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328 M U S
in eonfccmion than tWo 5th,. And henee likcwife the
¡IHerval or,the 4th, which \Ve have callcd an improper
concord, appears tO be'of a midcile "ature between con–
c.:ord and difcord; b::ing a rounh in n:une and appearance
in lhe nl tural order of founds; yel a 5th in name and
eff~tl: in comporition . as membc:r of that chord wherein
it Illdkes a pan or harmony .
Co R. 1[[ . The key, ,he 4th "nd 5th, admit in their
harmony a 5th .
S C HOLJA .
\Vh: n the key admi" a 5,h, ,he euncord i, that of
the key.
"Vhen ,he 4,h admits a· 5th, ,he chord is of Ihe 4th.
When Ihe Slh .Jmits" Slh, ,h<coneord is of,he sth.
H~nce, whcn a note :ldmllS a 5th, lh: harmony is the
concord of [he note.
CORo IV. Every no« bu, the 41 h admits" 61h; for,
lhe _¡lh having lIS con::ord for harmony, \ViII have o:1ly
its 5th.
E"eryno:e"dm;ts i" 8,h ; for "ny note may be fublli tu.
ted for its o.5't.1vo. Bu, 8,h, ore (by eorollary 4. of the
t~y) 10 be ,he moll fp.. in&ly ufed, as nOI proJueing
that "a riel}' or mixture of (o~nds rt:cpiGte lO bind Ihe
harnony, efpccially, wh~re it can bl! beH 3\'oidt;J, in rhe
compofition of twO parts.
From the foregoing demonCtratians and corollaries, .a–
riCe Ihe fol/owing obCervations.
The 3ds "od 61hs mo(l frequently oeeur in eompoG,ion.
This Iht;n demonn-rates what w ;u a{fc!rted, by way of pre–
cept, in the 4th corollary of the theory as well as part
of dle 4th axiom: n.lOl,::ly. that (he proportillns oE JIlu–
{ical Cüuods J and (he varic!ty emerging fronl rhem, poiot
O:.Jl tO us th:s \'.lrielY, and \Vdl Dor fufFer us tO depart
(rom the ell.blifhed preeept.
Ir \ViII be necdr.. , y (O f..e lhe! frUlhs comfirmed
¡... rIt.: defccndin!! O·J{!S. \Ve fh ... 1I thereCorc Cc:t down in–
ebo.nces of compofi:ion in (he defcending DOteS oC rhe OC–
(.• ve upan tho! ¡'ame principlts, and wht>rein the Cuue de–
monnrations an'1 coroll.lrics do takc olace.
E '<1ntple of eompoGlion in Ihe d"f~ending notes of Ihe
othve. No. 34 .
In th:: afcenrling note", '.\ nen Ih: u?per pHt rifes by a
femi,one, Ihe b"fs ~ene,"ily f""s a 51h; \Vhtn ,he Uppcr
part falls by a whole lone lO a clofe , Ihe hafs alfo falls a
5,h. This fall of ,he bafs, or greal cadence. mull be
effl!étcd when chromatic nOtes are inrroduccu arcend'in'" '.
ít being the pr QP~rfy of the new femit one, thus rorm~d
by the note rJling a h;lIf tOne, to imitate the kry or ciare.
By axiom 2 . the proparticns of (ouilds, "nd propeni('s
of {he fame, are deduced from {he natural order of lhe
notes. Now, by rhe Dew remitone introJLlcttl, lhe note
hclow imitares th~ grcater 7th lO the key : thndare, in
Ihi, cafe, as in a c10fe on Ihe key, thé b,fs mua fdll •
51h .
NOlwilhll, nding, ,his muf, h. underlloood not of Ihe
patrdge of quick natc::s i and chidly at a cJof~.
Seét. 2. OjC.m/,'!JÍti,,, ill a FLAT l\:EY.
FI\.O ~l the di~'LrC'~cc bctwc('n the n.u ano rhe fll:t rp
k~y WhlCh Ilts In t e ddi'erent rl,.ces oC the f~'mitone,
th.:rc wllI arirt: a vari..:tj· in lhc cUIJ:pofition in a fl.u key,
e K.
yet refliog on Ihe pri ncipies and demonfira:ioos delivered
in Ihe lall f, étion.
