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Sve to A, that is I to 2. For the mutual Relations of
the acute Terms, B, C, D, they are bad by taking their
primary Relations to the fundamental, and fubflrading
each leffer from each greater : Thus, B to C is 5 to 6,
a 3d i;  B to D is 5 to 8, a 6th , &c.-Lallly, to
find the fecondary Relation of the whole, feek the leaff
common Dividend to all the letaer Terms or Numbers of
the primary Relations, i. e. the leafl Number that will
be divided by each of them exadly: This is the Thing
fought; and Ibews that all the fimple Sounds coincide
after fo many Vibrations of the Fundamental as the Num-
ber expreffes.
So in the preceding Example, the leffer Terms of the
three primary Relations are 4, a, I, whofe leafl common
Dividend is 4. Confequently, at every 4th Vibration of
the fundamental, the whole will coincide.
Now Harmony, we have obferved, is a compound Sound,
confifling of three, or more, fimple Sounds. -  Its proper
Ingredients are Concords; and all Difcords, at leafl in the
primary and mutual Relations, are abfolutely forbidden.
'Tis true Difcords are ufed in Mufic; but not for them-
felves fimply, but to fet off the Concords by their Contrafl
and Oppofition. See DAscoRD.
Hence, any Number of Concords being propofed to fland
in primary Relation with a common Fundamental- we
difcover whether or no they conflitute a perfed Harmony
by finding their mutual Relations. - Thus, fuppofe the
following Concords, or primary Relations, viz. the greater
g d, 5th, and Odave given; their mutual Relations are
all Concord, and therefore may fland in Harmony.  For
the greater 3d and 5 th are to one another, as  : 6, a
lecffr third. Thc  greater 3d and Odave, are as 5: 8 a
leffer 6th. And the 5 th and Odave are as -: & a letter
fourth. But if 4th, 5 th, and 8 ve, be propofed, 'tis evi-
dent they cannot fand in Harmony; by Reafon betwixt
the 4th and 5th there is a Difcord, viz. the Ratio 8 : 9.
Again, fuppofing any Number of Sounds which are Con-
cord, each to the next, from the lowell to the highefi-
to know if they can fland in Harmony, we mull find the
primary, and all the mutual Relations, which mufl be all
Concord.  So let any Number of Sounds be as 4: 5: 6
: 8, they may fland in Harmony by Reafon each to each
is Concord: But the following ones cannot, viz. 4, 6, 9,
becaufe 4: 9 is I~fcord.
The neceffary Conditions of all Harmony, then, are
Concords in the primary and mutual Relations; on which
Footing, a Table is eafily form'd of all the poffible Vari-
eties : But to determine the Preference of Harmonies, the
fecondary Relations are likewife to be confider'd. - The
Perfedfion of Harmonies depends on all the three Relations:
It is not the belt primary Relations that make beft
Harmony: For then a 4th and 5 th mufl be better than
a 4th and 6th. Whereas the firfi two cannot fland to-
gether, becaufe of the Difcord in the mutual Relation:
Nor does the bell fecondary Relation carry it; for then
would a 4th and 5 th, whofe fecondary Relation with a
common Fundamental is 6, be better than a lefrer 3 d and
5th, whofe fecondary Relation is lo : But here alfo the
Preference is due to the better mutual Relation. - Indeed,
the mutual Relations depend on the primary ; tho' not fo,
as that the befd primary fhall always produce the bell
mutual Relation: However, the primary Relations are of
the moft Importance; and together with the fecondary,
afford us the following Rule for determining the Prefe-
rence of Harmonies.
Viz. Comparing two Harmonies, which have an equal
Number of Terms, that which has the bell primary and
fecondary Relations, is mofl perfed. - But in Cafes, where
the Advantage is in the primary Relation of the one, and
the fecondary of the other, we have no certain Rule:
The primary are certainly the mofi confiderable; but how
the Advantage in thefe ought to be proportion'd to the
Difadvantage lit the other, or vice verfa, we know not.
So that a well turned Ear muft be the left Refort in
thefe Cafes.
Harmony is divided into Simple and Compound.
Simple HARMONY, is that where there is no Concord
to the fundamental above an OWave.
The Ingredients of fimple Harmony, are the feven fimple
original Concords, of which there can be but i8 different
Combinations, that are Harmony; which we give in the
following Table from Mr. Malcolm.
T'able of fixpkI HHARRmIES.s
th
4th
6th g
3d g
1;   I
sth/
,Idsry Rel.
8ve   2
8 vc  3
8ve 3
8ve   3 4
8ve   4 ,
8ve   5 3
8 ve        4
,it
;dg9      5 th
; d       5th
1.th~,6th, &
;dg 6th g
;d 4, 6th I
~ th, 6th I
lary Rdel
4
I.
3
5
'5 .
