MUSI C. 
taken a minor fecond above the bafs; and is applied on 
the lower part of the major femitone. 
4. The fourth con lifts of a major fecond, a perfect 
fourth, and a minor fixth ; being an imperfect common 
chord, taken a major fecond above the bafs. 
5. The fifth conlifts of an extreme-fltarp fecond, an ex¬ 
treme-fliarp fourth, and major fixth ; and is properly the 
chord of the feventh, on the fifth of the minor mode. 
6. The fixth confifts of a minor fecond, a perfect fourth, 
and an accidental-fliarp fixth; and is a common chord 
with an extreme-ffiarp fifth, a minor fecond above the 
bafs 5 and is peculiar only to the minor mode. 
Of Chords by Supposition. 
The chords yet remaining for confideration, are 
the ninth, eleventh, and thirteenth, which, from their 
extending beyond the limits of an odtave, are called 
chords by Juppojition. Thefe chords, Mr. King obferves, 
are ufually conftrudted by placing one, two, and three, 
thirds, underneath the chord of the feventh. See Ex. 18. 
As placing founds under one chord to produce another, 
is inconfiftent with the natural principles of found, which 
can never gravitate, and all'o againft the direct principles 
of harmony, which, after eftablilhing a given bafs, ad¬ 
mits of no lower found ; a particular enquiry will now 
be made, firft, into the prefent theory, and afterwards 
into the more probable and natural conftrudtion of the 
chords in queftion. Thefe objections would not have 
bien confidered fufficient to jultify any deviation from 
the theory ufually followed, had not the greateft autho¬ 
rities themfelves (while they agree in principle) been di¬ 
vided as to the particular conftruction of thefe chords. 
Rameau, in his “ Principles of Mufic,” places two 
thirds fucceflively under the chord of the feventh on the 
fixth part of the fcale, as at Ex. 19. But he goes no far¬ 
ther, perhaps, becaufe he found the chord of the thir¬ 
teenth would have taken place in the feventh of the fcale. 
If this was his reafon, it was quite fufficient. Marpurg 
and mod other harmonifts place three thirds fucceflively 
under the chord of the feventh on the fifth part of the fcale; 
as at Ex. 20. Now, the firft of thefe two general fyftems 
appears to be the beft as far as it goes ; becaufe here the 
ninth is major; but in the fecond fyftem it is minor, which 
is not its real charafter; for, as the fecond part of the 
fcale Hands a whole tone from the firft, fo the ninth, the 
true reprefentative of the fecond, fliould be alfo one tone 
from the oftave of the firft part of the fcale. To this may 
be added, that Rameau makes ufe of the wrong funda¬ 
mental feventh, but produces a true ninth ; while Mar¬ 
purg, who ufes the real fundamental feventh, produces 
an imperfeft ninth. The confequence of the difagree- 
ment of thefe two celebrated authorities is, that, as moft 
harmonifts follow the opinion of one or the other, two 
• different and indeterminate characters are given to chords 
which it were to be wiftted had an unalterable and efta- 
bliffied theory. 
Another fyftem is now prefumed to be advanced, en¬ 
tirely different from either of the former, and wholly 
founded on the principles of Vibration, or the natural 
fucceffion of founds. See Ex. 21. Here, by adding the 
vibrations of a given found regularly as they arile, it di- 
reCtly appears, that the chords, of the ninth, eleventh, 
and thirteenth, are naturally felf-conftruCted ; and that 
by one, two, and three, thirds, being fucceflively added 
over, and not under, the fundamental chord of the feventh. 
If the feventh of each chord, being flat, fliould be confi¬ 
dered as an objection to this theory, it mult be recolleCted 
that flat-feventh exifts in Nature ; and, fince the above 
order of conftruCting thefe chords is wholly founded on 
the analogy of Nature, that very objection becomes an 
argument in favour of the prefent fyftem. 
Of the Chord of the Ninth. 
To the ninth belong 3, 5, 7. Plate VI. Ex. 22. Ihows 
the different fpecies of ninths. The ninth followed by 
Vql. XVI, No. 1115. 
