33a 
M U * 
The chord at It k may either refolve into 11 or mm; 
but that at nn muft firlt refolve into vo, before it can 
pafs into pp. Again, the fundamental bafs of the chord 
at hh is very different from that at nn, although the 
fame in found. See Ex. 8. 
Abrupt modulations are much ufed in recitatives. We 
fliall conclude the fubjedt with a beautiful inftance from 
the oratorio of the Meffiali. See Ex. 9. Here the abrupt 
modulation takes place by changing the minor third in 
the chord at qq into a new bafs note at rr. 
We may obferve in general, that no flats or {harps are 
placed at the clef in recitative; thefe are all regarded as 
accidental; nor is Italian recitative ever confined to any 
one key. Every note has its fignature. 
OF COUNTERPOINT. 
The term counterpoint originated in the ancient manner 
of writing notes as mere points, or large dots ; where it 
denoted “ point againft point,” or one part to another. 
This latter lignification it ftill has in modern harmony, 
where “ writing a counterpoint” denotes the harmo- 
niling of a fmgle part, by letting one or more parts to it. 
The part to be harmoniled is called the J'ubjeft, or princi¬ 
pal melody; and the parts fet to it are the counterpoint. 
But in general the fubjedl and counterpoint are under- 
Itood coiledtively, when counterpoint is fpoken of, with¬ 
out diftinguifliing them. And, as a fubjedl harmoniled 
produces a compofition in parts, or a harmony; fo the 
term counterpoint, in a more general fenfe, denotes mufic 
in parts, or mufic in full harmony. 
According to the above definitions, harmony or coun¬ 
terpoint may be fet either with regard merely to its fimple 
eorredtnefs, without the objedt of rendering the parts in¬ 
vertible ; or for the double purpofe of rendering the 
parts invertible, as w'ell as corredt. The former is called 
fimple counterpoint; the latter, double counterpoint. 
Of Simple Counterpoint. 
Simple counterpoint may be divided into plain and figu- 
trutive. Both forts may confift of harmonies of any num¬ 
ber of parts; and in any of their forms, the principal me¬ 
lody may be in the higheft, loweft, ormiddle, part, when 
there are more than two parts. 
It will be ufeful to obferve, that what is meant by JiriEl 
harmony, or counterpoint, is a compofition which confills 
of nothing but effential chords and their fyncopation ; 
and/ree harmony, is that in which the diatonic and.chro¬ 
matic means are introduced among the effential notes. 
Plain fimple counterpoint confifts of notes of the fame 
length. On Plate IX. Ex. 1. is a melody as higheft part, 
to which a bafs and two middle parts are to be fet. At 
Ex. 2. the melody is in the bafs; and at Ex. 3. in a mid¬ 
dle part. 
Figurative fimple counterpoint allows notes of different 
durations, both in the fame part and in different parts of 
the harmony ; as in Ex. 4. 
Of Double Counterpoint. 
Double counterpoint denotes a compofition calculated 
for inverfion ; and though, with particular regard to the 
number of invertible parts, there are not only double, 
but alfo treble, quadruple, and greater, counterpoints, 
every poffible inverfion of them muft be as regular as 
double counterpoint with any of the invertible parts; 
for qll depends on the knowledge of conftrudting any tw'o 
parts of a harmony, fo that the lower may be fet over the 
higher, or the contrary. The dodtrine of double coun¬ 
terpoint is one of the moft important branches of har¬ 
mony ; for it fhows how different harmonies can be pro¬ 
duced with the fame parts on melodies, or how aftridter 
unity can be combined with moft interefting varieties, 
than by mere fimple counterpoint. And thefe varieties 
confift either in different ftates of-the fame fundamental 
harmony, as in the counterpoint of the odlave, or in dilie- 
.4 
5 I C. 
rent fundamental harmonies, as in all the other counter¬ 
points, or alfo in the intermixture of both parts. 
Double counterpoint is to be confidered ; firftly, with 
regard to the interval in which the inverfion fliall take 
place; fecondly, with regard to the number of invertible 
and other parts; and, thirdly, with regard to the fort of 
motion in which the inverfion fliall be introduced. 
1. A counterpoint may be calculated for an inverfion 
in one interval only ; or in two or more'difterent intervals. 
And it is called according to its refpedtive interval ; viz. 
a counterpoint of the odlave, ninth, tenth, and fo forth. 
But the intervals that exceed a feventh are nothing more 
than odlaves of fmaller intervals, as in fimple counter¬ 
point. Thus, the ninth is a higher fecond, the tenth a 
higher third, &c. A counterpoint of the odlave, there¬ 
fore, admits of an inverfion in the odlave of the ffime in¬ 
terval ; one'of the twelfth, an inverfion in the odlave of 
the fifth, and fo forth ; and the double odlave may be 
ufed inftead of the fimple odlave where occafion permits. 
The general rules in double counterpoint are as fol¬ 
low : 1. The two parts muft be calculated fo that every 
interval is treated regularly, both before and after the in¬ 
verfion ; and then it is the fame thing, whether the in¬ 
verfion is produced by carrying the lower part over the 
higher, or the contrary. 2. The two parts muft not 
crofs each other before the inverfion, nor contain any in¬ 
terval greater than that in which the inverfion is to take 
place. 
Double Counterpoint of the Qclave. 
This confifts of two parts calculated to be inverted, by- 
carrying either of them hn odlave or double odlave towards 
the other. The rules of i t depend on the change of in¬ 
tervals which the inverfion produces, according to the 
following table : 
Intervals before the inverfion 1 2 3 4 5 .6 7 
Their inverfion in the odlave 8 7 6 5 4 3 2 
Here it appears, that, by this inverfion, the unifon pro¬ 
duces an odlave ; the fecond a feventh, the third a fixth 
and fo forth. A counterpoint of the odlave, therefore 5 
admits of any fundamental or inverted, effential or acci¬ 
dental, interval, that is treated regularly before the in¬ 
verfion, except confecutive perfedl fourths; becaufe in 
the inverfion they produce difallowed fifths. Neither 
ought ninths to be taken, becaufe they cannot be in¬ 
verted. At <?, Ex. 5. is a fhort fubjecl in the higher, and 
its counterpoint in the lower, part; at b is an inverfion 
.of it in the odlave; and at c an inverfion in the double 
octave ; d is another example of inverfion in the odlave. 
Of Double Counterpoint of other Intervals bejules the Odave . 
Thefe counterpoints may be divided into two claffes j 
viz. principal and derivative. The former are thofe of the 
three fundamental intervals befides the odlave; viz; the 
twelfth, tenth, and fourteenth. And the latter are thofe 
which arife from the inverfion of the three former ones 
in the odlave; viz. the eleventh, thirteenth, and ninth. 
Both forts rank in the order in w-hich they are here placed ; 
for an inverfion in the tw-elfth, as odlave of the fifth, 
leaves the tranfpofed melody major or minor as before, 
and confequently neareft related to its previous ftate; but 
an inverfion in the tenth, as odlave of the third, changes 
the tranfpofed melody from major to minor, or the con¬ 
trary, which renders it lefs related to its previous ftate 
than the former inverfion.; and that in the fourteenth, 
or odlave of the feventh, is llill lefs related to its previous 
ftate, becaufe it renders every interval diffonant to its 
former ftate; and the fame it is with the counterpoints of 
the eleventh, thirteenth, and ninth. 
The general rules are as follows: 1. It produces the 
fame change of intervals, whether the higher part is car¬ 
ried into its refpedtive interval over the lower, or the lower 
part over the higher; or alfo when the one part is carried 
but into its refpedtive fimple interval, and-the other part 
an 
