1000000031

356 / 868

M u s
fCrDltQnc, ,,:,d ene :ono: lO thc 5th; and tllene.: by twe
tones and a remirone tO lhe 8th. Thi, is tbe arder in í\
Jharp key; where note, \hat lhe [c:mitOflc, are ID rhe 4th
anJ 81h place.. No S.
In a AH key, lhe nOle••fcend aeeording 10 ,he {alioli'.
ine example. N° 9.
One: tone, a remitone, and two tones to lhe 5th i a
fc mitone Olnd (\Va tones tu lhe 8th.
[o· lhe neXl ex: .. mplc. lhe fame propon ían of rhe Rat
t hird is illull ra<ed by eo...parifon lY!lh lhe ioll~nce in lhe
fuarp key, No. 10.
The Dumber of lhe Iones and femlt oncs in bOlh lbl and
fha rp kcy ' are equa/. . 'The o:fi'erence a"fes {ro", ,he
places of lhe remitone: which, iD lhe OH key. "re the
3d .nd 61h. Thi. is lhal dfen,ió l dilference of ,one .I~
rcady mCDlloned, which creates fuch '\"aric:ty in muGcal
firaíns, as well as in lbe harmony.- are fome cr·
fells of ll<e femiloDe ; o,hers we fhall fee iD ilS pro!!er
"lace,
7 h( C/¡r.¡nalie Sea/e.
The chromatic rifes by a tone and S rc:mitones to the
,11b, and lbence by 5 femi,ones more la lhe 81h. Thu.
No. 11.
The chramatic (cale, which is no other than the na~
tunl femitoecs in their arder) exccpt the firCt tone, is
ooly ufcd when mixed with the diatonic. That is to fay,
when a femitooe, not bclongio~ to the harmony of the
, is introduced in lhe middle of • lune. And lhi, .nay be done by lbe nOle afcending . by • felT'~:one,
Or defcending: in eilher of ..hich 'cafes, ,he key i.
chaneed iD lhal par! of the arain. This is lhe cauf.
of great ,.ariety in (he sir ; as \YeH as it néw· moduJates
,he h.rmony, Thi. is anolher effell of lhe femiloDo,
on which turos Ca much l'ilriety and elegance. lt mllll
be execuled ~y lhe compofer with . 11 the addrefs .nd
art ima~inable. Far this \Ve mull rera to the fecoed pan
or praélice i where will be given ~be rules ror the mixture
~f the chromatic. P ieces ('f mufick \vhere it is frequeody
ufcd, arc no\ll' commonl y cal!ed chromatic muCick.
T he dialonic fc.l: bciDg ,h. , which we are ehiefly
conceroed tO underO:and, as well as the' lirO: iD order,
and befare any ure of lhe ch rom.uic caD take place; we
fryall proc~ed to ijew it in another lighr ,' \"hereby we
fhall difeover fuch propen ie. Df il as \ViII be ufeful lo lhe
compofer. key. No . 12.
From the key lhe thirds as io the above ex·
.mple, by ODe fha'r p 3d, ' wo a.t 3ds; lWO fharp 3d" •
1101 3d, 'Dd l.flly . nolher. aat 3d 00 .be ,d 'o ,he key.
AII lhe 4,h. being perfea, are like; excepl lhal one
\Vhich f .lI. on the fh1fp 7'th; lhis i. call.d a fhdrp 4th,
or f.. lfe 5th. No 13.
AII ,he 5'h. are perfea , .nd lherefore like ; exeepl
, hOl formed by lhe fh"p 71h and 4,h, which likewife i.
a al! s,h or fh"p 4,h. No. 14.
The 61h, flaod lhus: l\VO nlarp 6,hs, ODe al! 61b,
, wo nlarp 6ths, lWO au 61h>. No . 15.
There are bUl twO grtate.r 7lhs which are the (b¡UP
3d and fh Irp 7,h lO lh. key : they fI,nd uDder lhe lWO
(cmirones.