3-33 
any other figure, as 9 8, 9 7, 9 6, 9 5, or 9 3, is accompa¬ 
nied by | ; joined to any other figure, as 6> or 5> ’tis 
accompanied with 3. Ex. 23. Ihows the preparation and 
refolution of both thefe kinds. At Ex. 24. all the fore¬ 
going chords are prepared and relolved. 
Of the Chord of the Eleventh, and its Derivatives. 
The eleventh, or chord of the fourth, is figured by 
to which belongs 5. The different fpecies a\;e exhibited at 
Ex. 25. The chord of the eleventh figured thus, 7, jj, or jj, 
is accompanied by the fifth. Figured thus, f, it is accompa¬ 
nied by the fourth. Figured thus, |, it is complete in 
itfelf. Ex. 26. deferibes its preparation and refolution. 
Ex. 27. gives the chords at h, i, h, !, in, n, o, p, prepared 
and refolved. The third from the bafs of the eleventh, is 
ufed in its firft refolution. The ninth from the bafs may 
be figured by a 9, when that interval is uppermoft, as q, s; 
but in other cafes it is figured by a 2. To diftinguilh the 
chord of the eleventh, when in part figured by a 9, from 
the chord of the ninth itfelf; it is only neceflary to ob- 
ferve, that the former chord muft contain a fourth, which 
the latter chord can never do. 
The chords 4 3, and l ~, are taken out of the eleventh, 
as at Ex. 28. To the 43 belongs g ; to the \ 3, belongs 5. 
The chord 4 3 ufually takes place on a holding-hals. See 
Ex. 29. The fourth may refolve by an inveriion of the 
third, or pafs into another difeord ; in either cafe, the 
fourth is accompanied by g. See Ex. 30. 
The l generally takes place on the fame bafs ; but 
the l may Itand alone, and be refolved into another dif¬ 
eord : in either cafe, \ is accompanied by 5; as in Ex. 31, 
The 43 is often ufed in the perledl cadence. 
The chords § and | require no addition, but are com¬ 
plete in themfelves, and are derived by inverfion from the 
chord of the eleventh. See Ex. 32. The chord § is ge¬ 
nerally l'ucceeded by 6, but may be followed by £ ; as at 
Ex. 33. The 4 is ufually followed by g. See Ex. 34. 
The \ refolving into 6 is an inverfion of 43 ; and the £ 
refolving into § is an inverfion of \ 3. 
Of the Chord of the Thirteenth. 
The chord of the thirteenth, or difeord of £, is figured 
by l, to which belongs 2. See the different fpecies at 
Ex. 35. The chord figured thus, |, |, |, |, is com¬ 
plete in itfelf: at Ex. 36. are their preparation and refo- 
lutian. 
Progression of the Fundamental Bass. 
The progreflion of the fundamental bafs is of fuch im¬ 
portance, that, without a proper knowledge of its ufe, it 
is impoffible to be either a corredf harmonift or a good 
compofer: for, as the fundamental concord and dilcord 
are the foundation of all the derived chords, fo the pro- 
greffion and intermixture of the latter chords are entirely 
ruled and governed by that of the former. 
The fundamental bafs carries either the perfect concord 
or the difeord of the feventh; which chords may take 
place in any part of the fcale ; but in what manner they 
ihall fucceed each other is to be determined by pofitive 
rules, fuch rules being abfolutely neceflary to regulate the 
ule of the derived chords, which are all reducible to the 
two fundamental chords: for, if the progreflion of the 
fundamental bafs be regular, the harmony arifing from it 
will be regular alfo ; but, if harmony be reduced to its 
fundamental bafs, and an irregular progreflion appears, it 
is then a proof that the harmony has been improperly ufed, 
PrpgreJJions of the Fundamental Concord. 
Thefe progreflions are ffiown on Plate VII. at Ex. 1. 
from which it appears, that to afeend a third and defeend 
a fixth, or to alcend a fourth and defeend a fifth, and fo 
4 Q on. 
