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1\1 u s
AXIOM VI. T hc:re S tones , naOleJy, th:
J...~y, lhe 30, ph. 7th and 9th. are lhe: (ounda·
,ion (lf Ihe: whúlt! fl1p~rllruc.lure of OIu(jck.
\V~ I1lall conduoe: Ihis theory Wilh the harmonical di·
\':1100 o( a Jin~ .
70 di;;id~ n Lin~ ha"1JI~nicall;'. No. 2 J.
A rit ht "oe, i\ D , is (.lid to be divided harmonically.
ii, bting Cut into ,hree pans. A B, B e, e D . Ihe: cat"e
l'e fa. that. as the \Vhale A D (ar Z) is ta either ex·
treme a or e:: fo ! lhe other exuc.:me be la lhe in~
(ku~rminale pan 11/ ; that ¡s, .
X : a : : e: "'( ' Vhcrcfore Z 111=0 C.
L : e : : ,,: 1115
/\nd, tO divIde: t\ny given righ t lioe thus harmonically,
;,\5 (uppo(c A D : F,om cither cad al il draw a rigllt hn~J
~s O G ; make. an itngle with it, and of any leO&lh ;. con·
K. ~" -:>- ,)
oc(t lhe cnd of litis lioc. with Ihe other en,1 A , h~· (h .IW–
¡nh A G; an~1 Ihen t3king any point, ;!i D. :,l Il·;t"fuIC.
in lhe gi \ cn lin~, lhe!"!: drJ\v é. F p..II~lId 10 [) l~. and
in ill .. k.! ~ E rqual tO H f; then lh :nv 1-. G • .InJ Ih.t[
(hall lind t h~ p():nt C I 2nd lhen cdlltnr, :l~ ;1-
boY~. Ihe wl:o"'- Jm\!Z , .ti H-ü, U e-II/, 2nd D e -ro
J I, y L : n : : < : 1/1. - - _.
l-'or the lIiU'l:lls!\ o e, f\ B F', an~1 D E e, .ue aJl
fimil,, : ,nd canl<qllend y A D: A B:: J) G : : 13 F::
ar as D G: ta B F-Il E. 13m as l) G : Jl le: e o :
H C; (by wNkinz a'GOUI Ihe: l Cpl.d í1nj!lc:s D "nd E ,
B el whclerare. by '9ualll)', A D : II ll :: e D :
C IJ : th.. is,Z:a:: C:III. ~E . D .
Ano [rul}': h:.: nce il is plain, the ratio or the wllolc
line A D, to the fegmcm A B, may be takcn al plca–
rUle j bUI lhal Ihe intermediate pan II e mua be; kfs
thao ei:her A B or e D.
PAR T n . T HE P RACTI CE O F lUUSICK.
T HE pr>{tice o( mufick is (aunded an the pri ncipies
dell\crcd in lhe theory. l rs [everal p.HIS are,
compofiti on, tigUling the bar,. ruelody, trdn[pofi tio[).
~nd finging by nOlc.
or thef(! we (hall treal ftparateJy io lhe auove order.
COO1poCttian is lhe [etting IOgelher two or more nates
in harOlonv, tO be (ounded al the f.1me time.
\ Vhen i;l lhe fucceffion of coneords. in lhe parts, the
notes oC eaeh p.1l 1 are of the fame l<!ngth, or time of
founding. lhe compofilion is CJl ll!d countapoin t.
' Vhen lhe fucceffion oC concordi is by nOtes of differ.
!n( lenóths in the feveral parts, it is calJ~d plaio de(canr.
1 ·he lHiXlur~ uf dif..:oro élnd concord, by notes of lhe
¡,unl! or dilTt rent lengths or time in the IUrls. is c..lled
figurate delcan t, Of thefe iD lh,ir arder: and firll o(
cOl<nlcrpaint.
]n 0 1 der tO altaio more eafily lhe an of compofition,
il is n~cccr..ry to premife a few Ihings concc:rnillg otiler
.. ff\."ll ians or fourds; as the time or lengths or foundi ng
lhe nOlts ; lhe time of mu(jck. or mO\'tmeOl of Ihe air j
ar,d lhe dllf-:renl c1iffs wherein lhe parts uf mLlli~k are u–
fu .111)' wrinen.
