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1\1 u s
' en note : BUl [11: 6d.. ",';11 h.lVC (he 4th j t!lal!forl! the
dl!clJrJ of t'le 2d is a pro?~r dl(~ord .
By th~ 2d :lxiom of lhe theory, lhe propertics. pro–
partioos anJ rclation of (auneis ue deduced (r(lnl the na ·
t ura l ordc.: r of lhe f:llne. \Vhi.:h axiom io; extended tO
1he difcords, as lhe)' are cO:llbinc:cI of the nacural notes,
:ir.d d.lra lrom (he c..:-ncords cnly in formo
On this axiom, lhen. \..'C: are ro invefligare the next
f\lcc~eJing dil'c .>rd. T he 01 difcord i. ,he ,rl. 4fh. alld
flurp 7th la thcgiven notl!. Far thefe are. lhe neXl fue–
cceJinc di(cordJnt notes.
D (I.'IonjlraliM 0f Ihe [:,o·¡d difcor d.
T hc 2U and 4th c,¡nnot hay!! the Il,lt 7th; for lhe}' are
h ;vmony, or concord of the fl,l[ 7th; and the 81h isthe gi –
ven (lOle: therefore it remdins, lhu lhe (econd dlCcord
is lhe 2d. 4th, and Jharp 7th [Q lhe given note.
Example of ,he fccond difcord . No 75.
In'¡"'lIIonic difcord.
This is an ¡nharmon!c dif~ord ; being 3n abf..>lute dif
cord in ¡lfdr. lt hath bUI one c,JncordlOg note wllh the
b ars; which is lhe 41h . This 4th is lhe tLu 7 ~h (\' eh\!
giveo oOle's StP: which, th is (he l>ars 10 dHS dlrcord ;
lhe given note in this place being conliJcl ed only .it$
a point, or uni ty, from ""hidl we are ro invcHigatl! lhe
next di(cordant notes, according to che :d 2xiom .
The property of ,his ¡nharmonic dlfcord, or lhr 7' h,
is, lh-al iu own interval, or that which IS (orm·
'ed by lhe accompaniment, is alw;¡,ys a (harp 4th , or Ita
5'h, which dilbnguin,es i, al figh, (roOl evcry o,her dif–
cord. And ev>!ry inharmonic, where·everfoUIld, hath {he
[ame propeny . ' 1 'he r(folution alfo of tvery ¡nharmonic
is lhe Came ;' as we Chall Cte, whcn \Ve come. in the next
place, 10 Olew the refolutions of lhe difcorJs .
The neXl difcord. according to lhe 2d axiom, ¡s the
fharp 3d, 5th, and OClt 7th te lhe giHn no:e. Thls is
ai ro an ioharmonic, or 7th; 2nd having the fame pro ..
perty w1th the former, namely, the fLu 51h, muH OOt be
accountcd a ne'V difcurd. No. 76.
l n"armol1;c diftord,
T his is the inharmonic dírcord in tilat furm, whuCe
accompaniments ale rdative 10 the ba(s, or given note.
Tbe ,hird dircord lS ,he 3d, 5,h, ar.d (harp 7, h 'o ,h.
bafs, or givtn nott:.
D Ol/olljlration if th~ third difi·q,.d.
, he (h,rp 3d. 5,h•• nd OlJrp 7,h. mun conOilUre ,he
next d l(cold. For lhe 3d, 5 ~h , and tldt 7th, ale
·J¡arOloQY, or concord of the fI u 3d ; and the 8th with
1hc3J and 5th, are the chord of the baCs note; and the
.ft~t 7 th, with the (}ld rp 3d and ph, are the inhcHmonic
h.11 mentioned ; thcrefore, lhe nlarp 3d, 5th, dnc fhl , P
7th, are the ~d d ircord.
Ex''''ple o( ,he ,hird difcord. No. 77.
Proper difc0rd.
T his is a proper dircord, bt ing the concorel of the ...J
l o Ihe u ... fs; anJ lhe fh.trp 71h lhe direorUJnt nljle. ;)
To prúccc:d lhen ac~o:diJlg lO OUr 2U ax.i()nl¡ lhe next
e K.
d iCcor,hot nott i in order, are th~ 4rh, 6 th , 4i u.i ; Il,!
But th-::Cc l>\!in¡; t:H': nOtcs WhlCh conrtltule da: fir(j ll,:.
cord, varyln;: only in place anJ nAIllC of dIe '.11ft. {ur t:,::
2ti, are io df.:d Ihe r:lOle d~ r ord .
