HAR
Sve to A, that is i to z. For the mutual Relations of the acute Terms, B, C, D, they are had by taking their primary Relations to the fundamental, and fabfiraffine each leffer from each greater : Thus, B to C is 5 to 6,
% I l; r f? D ls ' t0 8 ' a 5th l < &c - — Laflly, to rind the lecondary Relation of the whole, feek the leaft common Dividend to all the leffer Terms or Numbers of the primary Relations, i. e. the leaft Number that will be divided by each of them exaflly : This is the Thins iougnt; and fbews that all the fimple Sounds coincide alter lo 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, z, 1, whofe leaft common
[ 205) ]
HAR
Thefe are all the poffiblc Combinations of the Concords that make Harmony : For the 8ve is compounded of a 5 th and 4 th, or a ffth and 3d; which have a Variety of greater and leffer; out of thefe arc the firft fix War- monies compofed : Then, the 5 th being compofed of the greater;d, and leffer 3d, and the sth 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 laft fix.
The Perfection of the firft twelve is according to the Order of the Table : Of the firft fix each has an Octave and their Preference is according to the Perfection of the other leffer Concord joyn'd to the Octave. — ■ For the next fix, the Preference is given to the two Combinations with the 5th, whereof that which has the 3d p- is beft;
nivid;^;„ '„ r£ r ■ *' ' ' , ,, ., "™™" the 5 th . whereof that which has the 3 d p is beft; then
4 " I ^ T? Nf CTer> 4 4tH Vlbration of t0 *efi two Combinations with the 6 th g, of which that
the fundamental, the whole will coincide.
Now Harmony, we have obferved, is a compound Sound, confifting of three, or more, fimple Sounds. — Its proper Ingredients are Concords; and all Difcords, at leaft in the primary and mutual Relations, are abfoiutely forbidden, "lis true Difcords arc ufed in Mufic; but not for them- felvcs fimply, but to fet off the Concords by their Contrail and Opposition. See Discord.
Hence, any Number of Concords being propofed to ftand in primary Relation with a common Fundamental; we found out of the Combinations"of th dncover whether or no they conftitute a perfect Harmony of feveral Octaves by finding their mutual Relations. — Thus, fuppofe the Harmony, again, may be divided into that of Concord following Concords, or primary Relations, viz. the greater and that of SifcordT thit of Coacoi ..S,
? lf'c„;ord nd ,°i l r g f TCn; ^f fl Rdati0 ' 1S 3re Thesis that we'have hitherto confider'd, and wherein all Concord, and therefore may ftand in Harmony. For nothing but Concords are admitted.
which has the 4 th is beft. — For the laft fix, they an not placed laft, as being the leaft perfefl, but becaufe they are the rnoft complex, and are the Mixtures of the other 12 with each other. In Point of Perfection 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 Octave, adds that of another Octave.
For the Compound Harmonies, _ their Variety is eafily
fimple Harmonies
the greater 3d and 5th are to one another, as 5 : 6. leffer third. The greater 3d and Octave, are as 5 : 8 a leffer ffth. And the 5 th and Octave are as 3 : 4. a leffer fourth. But if 4th, 5 th, and 8 ve, be propofed, 'tis evi- dent they cannot ftand 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 loweft to the higheft • to know if they can ftand in Harmony, we muft find the primary, and all the mutual Relations, which mull be all Concord. So let any Number of Sounds be as 4 : 5 : 6
- 8,^ they may ftand in Harmony by Reafon each to each
is Concord : But the following ones cannot, viz, 4, 6, 9, becaufe 4:9 is Difcord.
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 Perfection of Hi. r monies depends on all the three Relations : It is not the beft primary Relations that make beft Harmony: For then a 4th and 5th muft be better than a 4th and 6th. Whereas the firft two cannot Hand to- gether, becaufe of the Difcord in the mutual Relation : Nor docs the beft 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 leffer 3 d and 5 th, whofe fecondary Relation is 10 : But here alfo rhe Preference is due to the better mutual Relation. — Indeed, the mutual Relations depend on the primary; tho' not fo, as that the beft primary ihall always produce the belt mutual Relation : However, the primary Relations are of the moft Importance; and together with rhe fecondary.
