M U S I C. 
The table at the bottom of the preceding Plate, 
marked Ex. 10. contains an exabl meafurement of all the 
didances of founds in the natural and extended fcale ; 
and alfo lliows the method of exprefling the fame by the 
above figures. 
Of THOROUGH BASS and COMPOSITION. 
Intervals may be divided into Concords and Difcords. 
Concords are 
The perfect Prime ancl its Replicates the perfebt Obtave. 
The perfect Fifth-the perfect Fourth. 
The major Third--- the minor Sixth. 
The minor Third - -- the major Sixth. 
‘ Difcords are 
The Second, Seventh, and Ninth, alfo the extreme-fharp 
and extreme-fiat intervals. 
But, through the different combinations of intervals 
in harmony, concords may occafionally be treated like 
difcords. 
Of INVERSION. 
Changing an interval lo that its lower part is placed 
uppermost, or its upper part lowermoft ; or if, inftead of 
the regular way of counting them upwards, we count 
them backwards ; this is called inverfion. The two fol¬ 
lowing rows of figures placed under each other will Ihow 
what intervals are produced by inverfion ; and it will ap¬ 
pear that a lecond becomes a leventli, a third a fixth, and 
a fifth a fourth, and vice verfa. 
i 2 3 4. 5 6 7 8 
87654321 
Thofe intervals that exceed the compafs of the eighth, or 
obtave, as ninths, &c. bear no inverfion, as thereby no 
new harmony can be produced. By knowing the repli¬ 
cates of each kind and different fpecies, the more diffant 
intervals, fuch as fixths and fevenths, may be more ealily 
found on the inftrument; fince it is eafier to count a fe- 
cond or third backwards, than a fixth orfeventh upwards. 
Ex. 11. at the top of Plate IV. wiil fiiow the nature of the 
inverted fcale at one view, and will prepare the ftudent 
for other inverfions and changes. 
Of PROGRESSION. 
All progreffions whatever, may be made in the follow¬ 
ing three different motions : 1. By regular or fimilar mo¬ 
tion, when two parts afcend or delcend together. 2. By 
contrary motion, when one part afcends while the other 
defcends. 3. By oblique motion, when one part conti¬ 
nues on the fame degree, whilft the other afcends or de¬ 
fcends. All thefe are Ihown at Ex. 12. 
The rules for applying thefe different motions in re- 
fpebt to the progreffion of concords are as follow': 
From one perfebl concord to another, i. e. from an 
eighth to a fifth, or from a fifth to an eighth, you mult 
proceed either by the contrary or oblique motion. From 
this principle of compofition arifes the eftablilhed rule,, 
that two eighths or two fifths of the fame fpecies are not 
allowed to follow each other progreffively in a regular or 
fimilar motion, either gradually or by ficips. It may ea- 
fily be imagined, that eighths that follow by parallel mo¬ 
tion cannot fall under this rule, as not being progreflive ; 
nor can it be applied to fuch a caie when in a piece of 
mufic all the parts proceeded by eighths, or by unifons 5 
becaufe then all the parts are conlidered as one. Accord¬ 
ing to the above rule, it is allowed to pafs from a perfect 
fifth to an imperfebt, though only in defcending in fimilar 
motion, provided the imperfebt defcends or refolves after¬ 
wards: all which fhows that, this cafe only excepted, no 
concords are allowed in compofition to follow in fimilar 
or regular motion, but thirds and fixths. An example 
of wrong progreffion of eighths and fifths, in fimilar mo¬ 
tion, is given at Ex. 13. and the lame rebuffed by con¬ 
trary and oblique motion, at Ex. 14. 
From an imperfedl concord to a perfebt one, i. e. from 
a third or fixth to an eighth or fifth, you are, only to pro- 
Vol. XVI. No. 1115. 
820 
ceed by contrary or oblique motion. By this rule the 
confecutionof two hidden eighths and fifths is forbidden, 
as the latter will become vilible on filling up the fpace of 
thefe intervals by its intermediate note. See Ex. 15. 
