32 6 M U ! 
repeat individually the very fame notes, without any dif¬ 
ference. Now, to make ufe of the fame progrefiion, the 
fame harmonics and relations, or to be in the fame key, 
is not this one and the fame thing ? Confequently to be 
in the key of A minor, or that of C major, will be per¬ 
fectly the fame thing: and therefore both are marked 
In the fame manner, without any alteration of lharps or 
flats on the clef. The whole difference is this; that in the 
major key the fundamental is C, and in the minor it is A ; 
and confequently the dole, or cadence, in the firft cafe 
will be on C, and in the fecond on A. And we may add, 
that the harmonics in C are both given and combined by 
nature; and in the key of A, they are given by nature, 
but combined by art. Or, ftill keeping in the key of C, 
you have only to reverie the two thirds, making the firft 
minor, i. e. C to Eb, and the fecond lharp, as Eb to G, 
the fifth and oftave remaining the fame. Thus it is evi¬ 
dent, that each major key has its relative minor; and, 
there being twelve major keys, there will be alfo twelve 
correfponding minor keys; and therefore the number of 
keys derived from the progrefiion of the fcale, will be 
twenty-four.” 
A third mode, differing from both the major and minor, 
was propofed by a Monf. Blainville, in France, under the 
name of the mixed mode, the generation and properties of 
which he explains in his Hillory of Mufic. This, how¬ 
ever, was nothing more than the ecclefiaftical mode of E, 
(fee Ex.6. C.) with a minorfecond, as well as third. And 
it is extraordinary that this pretenfion Ihould have had 
any abettors in a Roman-catholic country, where old 
compofitions in this mode are daily performed in cathe¬ 
drals and collegiate churches. However, it was a matter 
of wonder and debate, during fome time, in France. See 
the Mercure de France for 1751. 
Modern mufic has its genera as well as the ancient. The 
diat.onic is the moft common, and is that molt agreeable 
to what is pointed out by nature ; but the moderns have 
their chromatic alfo, and even in certain refpeCts their 
enharmonic, though in a fenfe fomewhat different from 
that alligned to thefe words by the ancients. 
Thus, the modulation is chromatic when feveral femi- 
tones are paffed over in fucceflion, as if we fliould fay 
F, E, Eb, D, or G, F*, F, E. It is very rare to have 
more than three or four femitones following each other 
in this manner ; yet, in an air of the fecond act of la Zin- 
gara, or the Gypley, an Italian interlude, there is a whole 
defcending odtave almoft from C to D in confecutive femi¬ 
tones. It is the longeft chromatic paffage with which we 
are acquainted. 
Rameau finds the origin of this progrefiion in the na¬ 
ture of the fundamental bafs, which, inftead of proceeding 
from fifth to fifth, (its natural movement,) proceeds from 
third to third. But it muff here be remarked, that in the 
firft paffage from E to Eb, there ought ltridtly to be only 
a femitone minor, and from Eb to D a femitone major; 
but the temperament and conftitution of moft inftru- 
ments, by confounding the D& with Eb, divide into 
equal parts the interval from D to E; and the ear is af¬ 
fected by them exactly in the fame manner, efpecia'ily by 
means of the accompaniment. 
There are two enharmonic genera, the one called the 
diatonic enharmonic, and the other the chromatic enhar¬ 
monic ; but they are very rarely employed by muficians. 
Thefe genera are not fo called becaufe quarters of a tone 
are employed in them, as in the ancient enharmonic; but 
becaufe, from the progrefs of the fundamental bafs, there 
refult founds, which, though taken one from the other, 
really differ a quarter of a tone, called by the ancients en¬ 
harmonic, or are in the ratio of 125 to 128. In the dia¬ 
tonic enharmonic, the fundamental bafs goes on alter¬ 
nately by fifths and thirds, and in the chromatic enhar¬ 
monic it goes on alternately by thirds major and minor. 