The n~xl CuccdIlve dl (c,¡rCd!1t nores are, accorchnr. h J
our v. ell known aXlom, Ihe 41h. nlHp 7th , ~nd Otll.
BlIt thd;; Itkc:: wife eon(lnu lc lhe 2<1 ddcord in like m:1n~~ r,
as \l'as (;ud iR lhe (ormer e Ife; and thereforc:: cannOl oe
rtckoncd a new ¿ifcord.
'r o procced then by our axiom: T hc next afcenJinJ
notes, hy l he CmAlleH iOlel vnls, are Ihe Ch ,lrp 4 th, 6th,
OI nJ 8th. TllIs i!: í!.n inllarmenic, or fI,tt 7Lh; ils Ildt
5th bcio!! formed by I~,e O.aIP 4'h and '8Ih; tllerc!'ore
no new dircurd . NO . 78.
, T o go on , lhe ndxl J lrcor¿a:1t notes wiJl be found
,he (harp 4, h. 6,h, .nd 9,h.
D ,,"onjlralion iflh:fourlh difi:erd.
From rhe proof of lhe: inharmonic d¡Ccord, the
(harp 4th anu 6 th can fOI m 3 proper dlrcorJ \~ idl no olher
interv¿1 bLlt the 9th; for lhe 7.h \Vould pr... duce three
'1orf'S in tbe n.Hura l ord~r, anti iOlule;abl~ d¡rcord.
Thcre{ore Ihef(.Hlnh c11(cord is tht.' lhup 4th . 6th. and 91h ..
Ex. m!,lc o( ,he loun" d,(cord . No 7').
Thls js d propcr ddcord, b~iog a concord in ¡trdf, ani
only dlfeordam to the u:lfs note. 1 ·h e d Dotes
o( i, are ,he (harp 4fh "nd 9,h.
The next wh,ich pref::nls itfeit", is the 5lh, /hup 7th, anJ
9,1; , by ,he fdme ."iom.
D mlollf/ralion o.f lb. fifih difc0rJ .
The sth w¡'1I admit no olher di Ccordant notes bu t rbe
(harp 7fh . "d 9,h. for ,he 8,h .nd ,o,h m. ke ,he Con–
cora of lhe note; and lhe nlarp 7th aod loth ¡s,
with lhe 5th, the third d,rcord :dreOldy proved : ar.u any
o,hcr no,< woulJ be douhle di(cord••nd i"",lerable :
therefore, the (l;,h dlrcord is the 5th, f'h iHp ilh, 9th.
E xamplc o( ,he li a h Ji(cord. No . 80.
J' /'op" difc:ord.
Thisis a prop<'r dircord, being i\ cO'lcord in ¡rrelr ; an.:!
dircordant only wnh the given note. l es dlCcordant RlJleS
are ,he 7,h and 9th.
W e hdve purpn(cly rc(ervcd ,he di(cord o( ,he le/fcr
,d tO lhe li xth aod Jan pld~el l n. Oecaufe. as lhe inter·
val ncxt OIbuvc the key is ahvays <1 \vholc IOne, \Ve can-
0..>1, :1ceorJing to our 2d axiom. ereél this difcord as
rd alive tu lhe s.!iven note, or ke .... ; as \Ve )1.1ve done the
otller fi \'f. 2Jl y. Tht: Ic(oluti¿n o( chis cl ft.:orJ. will b<
ff)~nd dilYcrt'n l Iro01 that of the bn~iltcr Cc:!~:)l1d; for rea ·
{OI1S which will al,uaulntly appe lf. ~hen \\e fpeak o(lhe
r. fulu, ior. . 'r h" Jdcurd IllJy propcrly be called dI<
J ,fl.:orJ of the remitone.
D OII':",jlra/h ll of t¡'~ difi"crd "r Ih·¡:w,il<; ,or.
Tht: J lf,:OIJ o(dlc Ce01itolli:. or len::, :J, il=, Illie d:.;.{
of tll~ grca lcr 2d , or whole tvn ~t thl.: : J, ..)th, ;¡n,1("\Ih .
1 'hc uCIIIl)nlh arion is lhc f.¡mc .1.9 t l1.1I of th..: bn:.Hcr :J,
",lid d ll'lc(tlrc: !leed n,u be re1'1.!í!. [~J here.
E XítlH plc of lhe fi 'i. lh Jlrl orJ. No. S I .
'r his !S a propcr JI!"' Jrd, Id ...c t1lJt of lhe: grc.J( ·'r : ..\ ,
bl lJ1Z;