SOUND, 



placing the finger lightly in certain divifions of the chord or 

 Uriiig. On account of their fweetnefs, they are called 

 Jluted founds. By Aiding the finger lightly from {harp to 

 flat, from the middle of a chord which is touched at the 

 fame time with the bow, we hear dittinftly a fucceflion of 

 harmonic founds from flat to (harp, which are very aftonifli- 

 ing to thofe who are not acquainted with the theory. See 

 Sons Harmonlques. 



The principle on which this theory is founded is, that if 

 a chord be divided into two parts which are commenfurable 

 with each other, and confequently with the whole chord, 

 and the obllacle placed at the point of divifion obftrufts, in 

 an imperfeft manner, the communication of the vibrations 

 from one part to another ; when it is founded, it will not 

 yield the found of the entire chord, nor that of its greater 

 part, but that of the fmaller part, if it exaftly meafures 

 the other ; or if it does not meafure it, the found of the 

 greateft aliquot common to thefe two parts. Let a chord, 

 as 6, be divided into two parts, as 4 and 2, the harmonic 

 found will be produced by the fmall part, 2, which is the ali- 

 quot of the other, 4 ; but if a chord, as 5, be divided into two 

 parts, as 2 and 3, then, as the fmall part does not meafure 

 the greater, the harmonic found will proceed from the half, 

 I, of the fmall part ; unit being the greateft common mea- 

 fure of the two parts 3 and 2, and of the whole chord 5. 

 By means of tins law, which is conformable to the experi- 

 ments of M. Sauveur and of Dr. Wallis, it is eafy, by a 

 very fimple calculation, to ailign to each tone the harmonic 

 found which anfwers to it. Whilll the finger Aides the 

 length of the chord, we obtain a feries of harmonic founds, 

 which fucceed each other rapidly according to the order of 

 the divifions of the chord, to which the finger is fucceflively 

 applied. 



The firft column of the following table exhibits the founds 

 ■which the divifions of the inftrument would yield when 

 touched full, and the fecond column fliews ih^ jluted founds 

 correfponding to them when the chord is touched harmoni- 

 cally. 



Table of Harnionic Sounds. 



The whole chord") Tthe unifon. 



The minor third the 19th, or double oftave of 



the 5th. 

 the 17th, or double ottave of 



the major third, 

 the double oftave. 

 the 1 2th, or oftave of the fame 



jth. 

 the triple oftavc. 

 the 17th major, or double o£tavc 



of the 3d. 

 _the oAave. 



After the firft oftave, i. e. advancing from the middle of 

 the chord towards the bridge, we fliall have again the fame 

 harmonic founds in the fame order on the fame divifions, i. e. 

 the 19th on the minor 10th, the 17th on the major lOth, 

 &c. Encyclop^die, art. Harmoniquis Sons. See Har- 

 monics, and Harmony. 



Sounds, Third, denote thofe which are produced by 

 founding two notes at the fame time, either on the fame or 

 on two different iullruments ; and which are almotl always 

 graver than the loweft of the two tones that generated them, 

 and are their proper fundamental bafe. 



The difcovery of tlicfe founds has been generally afcribed 

 to Tartini, who publifhed an account of them in his " Tratto 

 di Mufica, fecundo la vera Scien/.a dcll'Armonia," printed at 

 Padua, 1754; but the Encyclopedic, art. //armonfV, attri- 



The major third 



The fourth 

 The fifth 



The minor fixth 

 The major fixth 



The oftave 



gives ; 



butes the firft. difcovery, though probably unknown to 

 Tartini, to M. Romieu, of the Royal Society of Sciences 

 of Montpellier, who pablilhed an account of it in a memoir 

 in 1752. 



The experiment may be made by founding the perfeft in- 

 terval of a 3d, 4th, or 5th, &c. either on two ftrings of 

 the fame violin, or on two viohns played upon at the diltance 

 of about thirty feet, with a ftrong bow, and holding out 

 the notes ; or with two trumpets, hautbois, or German 

 flutes ; the hearer, in the latt mentioned cafes, playing him- 

 felf in the middle of the interval between the two inftru- 

 ments. Thus, e. gr. the interval C r, or a major 3d, pro- 

 duces C, the oftave below the lower note ; C ftiarp e, a 

 minor 3d, produces A, a tenth below the graver tone ; 

 B f, a 4th, gives E, the oAave of the upper note ; By" 

 ftiarp, a 5th, produces an unifon to B ; B^, a 6th, gene- 

 rates the double oftave below the upper note ; and B flat^, 

 or the major 6th, produces E flat, the 5th of the lower 

 note, &c. 



M. Tartini obferves, that the third found refulting from 

 the 4th, from two 3ds, from two 6ths, whether major or 

 minor, is the moft eafily dillinguiftied, becaufe this found is 

 always more grave than either of the two which produce 

 it ; that the third found produced by the jth is diftinguifhed 

 with greater difficulty, becaufe it is an uniU)n of a graver 

 found ; and that it is more difficult to diftinguiih it in the 

 tones major and minor, becaufe thefe tones, differing httle 

 from one another, are eafily confounded in the intonation ; 

 and for the fame reafon, with greater difiiculty, in the femi- 

 tones major and minor. 



The author, in a fong compofed of two parts, difcovers, 

 by means of two correfponding founds, the third found re- 

 fulting from them ; and this, he fays, is the true bafe of 

 the fong ; and every other bafe will be a paralogyfm. From 

 his experiments and reafoning he concludes, that if any ad- 

 joining two fimple intervals in the harmonic feries i, -5) j» i» 

 &c. be founded, the third found will always be that of half 

 the ftring ; that the fmaller the interval is, the farther dif- 

 tant is the third found : fo that, e.g. the third found to the 

 interval of the femitone minor G G (harp, is the 26th below 

 G natural. 



M. Serre, of Geneva, in his '< Eftai fur les Principes de 

 I'Harmonie," printed at Paris in 1755, mentions this dif- 

 covery of Tartini as a faft fufficiently al'ccrtained ; and adds, 

 that he has produced the fame effedl by means of two fine 

 female voices, as Tartini Iiad done by inftruments ; but he 

 mentions only the third (ound produced by the third major, 

 and that produced by the third minor : and there is this dif- 

 ference between the refults of thefe two gentlemen. Accord- 

 ing to M. Tartini, the two founds of a third major, as ut mi, 

 produced the oftave ut below ut ; and according to M. Serre, 

 a double odave : according to the former, the two founds 

 of a third minor, /a ut, produced the tenth major, fa below 

 la ; but according to the latter, the feventeenth major below 

 la, or the ottave under the tenth/j. M. Serre takes no 

 notice of a third found produced by any other two founds, 

 and it does not appear that he made any trials of this 

 kind. 



As to the phyfical caufe of thefe third founds, it is much 

 more difficult to ofler any plaufible conjefturcs concerning 

 it, than concerning the harmonical notis mentioned in the 

 preceding article ; becaufe all thole of the latter kind being 

 more acute than the principal, or generating tone, are, for 

 that reafon, capable of being actually and immediately pro- 

 duced by the vibrations of certain portions ut tlie firing or 

 other foundiiij; bidy ; whereas, in the third (ounds, a tone 

 is heard always (except m the caie of the fifth), and often 



conii- 



