CON
(296*)
another
CON
V. Mcrfcnne, indeed, after Kircber, gives Standard tor fettling the comparative Perfection of Intervals with regard to the Agreement of their Extremes in Tune : And 'tis this. . .
The Ycvccvtionot Concordance, fay they, is nothing but the comparing of 1 two or more different Motions which in the fame time affect the auditory Nerve : Now we can t make a certain Judgment of any Confonance, till the Air be as ott ftruck in theTame time by two Chords, as there are Unites in each Member expreffing the Ratio of that Concord, v.g. we can't perceive a Fifth, till two Vibrations of the one Chord, and three of the other are accomplifti'd together 5 which Chords are in length as 3 to 2 : The Rule then is that thofeConcords are the moft fimplc and agreeable, which are generated in the leafl time ; and thofc, on the contrary, the moft compound and harfh, which are generated in the longeft time.
For inftance, let r, 2, 3, be the Lengths of 3 Chords 1:2 is an Octave 52:5a Fifth 5 and 1 : 3 an Octave and Fifth compounded, or a Twelfth. The Vibrations of Chords be- ing reciprocally as their Lengths, the Chord 2 will vibrate once, while the Chord 1 vibrates twice, and then exifts an Octave ; but the Twelfth does not yet exift, becaufe the Chord 3 has not vibrated once, nor the Chord 1 thrice, which is neceffary to form a Twelfth.
Again, for generating a Fifth, the Chord 2 muft vibrate thrice, and the Chord 3 twice ; in which time, the Chord 1 will have vibrated 6 times ; and thus the Octave will be thrice produe'd, while the Twelfth is only produced twice 5 the Chord 2 uniting its Vibration fooner with the Chord 1, than with the Chord 3 ; and they being fooner confonant than the Chord 1 or 2 with that 3.
Whence, that Author obferves, many of the Myfteries of Harmony, relating to the Performance of Harmonious In- tervals and their Succeffion, are eafily deduced.
But this Rule, upon examining it by other Inftances, Mr. Malcolm has fhewn defective, as it does not anfwer in all Poiitions of the Intervals with refpect to each other 5 but a certain Order, wherein they are to be taken, being requir'd : and there being no Rule, with refpect to the Order, that will make this Standard anfwer to Experience in every Cafe: So that at laft we are left to determine the Degrees of Con- cord by Experience and the Ear.
Not but that the Degrees of Concord depend much on the more or lefs frequent uniting the Vibrations, and the Ear's being more or lefs uniformly mov'd, as above 5 for that this Mixture or Union of Motion, is the true Principle, or, at lead, the chief Ingredient in Concord, is evident : But becaufe there fecms to be fomcthing further in the Propor- tion of the two Motions, neceffary to be known, in order to fix a catholick Rule for determining all the Degrees ofCo?i- cord, agreeable to Scnfe and Experience.
The Reiu.lt of the whole Doctrine is fumm'd up in this Definition.
Concord is the Refult of a frequent Union, or Coincidence of the Vibrations of two fonorous Bodies, and, by confe- quence, of the undulating Motions of the Air, which, be- ing caus'd by thefe Vibrations, are like and proportionable to 'em ; which Coincidence, the more frequent it is, with regard to the number of Vibrations of both Bodies, perform 'd in the fame time, ceteris paribus, the more perfect is that Concord: till the Rarity of the Coincidence, in refpect of one or both the Morions, commence "Difcord. See forae of the re- markable 'Phenomena of Sounds accounted for from this theory, under the Word Unison 5 fee alfo Interval, &c.
Concords are divided \\\\o fimple, or original, and compound.
Afitn/de, or original Concord, is that whole Extremes are at a Diftance lefs than the Sum of any two other Concords.
On the contrary, a compound Concord is equal to two or more Concords.
Other Mufical Writers date the Divifion thus : An Oc- tave 1 : 2 and all the inferior Concords above exprefs'd are all fitnple and original Concords : and all greater than an Oc- tave, are called compound Concords ; as being compos'd of, and equal to the Sum of one or more Octaves, and fome An- gle Concord lefs than an Octave, and are ufually, in practice, denominated from t\\a.t fimple Concord.
Js to the Cvmpofition and Relations of the original Con- cords, by applying to them the Rules of the Addition and Subtraction of Intervals, they will be divided into fimplc and compound, according to the firft and more general Notion $ as in the following Table.
Si mple Concord s. 5 : 6 a 3d leff. 4:5a 3d gr. 3:4a 4th.
Compound Concords. [ 5th rsdg.and 3d I. J (5th I. <4th 3d 1.1 <5thg.C4th 5 dg.i
>vc. com- pos'd of
- 5 th 4 or itfthg-sd 1.
w 5 d g. -3d 1. 4th.