This progrefiion introduces, both into the melody and 
the harmony, founds which, belonging neither to the prin¬ 
cipal tone nor its relatives, convey aftonilhment to the 
I c. 
ear, and affefl it in a harfir and extraordinary manner; but 
are proper for certain terrible and violent exprefiions. Ic 
was for this reafon that Rameau employed the diatonic 
enharmonic in the trio of the Fates, in his opera of Hip- 
politus and Aricia ; and, though he was not able to get it 
executed, he was firmly perfuaded that it would have pro¬ 
duced a powerful effeft had he found performers difpofed 
to fall into his ideas, fo that he fuffered it to remain in the 
part which was printed. He mentions, as a piece of the 
enharmonic kind, a fcene of the Italian opera of Coriolano, 
beginning with thefe words, O iniqui marmi! which he 
fays is admirable. Specimens of this genus are to be found 
alfo in two of his own pieces for the harpfichord, the 
Triumphant e and the Enhannoniqne ; and he did not de- 
fpair of being able to employ the chromatic enharmonic 
at leaft in fymphonies. And why indeed might he not 
have done lo, fince Locatelli, in his firft concertos, em¬ 
ployed this genus, leaving the flats and lharps to exitt, 
and diftinguilhing for example the D* from Eb. This, 
fays M. de Blainville, is a piece truly infernal, which 
throws the foul into a violent ftate of appreheniion ami 
terror. 
Of the Ecclcfiajiical Modes. 
Under this denomination are comprehended thofe an¬ 
cient modes, derived from the Greeks, which depend on 
the different difpofitions of the diatonic oftave, already 
Ihown, when every fuch difpofition is confidered as the 
diatonic'fcale of a key-note ; and they are called ecclejiaf- 
tical, becaufe they have been chiefly attended to in com¬ 
pofitions of the ancient church. See p. 324. 
The two principal things, on which tire doctrine of the 
modes in queftion depends, are: the difpoftion of the dia¬ 
tonic offave; and the authentic or plagal divifion of it. 
Concerning the difpofition of the diatonic oflave, the an¬ 
cients did not confine themfelves to one major or minor 
fcale and mode, with its tranfpofitions, like modern com- 
pofers; but they made every difpofition of the diatonic 
offave, as Ihown on the back of Plate III. at Ex. 6. C, D, 
E, F, G, A, a diatonic fcale of a ke} r -note, which had its 
own peculiar mode. And the reafon why they did not 
do the fame with that of B, was becaufe it has no perfect 
fifth to the key-note, and confequently no perfect fun¬ 
damental concord to the principal note. Each of thefe 
modes had fome charafterifics which were peculiar fo that 
mode alone, according to the deferibed difpofition. of its 
diatonic oftave 7 viz. The mode of D with the minor 
third, admitted of natural digreffions to its fourth with 
the major third ; and to its fecond with the minor third,, 
and perfect fifth. That of E with the minor third,—to 
its fecond with the major third; and to its feventh with 
the minor third. That of F with the major third,—to 
its fecond with the major third ; and to its feventh with 
the minor third, and perfeft fifth. That of G with the 
majorthird,—toits feventh with themajor third; and to its 
fifth with the minor third. The one of A was nearly like 
our modern A minor, and that of C like the modern C 
major. 
The feemd objeft, effential in the dodfrine of the an¬ 
cient ecclefiaftical modes, is the authentic or plagal divr- 
fion of the diatonic oftave. This is the divifion which 
nature propofes in the ratios 2, 3, 4 ; and which has been 
particularly attended to in thofe antiphonies (or anthems) 
of the ancient church from which our fugues have arilen. 
For, at the time when the laid antiphonies were firft com- 
pofed, the fubjedts of their melodies were in general of fo 
lmall a compals, that they did not exceed half an odtave, 
according to the divifion in queftion. When therefore a 
Ihort fentence had been fung in the loweff’part of the 
odtave, i. e. from the key-note to its fifth, an imitative re¬ 
ply to it was made in the higher part, or from the fifth of 
the fcale to the odtave, or the contrary. A melody or 
modulation in the lower part of the diatonic odtave was 
then called authentic, or “principal,” becaufe it depended 
on the key-note itfelf, and admitted of the authentic or 
perfect 