The fecond is that wherein Difcords are ufed, intermix'd with the Concords. See Harmonical Compofition.
Compofition d/Harmony. See Harmonic Compofition.
Harmony, is fomctimes alfo ufed in a laxer Senfe, to denote an Agreement, Suitablcncfs, Union, Confor- mity, %$c.
The Word is form'd of the Greek dg/aria, of the Verb
- f!'-K°-™> con-venire, congruere, to agree, match, iSc.
In Mufic, we fometimes apply it to a Angle Voice, when fonorous, clear, and foft; or to a fingle Inftrument, when it yields a very agreeable Sound. — Thus, we fay, the Harmony of her Voice : of his Lute, £?c.
In Matters of Learning, we ufc 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, £?c. See Period, Numbers, &c.
In Architecture, 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 Picture. — In the Ordonnance, it fignifies the Union, or Connection between the Figures, with Refpect to the Sub- ject 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 infills on at large, in his Treatife of the Colours of the Iris. On this Principle, he lays down green, as the moft agreeable of Colours, correfponding to the Octave in Muhc; red, to a fifth; yellow, to a fourth, £5?c.
1 he Name Harmony, or Evangelical Harmony, is ufed afford us the following Rule for determining the Prefe- J s the Tltle of <iivt ' 1 ' 5 Books, compofed to fhew the U rence of Harmonies. ' formity and Agreement of the four
Viz. Comparing two Harmonies, which have an equal Number of Terms, that which has the beft primary and fecondary Relations, is moft perfect. — ' But in Cafes, where the Advantage is in the primary Relation ol the one, and the fecondary of the other, we have no certain Rule : The primary are certainly the raofl confiderable; but how the Advantage in thefe ought to be proporrion'd to the Difadvantage in the other, or vice verfa, we know not. So that a well turned Ear muft be the laft Rcfort in thefe Cafes.
Harmony is divided into Simple and Compound.
Simple Harmony, is that where there is no Concord to rhe fundamental above an Octave.
.. Evangclifts. See Evangelist.
The firft Attempt of this Kind is attributed to Tatian or Tbeophihis of Antioch, in the lid Century. — After his Example, divers other Harmonies have been compofed by Ammonias of Alexandria, Eufebius of C^farea, Janfe- nms Bifhop of Gam, Monf. Toinard, Mr. Ifhifton, Sic.
Harmony of the Spheres, or Celeflial Harmony, is a Sort of Mufic, much fpoke of by many of the Philofephers and Fathers; fuppofed to be produced' by the regular fweetly tuned Motions of the Stars and Planets. See System.
JPlato, <Philo Judzns, St. Auguftine, St. Ambrofe, St. lpdore, Soetius, and many others, are ftrongly pofiefs'c!
The Ingredients of fimple Harmony, are the feven fimple w ' t ' 1 l ' ie Opinion of this Harmony, which they attribm. original Concords, of which there can be but 18 different t0 the various and proportionate Impreffions of the hea Combinations, that are Harmony; which we give in the Vi
following Table from Mr. Malcolm.
Table of fimple Harmonies.
5 th
8ve
2
3 d S 5*h
4
3d g, 5 th 8 ve
4 th
8ve
3
3d / 5 th
10
3d /, 5th 8ve
6th g
8ve
3
4 th, 6 th, g
3
4th, 6th, g 8ve
3d&'
Sve
4
3 d g, 6th g
12
3 dg,6th s 8ve
3d I
8ve
5
3d /, (5th /
5
3d /, 6th /, Sve
6 th/
8ve
5
4 th, 6th I
'5
4th, 6th /, 8ve
venly Globes upon one another; which acting under proper Intervals, form a Harmony.
It is impoflible, according to them, that fuch fpacious Bodies, moving with fo much Rapidity, Ihould be filent; on the contrary, the Atmofphcre, continually impell'd by them, muft yield a Set of Sounds, proportionate to the Impulfions it receives : Confcquently, as they do not all run the fame Circuir, nor with one and the fame Velocity, the different Tones arifing from the Diverfity of Motions, directed by the Hand of the Almighty, form an admirable Symphony, or Concert. See Music.
- Ggg
St
