33S 
MUSI C. 
both parts at once, it is neceflary to avoid the fecond, 
fourth, and fixth, as eflential intervals; to ufe no long 
accidental intervals ; and to avoid the equal motion 
throughout. But if both parts be doubled in thirds, not 
only before, but alfo after, their inverlion, the following 
rules mud be attended to. 
Rule I. II no other intervals are ufed as eflential than 
the third, fifth, and oCtave, the thirds may be ufed, firft 
before the inverlion of the counterpoint, and fecondly 
after its two inverfions in the twelfth. 
Rule II If no other eflential intervals are ufed than 
the third and fifth, the thirds in queftion may be ufed, 
firfl- before the inverlion, and fecondly after the two in¬ 
verfions in the fourteenth, as well as after thofe in the 
twelfth. 
Rule III. In all the cafes under the two preceding- 
rules, the thirds are added below the higher and above 
the lower part. But, though no long accidental notes 
ought to be ufed, any Ihort eflential or accidental note 
may be fet in a gradual progreffion to and from the al¬ 
lowed principal notes ; and the equal motion mull: be 
avoided as before. 
Rule IV. If both parts Ihould be doubled In thirds after 
their two inverfions in the tenth, the thirds mull be fet 
either over both parts or under both. But this produces 
no other variety than doubling the parts in the former 
manner after their two inverfions in the twelfth. 
The varieties of harmony and inverlion which can be 
produced by the doubling of a counterpoint in the de- 
feribed manner are as follows : When one part is doubled 
in thirds, it produces a triple counterpoint of the oClave ; 
and, when both parts are doubled, it produces a qua¬ 
druple counterpoint of the oCtave. Each fort may be in¬ 
verted in the octave as often as the order of its parts one 
over the other can be changed, as expreffed in the fol¬ 
lowing tables. 
A triple counterpoint admits of five inverfions in the 
oClave ; as follows: 
11 2 a 3 3 
23 13 12 
32 31 21 
A quadruple counterpoint admits of twenty-three in¬ 
verfions in the oCtave ; as follows : 
1 1 1 1 1 1 
'223344 
344223 
432432 
2 2 2 2 2 2 
I I 3 3 4 4 
3 4 I 4 I 3 
4 3 4 i 3 I 
3 3 3 3 3 3 
1 12244 
24141a 
4 2 4 1 z 1 
444444 
1 1 2 2 2 3 
2 3 1 3 1 2 
3 2 3 1 2 1 
In both the above tables, the firft rank of figures fhows 
the three or four original parts, and the other ranks their 
inverfions. Ex. 10. a, exhibits a counterpoint that is in¬ 
vertible in the twelfth and tenth ; at b, thirds are fet 
under the original part; at c, thirds over the original 
lower part; and, at d, both at once. 
When a counterpoint that has been inverted in the 
ninth or eleventh is to be rendered triple or quadruple, 
the thirds rnuft be added on the oppofite fide; that is to 
fay, above the higher and below the lower part; and in 
the inverfion in the thirteenth they mull be added in the 
fame manner as in that in the tenth. 
3. The inverfions of counterpoints may be calculated 
for a reverie, a retrograde, and a reverfe-retrograde, mo¬ 
tion. A reverfe motion is that in which every afeending 
interval becomes defeending, or the contrary. A retro¬ 
grade motion, that which introduces a melody backwards 
without reverfing it. And a reverfe-retrograde motion , 
that which introduces a melody both backwards and re- 
verfed. 
The firft, or reverfe motion, is very ufeful, becaufe it 
produces a fine variety of the harmony and progreffion 
without lofing fight of the fubjeCt. But the two latter 
motions are conlidered as a matter of curiofity rather 
than of utility in practice ; becaufe it is very difficult to 
trace the fubjeCl in retrograde or reverfe-retrograde mo¬ 
tion, except it be very Ihort. 
