitar, and 
monoc tuned and divided harmonically, feem a unifon, 
like a fingle key on the full organ. 
he term Harmonics generally implies the theory of found; 
the divifion of the monochord into harmonic intervals, by 
men{uration, or ratios, including concords, difcords, and tem- _ 
the founds generated bya fingle grave tone, either of a great 
Small b 
cal foundsin our fyftem of harmony. 
HAR 
or minor 3d to 
» when w 
Mathematicians exprefs thefe proportions by 
: acute 1, 2,35 to 325 t Braver iris ge dr go b- 
y thefe figures are expreffed, not only the feveral 
divifions of the ftring, or monochord into harmonical pro- 
ortions, but the proportional number of vibrations which 
each of thefe feveral confonances makes, compared with the 
If we produce a deep tone from a great bell, or the 4th 
ftring of a violoncello, we hear, befides the principal found 
and its o€tave, two other very acute founds, one of which is 
the 12th above the principal, or o€tave of the sth, and the 
other the major 17th, or double oétave of the fharp 3d. 
The principal found is called the generator, and the two 
other founds which it engenders, its harmonics, including 
the odtave. See GENERATOR. 
Harmonics. 
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wasnt ee 
Le - a fa 
se -6- -#-4¢- -- 
ie eh roar able 
CT ® a) i) 
a 
Another, and perhaps a clearer way of fhewing how a 
ring divides itfelf mto its harmonics, is by reprefenting the 
‘whole ftring, and indicating the proportions ‘which produce 
them. wae 
= 1 12 Ll } 
7 
Divide a ftring into half, and it will produce two o¢taves 
of the whole, _ | 
_Diwide it into three parts, and it will produce three 12ths 
of the whole, or three sths of the octave. — 
~ Divide it into four ‘parts, and each will be a double o€tave, 
% t5th of the whole. 
Divide it into. five parts, and each will be a fierce to the 
t5th, ora major 47th to the whole. 
fyftem of ke Bafe Fondamen- 
ct 
WwW Pp 
s*B.F 
es by a kind. of “und ai 
into ““ Demonftration 
three, and the other into five equal parts 5 ‘ehiatiac fwd 
this conclufion, that thefe vibrating filent ftrings pointed 
@Alembert feemed fatisfied with this origin of 
Though : 
the minor mode, when he publifhed the firit edition: of his 
nents,”” mathematicians were offended at the author, 
Elements,” 
Rameau, qualifying a tract 
du Principe de ? Harmonie,’” 
1 xy i 
“6 
: in explanation. of his fyftem 
de and the great 
