a Ne 8 ee ee ee ee orga Ss 
HARMONICS, 
ics, is also heard whenever the Beas of an imperfect or tem- 
ed concord (see that article) exceed 12 or 13 in a se~ 
Y ee dra a fell pana Cg Sauveur 
Ww. 
considered the reinforcement of sound must 
riodically take place, while we hear a musduaenen. of 
two musical sounds whose ratios are in small num 
3 and, as Dr Robert Smith has observed, impro- 
perly confounded these, which are grave harmonic 
sounds, (because rarely occurring so seldom as 12 times 
in a second,) with the beats (of imperfect concords) pro- 
perly so called, which can be separately heard, and dis- 
tinctly counted, in every instance where the of 
— or imperfection is sufficient] R 
tt the year 1754, M. Rameau and M. Tartini first 
made observations on the coincident of conso- 
3 that is, the 
supposed ; errors which few will wonder at, who have 
experienced the difficulty of avoiding errors of an oc- 
tave, or sometimes more than one, in estimating sounds, 
that are either very high or very low. 
- In 1807, Mr John Holder published a work on mu- 
sic, in which he attempted to build a deal of the 
theory of composition and harmonical effect on these 
grave harmonic sounds, accompanying consonances 4s 
ir “ dependants ;” but most of his speculations have 
failed, and many of them led to very absurd conclusions, 
ong to his having set up and used a defective or false 
rule, for assigning the grave harmonic of a given conso- 
nance. 
It is the more necessary, therefore, to give here a 
true rule for the finding the grave harmonic of any given 
consonance, viz. Find the vibrations made by each of the 
sounds of the given consonance in one second, divide 
these successively by the reversed terms of the given 
ratio of the consonance, and the quotient (in each case) 
will give the vibrations fer 1” of the grave harmonic ; 
the ratio of which vibrations, to the vibrations of ei- 
ther of the given sounds respectively, will give the in- 
terval of the harmonic below such given sound. 
If, for example, the major second CD were given in 
the middle of the scale, where the ratio is £, and the 
sound of the lowest note (on the tenor cliff line) makes 
240 vibrations per 1”, then 2% 240=270 is the vibra- 
tions of D, and *3°=30, or *4°=80, the vibrations of 
the harmonic note ; and its interval below the lower note 
Cis 33=4, or 3 VIII; and below the upper note D 
is 324, = 3VIII+II. The principal intervals of the 
scale, and some others, calculated as above, have their 
grave harmonics shewn in the following Table, viz. - 
3} VIII 40 20 4 1. 4 VIN 
% Vil 450 30 3% XXH j XXVIII 
$ 7 492 48 $ XVII % XXII 
fy 7 426: 962 % XXIII 3, XXIX 
+ VI.40 80 % XI XVII 
% 6 Sas 48 £ XVIE 4 XXII 
$V. 360-120 4 VIL °+ XU 
* No limits have yet been assigned to this harmonic or concordant series ; found by adding seven, fourteen 
. der’s defective rule for 
641 
} 4 39 80 x xv 
Ill 300 = 60 f XV XVII 
$3 288 48 4 XVII XIX 
fi 8 284 «88 XXXIV ¥ XXXVI 
It #70 90 4 XXIE XXII 
¢ «IE 266; 265 § XXII f, XXIV 
.ry XXVIIL ¥, XXIX 
$4 Merve 
The Jirst column of the above Table, shews the ratios 
of the given consonances ; the second, the intervals ex. 
pressed in numerals ; the third, the vibrations per second 
es ac, Be lower part to be the note on the tenor- 
cliff line of the stave ; the fourth column contains the 
calculated vibrations of the harmonic note ; column 
shews the ratio, and column siz the interval of this har- 
monic, below the lowest of the given notes or C; and 
columns seven and eight shew the same things with re- 
gard to the highest of the given notes. 
For the sake of more ready comparison with Mr Hol- 
i grave harmonics, the 
errors of which it seemed of some importance to place 
in as clear a view as possible, we have given above a far 
less simple rule for obtaining the ratios of the new 
sounds, with relation to either of their , thar 
the one which we are now about to add, viz. The ratio 
of any given consonance above a bass or fundamental 
note, being +, a being the least term of the ratio; 
then + is the ratio of the grave harmonic below the 
bass note, and + the ratio of the same harmonic below 
the upper note of the consonance ; which is too evi- 
dent, from an inspection of the above Table, to need a 
particular example. 2 
With regard to the other kind of grave harmonics, the 
results of tempered concords, which beat too fast to be 
separately counted or perceived: If, for instance, we 
were to consider the grave minor third 3} in the above 
Table to be a tempered concord, we should have, by our 
fourth method in the article Brats, 240 x 6 — 2845 x 5 
= 1440—14223=173, the beats per second, or vibrations 
of this grave harmonic, being just double, or an octave 
higher than those in the Table above, and so of others ; 
but our limits will not admit of our enlarging further 
on this subject. (¢) 
HARMONICA. See Mustcat Grasses. 
HARMONY, in Music, is a term which appears to 
have completely changed its signification since the first 
use of it. The ancient Greek writers, who seem to 
have contemplated only the succession of sounds which 
we call Metopy, (see that article,) attached to such 
successions as were pleasing and ble to the ear, 
the name of a woman celebrated among them. But in 
more modern times, when the simultaneous as well as 
the progressive effects of sounds on the ear came to be 
practised and considered by writers on this subject, the 
term melody was applied to successions of sounds, 
ticularly to such successions as are on the whole 
sing, and the term harmony was transferred to the 
newly contemplated and pleasing effects of certain in- 
tervals, when their limiting sounds are heard together, 
viz. 1, 3, 111,4,V,6, VE; vill, 10, X, 11, XII, 18, X11; 
XV, 17, XVII, &c.* whose ratios are }, $4, 4,3, & #5 
» twenty-one, &c. to each 
of the first seven numeral terms ; or by multiplying the terms of the first seven ratios by 4, 4, &c. to produce the ratios of eancorde 
in the successive octaves, 
YOu, X. PART I, 
Au 