T he follo'.\ ing account CJf die propon ions oC lhe lengths
\.ir oOt(oS. the time aod cldT.;; , be'0r. welJ ondert1c..od by
t:.very one ftcquAilllcJ c:vcr fo bule with mcfick, mieht
wc:1J hal·c bc,;en onliued in an clray of this kind; (wherr',
¡nncAd oC uling l epetitio~s. il is llOped wc htlvc. 0(–
fcred 10 lhe ~'lIblic romething new; al Jea(1 in lhe mo:.n·
ntr of dc:monrlrdting the 'UIeS of compofilion, both in
¿i(cord aod harmony;) lJu t thal \\le w(Jlld le Ive nvthing
in OUT" powtr unrold, which OIfty contrd.HHI! tO (orm a
(omplt;tl I'"Iluficlan. 1
T he J"ngcn notc, now j;encrally io ufc in inf!rumenlal
m\ is c.lllco a rCI~Hbrev.:. hs tlOle IS as lone <ti yuu
car. t1iHinfl Jy tounl fur.
Out of lh'! rlivilion ~nd r Ibdivifiun of lhe r~n'¡brc\'t:
are: formc.d Ihe I:o:.dls of alJ ot)¡cr n01( S ; accolJmc to
,he: following prup ·nions No. 22.
A fcmlbr:·.e, ""ho[e lime is as one, t ·0, tlllee, fou r,
js as lO:ll!
2 i\Iinums,
4 Crotchtts
as] 8 ~dvers,
16 Semiqu:wers.
32 DemitemiGuavcfs.
A dOI arter aoy nOle, figni lits lhe time of fllch nOte
mult be len¡:thencd \0 ane hale a( the plain note. .
The proponions are Ihusj
A doltcd femiureve is equal la 3 ruinuOls.
A doucd minem 10 3 crolchels.
A dOI(~d crolchet to 3 qUa\'Cts.
And ro a( the re{L
" illlS we ar~ ruroiOled with no:cs accord;ng 10 ~l.~ ...H.!..!
ar.e c"'en l.umUCIS. :\nd [hi~ :l:1tur::lly JI\'ldcs t1H! llUl"!
of any long ur IIH:fi..: inru o:.Jd anJ C\"en time.
eü:\IMON TDíE.
" ' hen lhe air movcs according tO the e\'en oumbers ;
end t:vcry bar IS mCdfured uy u<.ating the tillle iOl o t\\'o
(qUd¡ ... r.d t:veo parts, the mu!;t:k IS compofcd in cammon
time: knowo t:)' one of Ihe foJ! owi ng ,"..tI ks prefixed 10
l ~e"lIlHle ; a.~ the lellt.r e, having 4 (IOiChels in a bar j
or ;:-, dcoollog t\\O 1I 0tchcts in ,J bar.
TIUPU: T IME,
BUI when lhe n;u(i( k mores ::Iccoldir.g 'o lhe ocJd num–
Lers. and c\',: ry blt l 15 rncaJuHd by l'calillg Ihe linle ioto
1\'10 llllt"fJL:¡¡\ p... lS, ..s , ·.vo :l nJ OnL', Ihe (ong is compol, d
in triple I·nh..'. whidl is !tnuWII by one uf tI,l:C figm, r1t:–
fixcJ (Q d l\: tune.
3. or ~. for 3 r"i.l¡Jms in abar.
! 3 e mclllts In a har.
i 3 ~ ..I'JI.1S 10 el Un.
-! ') CWlcI:dS in ..
~' c; l..l'.¡.' \ (·1 S in .> b4r.
'10 111: n,p'!:lllloH r.urnbC'r being lhe nU!1lerator Clr a 'uI–
gAr rl ol~lillo; 4nd Ihe Ic\Vc r, or .• ~ur) lhe rlJi\1uot
pArI 01 Ihe fcmílH c.·te.
1 hcre 15 .dfu ,U:C-tlILr tlrnronion of lhc Ic:nr,th of nOl es
in ufc. Anu thl~ IS, wilclI thrcc qU4v,"rs dll', b) "Imi–
nULiC'!!