The pl.ces of Ihe femitone in the fhup key are ,he
4th and 8th. I n a fla! key . the femitooe n ands 10 Ihe 3d
and 6th placos. The . arie,y in Ihe eompoGlion will h,p–
pen where [he femi tones are concerned. For, as [he mido
die c10fe is made in Ihe olarp key on the 41h. which is
,he femitone; or, as ,he 41h in the fh arp key halh (by
demonHra!ion of the harmony of Ihe 41h) i" own coneord
for hatmony: fo ,he middle c10fe io ,he oa, key j,
on the 3d, which is che Cemilone; or the (Ile 3d \Vil!
hav\! fo r harmony i's own concord . Naw, ;1.5 the 4th harh
j" 3d "od Slh for h.rmony, (whieh are the 61h and 8,h
of Ihe key ;) fo ,he ft.. 3d ..ill have its 3d aod 5th, whieh
are Ihe Slh and 71h of ,he key.
Ag. n, ,he oa! 71h of ,he key beiog Ihe 5'h to t~e 3d,
wiJl, likc the 5,h of ,he fh. rp key, have (or harmon)' j"
o'.lln concord. This wil! eaufe ,he 2U of Ihe key lO . p–
pear as Ihe fharp 7th to ,he 3d, and ,he 4,h 01 Ihe kcy
as a 2d (wh;eh i, r"l/y is) 10 Ihe 3d . Thus Ihe "Iule–
harmony will be new modulated hy ,he power of Ihe fe·
mitane. Ag~in, che nH 6rh bc:ing the f~lIlilOc e, a mid–
die clofe m.y be made on th", n.",e; and then Ihe
propartiooal variely fuc cceds, and new harmony, as in
[he former cafe.
L allly, a, ,he end of the mufiek, where there mufl of
oeeeffi,y be a elofe, the key wil l ave ,he gre.ter 7,h,
like Ihe fharp one. Of fo g'""' con fequcnce is ,he fe–
miloue. Nor indeed can a cIore be mOlde at all, withuut
the pafTagt! 01 a (emitonc in one Or othcr af che pans.
No. 35.
D iffamcu ;11 /h, j/tr/ ' " no/d.
I n the fi rfi <"'",pi< ,he harmony of the 7d is the eon-
corel of {he !Lu 7th, .as b~;ng 5th to the IhiH.L
T he clofe i, ",ad. on Ihe 3d, the bafs fa lling , Slh.
T hc 4th h:\th its Qwn concord, as in the (harp key.
T he 5th !h.nding in an oEtave, may b~ undcdtood as
par! of Ihe h.rmony of Ihe 3d, ., the 3d to Ihe key, in
a fh..-p key.
T he 61h is par! of Ihe 41h', coneord, ' as in the fharp
key; as above: in the remHk on the 4th.
Al rhe c1ofe, Ih<re is the fharp 7,h, from wbieh Ihe
ba rs makes the greH cadenee.
In th is ex ampic Ihere happen four 8lhs: Ihe firll "nd
lall are "bfohne ly necdfary to afcen ain ,he key; by Ihe
fecond there is a c10fe rolde on the 3d ; and Ihat 00 Ihe
¡th, is for ,h. fake of , he ai r in Ihe bar,.
In Ihe fecood ex.unpl., ,he harmony of the 4th is Ihe
eoneord of ,h e OH 7 h, as Slh 10 ,he 3d. .
T he hannony of (he fiar 6th is it own cancord, bCln~
the place of che (e;:miwne; where lhe baf, nfes a 4th (lhe
(.,me . s falling a 5'h)"s on a c10re in 10t Il"<bl< aí~eDdlog
by Ihe f, mrlone.
In the 3d e~amplc, ther~ difTerences of (he filt key "re
leCt out; 31J the notes let .tS if chey wer~ parl of a Ol:\rp
kl!y! that is te . lhere is no clo(e m~dl' on th~ 3d . thl!
4th hath ics chunt Cor J1.lrmony; and the 6th is I.k~wl(e
pan ol' the harmon)' of the .• ~h.
For, no", ilhU.lnding ,he proprie,y of makin¡; a dofe
on lhe! 3d a:!u 6th, which are 1"c:llllonc.:s j yct the c~mp\)l~ r
lS