CON 



109 



C ON 



and XVII, to their respective originals, seems to point 

 out one reason of these and the double octave being the 

 only Tartinian sounds that are heard to accompany a 

 note; since no other doubled concords but XII and 

 XVII, have a less sum to the terms of their ratio, than 

 their originals have. It is further observable, that X 

 and XIX or VIII + III and 2 VIII + V, are interposed 

 here, between the 4th and VI of the original series ; 

 that XXII or 3 VIII is interposed between III and 3d ; 

 and 11th and XXIV or VIII + 4th and 3 VIII + III 

 between 3d and 6th. 



Whatever confirmation Dr Smith's position {Harmo- 

 nics, 2d edit. p. 2 ! ), respecting the comparative simplicity 

 of the concords, as above, agreeing with their order as 

 to smoothness and pleasant sensations that they excite on 

 the ear, may receive from the preceding Tables, it must 

 be plain, from an inspection of his general Table of the 

 order of the simplicity of consonances, including both 

 concords and discords, those beyond, or expressed by 

 larger primes than 5, as well as those in the received 

 system of music that involve no such large primes, that 

 this is an imperfect and false rule of judging of the 

 smoothness or harmoniousness of consonances in gene- 

 ral, since in his table, the false tripled minor seventh 

 of the trumpet, 4, or 2 VIII + 7th— 1:1.947 1 2 — m, oc- 

 curs before the perfect VI, and the tripled major tone 

 §, or 2 VIII + 11, a discord, before the perfect 3d! 

 which must be quite contrary to their comparative ef- 

 fects on the ear. 



We should, perhaps, earlier have pointed out, from 

 our series of the fifty concords in seven octaves, given 

 above, that the three least, or 3 rd , III, and 4 th , being 

 considered as the simple concords, or concordant ele- 

 ments, the three next largest, V, 6, and VI, are genera- 

 ted by adding these simple ones in pairs, in every pos- 

 sible way, and the next, or VIII, by adding the three 

 together ; and that every succeeding concord in the 

 scale, is generated by adding an octave (3 + III + 4), 

 or two octaves (2 3, 2 III, 2 4), or three octaves, &c. to 

 each one of the seven original concords in the first oc- 

 tave. Whence it appears, that no concord but the oc- 

 tave will bear adding to itself once, or any greater 

 number of times, (without other combinations,) with- 

 out becoming a discord ; but that the addition once, or 

 any greater number of times of the octave, to any con- 

 cord, will produce another concord. 



That the complement, or remainder, when any one 

 of the original concords is taken from the octave next 

 above, or VIII, or from any of the succeeding octaves, 

 the remainders are all concords; and so are the comple- 

 ments of any of the doubled, tripled, quadrupled, &c. 

 concords in the second, third, fourth, &c. octaves, to 

 the next, or any succeeding octave above them ; and 

 in like manner, in the second, third, fourth, fifth, &c. 

 octaves, one or more VIII ths may be taken away from 

 any of the concords therein, and still leave remainders 

 that are concords, &c. 



Among the various attempts of philosophers to de- 

 fine the limits, or shew characteristic distinctions be- 

 tween concords and discords, generally, Mersenne and 

 Kircher maintained, that those consonances are most 

 simple or agreeable which are generated in the least 

 time, or have the smallest least terms to their ratios ; 

 and those, on the contrary, the most compound and 

 harsh, which are generated in the largest time, or 

 have the largest least term or numerators to their ratios. 

 This ride is shewn, however, by Malcolm, to be defec- 

 tive; and Dr Smith has done the same thing, and 



Condalia. 



thence concludes, " that the frequency of coincidences Concord 

 is of itself too general a character of the simplicity or 

 smoothness of a consonance, and therefore an imper- 

 fect one." {Harmonics, p. 23.) In another place, Dr 

 Smith says, (p. 1 5.) that it is the " mixture of pulses 

 succeeding one another in a given cycle of times, ter- 

 minated at both ends by coincident pulses, and suffi- 

 ciently repeated, which excites the sensation of a given 

 consonance ;" and " one consonance may be consider- 

 ed as more or less simple than another, according as 

 the cycle of times belonging to it, is more or less sim- 

 ple than the cycle belonging to the other." 



M. Elder says, when the ear readily discovers the re- 

 lation subsisting between the terms of the ratios of two 

 notes, their combination is denominated consonance or 

 concord ; and if it be very difficult, or even impossible, 

 to catch this relation, the combination is termed disso- 

 nance, or discord." Letters, vol. i. 



Mr Holder attempts, but without any success, to ac- 

 count for the pleasure derived from concords, or sounds 

 in the more simple musical ratios, by the mind being 

 occupied in parcelling out the numbers, but not by 

 division, (which with primes is indeed impossible,) but 

 by unequal and fanciful partitions of them into what he 

 calls factors or parcels, as 5 into 2, 1, 2, 7 into 3, 1, 3, 

 &c. ; and principally on this whimsical ground, he la- 

 bours to shew, that 7 ought to have place among mu- 

 sical ratios ! &c. " No combination," says he, " ought 

 to be esteemed concord, however simple and eligible 

 its terms may be in every other respect, if the implied 

 sound (that is, its grave harmonic) be three octaves or 

 more below the lower term." Essay, p. 376. And 

 again, " An interval which is concord in the upper 

 parts, is often no concord when taken in the bass !" 

 for " we lay it down as a rule, that the implied sound 

 of a concord ought always to be within the limits of 

 audible sound." The introduction of which last ab- 

 surdities into his Essay, Mr Farey has shewn to have 

 arisen, from Mr Holder being unacquainted with the 

 true nature of the grave harmonics, or the rule for cal- 

 culating those belonging to any assigned consonances. 



Dr Robison says, " a musical sound is the sensa- 

 tion of a certain form of the aerial undulation which 

 agitates the auditory organ. The perception of har- 

 monious sound, is the sensation produced by another 

 definite form of the agitation : This is the composition 

 of two other agitations ; but it is the compound agita- 

 tion alone that affects the ear, and it is its form, or 

 kind, which determines the sensation, making it plea- 

 sant or unpleasant, or in other words a concord or a 

 discord." Our limits will not admit of enlarging fur- 

 ther on this very curious and intricate subject, which 

 presents yet a rich field for the successful cultivator of 

 it. ( s ) 



CONCORDANT Elements, m Music. Consonant 

 elements, or simple concords, are the minor and maior 

 third, and the minor fourth, 3 rd , III, and 4 th , or three 

 least concords, which by addition form all other con- 

 cords that are known ; every combination of them, 

 singly, by two's and by three's, being concords, &c. as 

 shewn in the article Concord. Intervals when ex- 

 pressed in the notation by concordant elemtnts, are ca- 

 pable of being tuned by means of perfect concords on- 

 ly, on instruments like the euharmonic organ of Mr Lis- 

 ton, having a sufficient number of pipes, {e) 



CONCUSSION. See Surgery. 



CONDALIA, a genus of plants of the class Pentan- 

 dria, and order Monogynia, See Botany, p. 177- 

 1 