AII the 81h. ore perfell and a ike.
aL. 11l. °.82.
e K.
F rom lhefe lhcorem., and axioms, lbe 2d aod 4,h,
we deduce thi. prallical corolluy.
COk. IV. Tbe 3d, and 61bs .re lhe iOlervals ",on
fre'luently lO be ufed iD compofitioD; lhe 81h., 5,h.,
'and 41h. rilDfI r¡rely.
The 41h ~ing aDimproper ~oncord, and ,he ¡th a dif–
cord; we cannot arccelaio their ure tlll we come to the
dcruonnuIion of the harmony and accompanimeDu of
,he difcofds in lhe :!d parto
On lhis 41h corollary is grounded lhe re. fon of forbid–
ding tWO 8ths and two Sths in CDorecution, elther iD com·
polition, or pcrforming lhorough bar,.
.Nexl follow example. of lhe fame in anal key. NQ,
16, '7, 18, 19·
Tbere are bUl lwo fharp 71h. whieh are lhe 2d and
S'h lO ,he key. They flln-d onder lhe feOlilDses.
AII lhe oélaves are perfell. and ."ke.
It is n ideot to f'ight, that tbe uuervals io'"the tlat aod
f'harp key do not in the lean 'n.r,. ; except in the arder
lbey fucceed each olher, beginning from tbe key. And
il is equally (vident, thu this: v.uiation is owiog lO (he
diffcreol places of the fcmi,one.
T~i. demonfl",,, \VhOl has been in pase 319'
col. 1. concerning tbe fem¡tone; and ilh~nratcs what is
a{ferted io the 4th axiom, thal vJriety, amidll uoiformiry,
mu{! be lbe greal o~jell allended la b mufiek, finee lh~l
uniformi,y and variely bOlh fubfifl in lhe very principIe•.
Let it be obfervc:d, tbat this ut:'iformiry is prefervcd by
b,inging in lhe fin 6,h aDd Aal 71h lO lhe key. And
lhlS mua of necem,y be fa, fiAee lhey are the place. of
the femitone and lelfer tone in tbe nalural B.H key wherei~
the example is fet, according lO th: demanflration of
lhe fame .
For, b-y coroll3ry J . oothing can be admiHed in com·
pofilion "hieh dotb nOl iOlmedi. ..!y dcpend on lhe 2d
axiom, and which cannot be demonfl r2tcd from it ; name-.
Iy, that the proportioos of found" and their re"latiOD$,
mun .be deduced írom lhe natural order of the Dotes,.
This is the true rearan for imrodu"cing the Aat 6th and
11.. " h in eyer)'.Jlat key .
T he harmonic proponioos :lod difcords haviDg beell
demonO:rated lrom ':le divifion al a Jioe' in aritbmeti..
cal progreffioDi we lhall, in the next placc, try what
are the effell. of a muGc.1 driog divided in georu,rrical
proponion. No. 20 .
Lel A B, • muflc.1 flring, be divided. equll1y in C;
C 13, lhe balf DeXl the bric!ge, will fouDd ao ollave la
the whole or opeo nring, as we have rhewn iD the har–
monie propon ion,.
, let C 13 be equally divided iD D¡ D 13 will
fO~Dd .the oflave la C 13, or double oélav.. la lhe open
flring; A B.
And lhus, by an equ. l di,ifioDof • flring belween ei–
lher lhe nUl an¡l bridge. or flop and bridge ; lhe half
next the bridge will give the olbve above conlioually.
BUI the fame propordoo is nOl prefcrved ln the ec¡ual
diviCion between ,he out and flap, or between any tW(t
flops . For ,h, leDglh 01 the 08.. e tO lhe open [¡riDg.
whic.h. is b".w~~n lhe OUl and flap, being equally divi·
ded; lhi b,lf next lhe nUl 'giv.s lhe founo of the 4th 19
,he apeo flriDg ; a.d lh< half nex' loe flop, or br~dge,
.M 1 ~~