Of CADENCES. 
The termination of any progreffion is called a Cadence. 
The word feerns as it were a metaphor drawn from the 
dancing-fchool, where it properly fignifies a paule, or fall 
from motion to reft. A cadence is properly when the 
parts fall, and terminate on a chord, or note, the ear 
leeming naturally to expect it; and on the proper manage¬ 
ment of cadences a great part of the mulician’s ikill depends. 
Dr. Pepulch’s definition of cadences in mufic is, per¬ 
haps, the molt (hort, clear, and comprehenfive, to be found 
in any elementary book. “ Cadences in mufic are the 
fame as ltops in fpeaking or writing ; that is to lay, they 
are endings or terminations either of a part or of the whole 
piece of mufic, as ltops are of a part or of the whole fpeech.’ 
For which reafon they are diftinguilhed into full cadences 
and middle cadences; thefe laft are like commas and femi- 
colons, after which more is expebted to follow, they not 
making fo full a Hop as the others; whereas after a full 
cadence we are fenlible that we are come to a conclufion.” 
Treatife on Harmony, p. 4. 
The proper cadences are—the perfebt, the imperfebt, 
the interrupted, and the fufpended. 
1. Of the Pei feel Cadence. —As the dominant governs 
the key, the perfebt cadence can only be made by the 
former tone preceding the latter, with the perfebt con¬ 
cord as at h, or the difcord at i, Ex. 16. The common 
chord of the fifth of the key may likewife be preceded by 
the | as at h; or by the 4 only as at l. The cadence at k 
is moitly ufed in mufic of a cheerful nature ; thatat i, when 
ferious. The perfebt cadence may alfo be made by the 
fubdominant and key, as at m. This cadence is much ufed 
at the conclufion of folemn and facred mufic. Some au¬ 
thors treat this as an imperfebt cadence, which it cer¬ 
tainly is, when not ufed as final: it may therefore be con- 
fidered perfebt in a conclufion, and imperfebt in a pro¬ 
greffion. 
2. Imperfed Cadence. —The imperfebt cadence is made 
by the key-note preceded by its fifth, as at Ex. 17. q, r ; 
or, by the key-note appearing only in an upper part, as 
at s. Or by a retrograde motion of the. perfebt cadence, 
as at t, and its inverfions, ?>, w. 
3. Interrupted Cadence. —The interrupted cadence, is 
occafioned by the fifth of the fcale not pafllng immedi¬ 
ately to the key-note, as at Ex. 18. x, y; or by the key¬ 
note bearing a difcord, as at 0. 
4. Sufpended Cadence, or point d'orgiie. —The fufpended 
cadence is a withholding of the key by the dominant, on 
which various chords may pals and repafs ; and is called 
(by the French) point d'argue, or organ-point, from its 
being much ufed on, and peculiar to, that inftrument; 
and confequently to church-mufic. Ex. 19. 
The refolution of a difcord, according to Roufleau, is 
a kind of cadence : “ And, as all harmonic phrales are 
neceffarily connebted by difcords, exprefied or under- 
ftood, it follow's, that all mufic may be laid to conlift of a 
1’ucceflion of cadences.” The regie de Vodave feems to 
favour this idea ; as every other lound carries a difcord. 
Padre Martini’s cadences, in his Saggio di Contrap- 
punto, being fuch as are peculiar to the ecclefiaftical 
modes, will be of little ufe in fecular mufic. The doles 
of Haydn, Mozart, and Paefieko, however new, elegant, 
and ingenious, the treble may be, are all built on the 
-bailes and harmony of the old clofes of a hundred years 
ago ; for in a full dole, as the bafs mnji fall a fifth or rile 
a fourth, the treble mull either fall from the ninth to the 
eighth, or rife from the feventh to the eighth. 
I11 early days of counterpoint, the great ftudy of com- 
polers was cadences. A Studio of Paleftrina being found 
at Rome in-the year 1770, it was chiefly filled with ca¬ 
dences and chants, in his own hand-writing. 
4 ? In 