The rules for counterpoint reverfed are as follows; 
1. Any counterpoint of the oCtave, tenth, twelfth, or four¬ 
teenth, may be reverfed before as well as after all its re- 
fpective inverfions, if it contains no difeord, except in a 
tranfient gradual progreffion to and from the concords 
allowed in it. And, if it is calculated to be doubled in 
thirds, it may alfo be reverfed with thofe thirds. 2. The 
reverfion mull be made in both parts according to the 
fame fixed nott, and not according to the different notes 
with which the two parts of a counterpoint may begin. 
At Ex. 11. a, the key-note, as a fixed note, is exp relied 
by a large dot. The figures Ihow the different intervals ; 
figure 1 denotes the unifon, 3 the 3d, See. At b, fee the 
fame reverfed. At c, the fecond of the fcaie is marked by the 
large dot, as a fixed note ; and at d, the fame is reverfed. 
Of RHYTHM. Plate X. 
Mufic may be confidered as confifting of three com¬ 
ponent parts; melody, harmony, and rhythm. Rhythm 
is an agreeable fuccelfion of founds confidered with re- 
fpeCt to the time of their whole duration. Melody 
is an agreeable fuccelfion in refpeCt to the pitch, or the 
frequency of vibrations of each found. Harmony is 
an agreeable combination of feveral founds at the fame 
time. It is evident that rhythm and melody are al- 
moft infeparable; but that "harmony is by no means 
necelfary to the exiftence of mufic. In the firft place, 
it is eafy to conceive that a love of rhythm, or of the 
periodical recurrence of the fame or fimilar fenfations 
at equal intervals of time, may be derived from the habit 
of a certain equality and recurrence in the motions of the 
body, fuch as walking, or, in children who cannot yet 
walk, from the palfive motion of geftation; this predi¬ 
lection for the return of cuftomary fenfations appears to 
be an innate and fundamental tendency of the human 
fyftem, to which phyfiologifts and metaphyficians have 
been obliged ultimately to refer many properties, both of 
body and mind. But be this as it may, the love of rhythm, 
which is perhaps the lowell ingredient in mulical tafte, 
is, in modern times, Hill more univerfal than the love 
of harmony and melody. Poetry, or rather metrical 
compofition, is diftinguilhed from profe only by the regu¬ 
larity of its rhythm; and the knowledge of metre and 
profody, however high it may rank in the critic’s eftima- 
tion, is a fubordinate and comparatively infignificant 
branch of mulical firience. The natural fondnefs for 
rhythm is the principal foundation of the pleafure of 
dancing, an amufement intimately connected with mufic, 
and no lefs popular. The rhythm of a mulical compofi¬ 
tion is almoll always at leaft two-fold, often three or four 
fold, confifting of fubordinate divifions or bars, and pe¬ 
riodical returns of larger members, either phrafes or 
ft rains, containing equal numbers of thofe divifions. All 
this is perfectly natural, but perhaps not fo necelfary to 
mufic as Mr. Walter Young, in his excellent ellay, printed 
in the Edinburgh TranfaCtions, appears to imagine; for 
thofe who are already experienced muficians are generally 
obferved to delight in recitative, where the rhythm is 
almoll entirely loll; and Hill more in fugues, where two 
or three feries of rhythms, almoll independent of each 
other, are carried on at the fame time, one part beginning 
its fubdivifions when another has made fbme progrefs, 
and a third is Hill to follow. But the pleafure derived 
from fuch compofitions is, as Kirnberger has obferved, 
more intelleClual than fenfual, arifing in a great meafure 
from the confcioufnefs of being able to comprehend that 
which is “caviare to the general.” Rhythm is generally- 
marked in performance by a flight increafe offeree at the 
beginning of each fubdivilion or bar; lometimes, and in 
fome inftruments always, the change of founds, in point 
of acutenefs and gravity, or the interruption of the fame 
found, is a fufficient diftinClion ; and lometimes, after the 
rhythm has already been firmly imprefled on the mind, 
neither change of found nor of ftrength is perpetually re¬ 
peated, the imagination alone being fufficient to conceive 
the continuation of rhythm 1 but this conftitutes a kind 
of 