The Octave is not only the firft Concord in point of Perfec- tion, the Agreement of whofe Extremes is greatest, and the neareft to Unifon j infomuch that when founded together, 'tis impoflibic to perceive two different Sounds 5 but 'tis alio
the greateft Interval of the feven original Concords $ and as fuch, contains all the lefTer, which derive their fweetnefs from it, as they ariie more or lefs directly out of it; am j which decreafe gradually, from the Octave to the leffer Sixth which has but a frfiall degree of Concord. See Octave. '
What is very remarkable, is the manner wherein thefe lef. fer Concords arc found in the Octave, which Ihews their mu- tual Dependencies.
For, by taking both an Harmonical and Arithmetical Mean between the Extremes of the Octave, and then both an Harmonical and Arithmetical Mean betwixt each Ex- treme, and the molt diftant of the two Means laft found, viz. betwixt the leffer Extreme and the firft Arithmetical Mean, and betwixt the greater Extreme and the firlt Har- monical Mean, we have all the leffer Concords.
Thus, if betwixt 5^0 and 180 the Extremes of Octave we take an Arithmetical Mean, it is 270 ; and an Harmo- nical Mean is 240 : then, betwixt 360 the greatelt Extreme, and 240 the Harmonical Mean, take an Arithmetical Mean, it is 300 ; and an Harmonical Mean, is 28S. Again, be- twixt 180 the leffer Extreme of the Oftave, and 270 the firlt Arithmetical Mean, it is 225, and an Harmonical one 216.
Thus have we a Series of all the Concords, both amending towards Acutenefs from a common Fundamental, 360 ; and descending towards Gravity from a common acute Term, 180 : which Series has this Property, that taking the two Extremes, and any other two at equal Diftances, the four will be in Geometrical Proportion.
The Octave, by immediate Divifion, rcfolves it felf into a Fourth and Fifth 5 the Fifth, again, by immediate Divi- fion, produces the two Thirds , the two Thirds are there- fore found by Divifion, tho not by immediate Divifion 5 and the fame is true of the two Sixths. Thus do all the origi- nal Concords arife out of the Divifion of the Octave ; the Fifths and Fourths immediately and directly, the Thirds and Sixths mediately.
From the Perfection of the Octave arifes this remarkable Property, that it may be doubled, tripled, &c. and yet itilt perlevere a Concord, i. c. the Sum of two or more Octaves are concord 5 tho the more compound will be gradually lefs agreeable : Bur it is not fo with any other Concord lefs than Octave ; the Doubles, &c. whereof, arc all Difcords.
Again, whatever Sound is concord to one Extreme of the Octave is concord to the other alfo : and if we add any other fimple Concord to an Octave, it agrees to both its Ex- tremes ; to the neareft Extreme it is a fimple Concord, and to the farthelt a compound one.
Another thing oblervable in this Syftem of Concords, is, that the greater! Number of Vibrations of the Fundamental cannot exceed five; or that there is no Concord where the Fundamental makes more than five Vibrations, to one Coin- cidence with the acute Term. It may be added, that this Progrefsof the Concords may be carried on to greater degrees of Compofirion, even in infinitum 5 but the more compound, the lefs agreeable.
So a fingle Octave is better than a double one, "and that than a triple one 5 and fo of Fifths, and other Concords. Three or four Octaves is the greateft length we go in ordi- nary Practice : The old Scales went but to two ; no Voice or Inftmmcnt will well go above four. See Third, Fourth, Fifth, &c.
CONCORDANCE, a Diftionary or Index to the Bible, wherein, all the Words, uled in the Courfe of the infpir'd Writings, are rang'd alphabetically - 7 and the various Places where they occur rcferr'd to ; to affift in finding out Paffagesj and comparing the feveral Significations of the lame Word.
Cardinal Hughs is laid to have employ'd 500 Monks at the fame time in compiling a "Latin Concordance : Befide which, we have feveral other Concordances in the fame Lan- guage ; one, in particular, called the Concordance of Eng- land, compiled by J. 'Darlington of the Order of Predi- cants ; another more accurate one, by "Lamora.
R. Mardocbai Nathan has furnifti'd us with a Hebrew Con- cordance, printed at Safil in 1541 ; containing all the He- brew Roots branch 'd into their various Significations, and under each Signification all the Places in Scripture wherein it occurs : But the beft and moft ufeful Hebrew Concordance is that of "Buxtorf.
The Greek Concordances are only for the New Tefta- ment : indeed we have one of Kircher's on the Old ; but this is rather a cancer dantial Dictionary than a Concordance; containing all the Hebrew Dictions in an alphabetical Order ; and underneath, all the Interpretations or Senfes the Seventy give 'em ; and in each Interpretation, all the Places where they occur in that Verfion.
Calafius, an Italian Cordelier, has given us Concordances of the Hebrew, Latin, and Greek, in two Columns ; the firft, which is Hebrew, is that of R. Mardocbai, word for word, and according to the Order of the Books and Chap- ters : On the other Column is a Latin Interpretation of each Paffage of Scripture quoted by R. Mardocbai : This Inter- pretation is CalafivSs own ; but in the Margin he adds that