I3d /   5th 8ve
4th, 6th, g 8ve
3d g, 6th g Bye
3d 4, 6th l, 8ye
4th, 6th 1, 88e
Thefe are all the poffible Combinations of tie Concods
that make Harmony: For the 8ve is compounded of a
5th and 4th, or a 6th and 3d; which have a Variety
of greater and leier; out of thefe are the firli fix libr-
monies compofed: Then, the 5th being compofed of the
greater 3d, and leffer 3d, and the 6th of 4th and 3d;
from thefe proceed the next fix of the Table: Then an
Sve joyn'd to each of thefe 6, make the lafl fix.
The Perfedlion of the firft twelve is according to the
Order of the Table : Of the firfl fix each has an Oclave,
and their Preference is according to the Perfedfion of the
other leffer Concord joyn'd to the 06tave. - For the next
fix, the Preference is given to the two Combinations with
the 5th, whereof that which has the 3d g is bell; then
to thefe two Combinations with the 6th g, of which that
which has the 4th is beff. -For the lafd fix, they are
not placed lafl, as being the leall perfed, but becaufe they
are the moll complex, and are the Mixtures of the other
IX with each other. In Point of Perfeffion they are plainly
preferable to the preceding fix, as having the very fame
Ingredients, and an Octave more.
Compound HARMONY, is that which to the fimple Har-
mony of one Odave, adds that of another Odave.
For the Compound Harmnonies, their Variety is eafily
found out of the Combinations of the fimple Harinonies
of feveral Ocdaves.
Harmony, again, may be divided into that of CConcor.is,
and that of fDifcords.
The firfl is that we have hitherto confider'd, and wherein
nothing but Concords are admitted.
The fecond is that wherein Difcords are ufed, intermix'd
with the Concords. See HARMONICAL COXipoficion1.
Compofirion of HARMONY. See HARMONIC Comtpoftionl.
HARMONY, is Sometimes alfo ufed in a laxer Senfe,
to denote an Agreement, Suitablenefs, Union, Confor-
mity, Ec.
The Word is form'd of the Greek eovMX    of the Verb
convenire, congruere, to agree, match, &c.
In Mufic, we fometimes apply it to a finale Voice, when
fonorous, clear, and foft; or to a fingle Infirument, when
it yields a very agreeable Sound. - Thus, we fay, the
Harmony of her Voice: of his Lute, Uc.
In Matters of Learning, we ufe Harmony for a certain
Agreement between the feveral Parts of a Difcourfe, which
renders the reading thereof agreeable. - In this Senfe we
fay Harmonious Periods, E'c. See PERIOD, NUMBERS, SC.
In Architedure, Harmony denotes an agreeable Rela-
tion between the Parts of a Building. See SYMMETRY.
In Painting, they fpeak of a Harmony, both in the
Ordonnance and Compofition, and in the Colours of a
Pidure. - In the Ordonnance, it fignifies the Union, or
Connecdion between the Figures, with Refped to the Sub-
jed of the Piece. See ORDONNANCE.
In the Colouring it denotes the Union, or agreeable
Mixture of different Colours. See COLOURING.
M. de la Chambre derives the Harmony of Colours from
the fame Proportions, as the Harmony of Sounds. - This
he infibfs on at large, in his Treatife of the Colours of
the Iris. On this Principle, he lays down green, as the
mofd agreeable of Colours, correfponding to the Od6ave in
Mufic;   red, to a fifth yellow, to a fourth, Wc.
The Name Harmony, or -Evangelical Harmony, is ufed
as the Title of divers Books, compofed to fhew the Uni-
formity andL Agreement of the four Evangelifls.    See
EVANGEL1T.
The firfl Attempt of this Kind is attributed to l'arian,
or T'heophizlus of Antioch, in the I1d Century. -After his
Example, divers other Harmonies have been compofed, by
A4mmonius of Alexandria, Eufebius of CGarea,   Yanfe f
vius Bifhop of Gant, Monf.  2.iinard, Mr. Whijfon, &c.
HARMONY of the Spheres, or Celeflial HARMONY, is a
Sort of Mufic, much fpoke of by many of the Philofophers
and Fathers;   fuppofed to be produced by the regular,
fweetly tuned Motions of the Stars and Planets.    See
SYSTEM.
Plato, Philo 7ud'fus, St. 4ug ufline, St. Almbrofe, St.
IEdore, Boetius, and many others, are firongly poffefs'd
with the Opinion of this Harmony, which they attribute
to the various and proportionate Impreffions of the hea-
venly Globes upon one another;   which ading under proper
Intervals, form a Harmony.
It is impoflible, according to them, that fuch fpacious
Bodies, moving with fo much Rapidity, fhould be filent -
on the contrary, the Atmofphere, continually impellk!
by them, muil yield a Set of Sounds, proportionate to
e   Impulfions it receives:  Confequently, as they do not
all run the fame Circuit, nor with one and the fame
Velocity, the different Tones arifing from the Diverfity of
Motions, direded by the Hand of the Almighty, form an
admirable Symphony, or Concert. See Music.
*Ggg                                           St.
14 A k