B A S 



college, witliout knowing- that Mr. Noble had difcovered it 

 before." As we are now only proving a claim, we need 

 cite no more of this paper ; at the end of which another 

 paper is referred to (N^ 135. p. 879.), which reference fays: 

 " Concerning thefe phenomena, an exquifite folution is given 

 b? Dr. NarcifTus Manli, in Dr. Plot's -Natural Hiftory of 

 dxfordlhire." 



D'Alembert (Elemensde Mufique) fpeaks of Rameau 

 as the difcovf rer of the harmonics, as well ai; author < f the 

 fyftem built upon them. In the preface to the fccond edi- 

 tion of his Elements of Mufic, in which he has abriilged and 

 methodized the mufical tratts of Rameau, he fays ; " it was 

 Rameau who firft bega:! to reduce chaos into order, and 

 throw a light upon the principles of harmony. 



" He found in the relonance of a fmgle ftring or founding 

 body, the moft probable origin of harfnony, and of the plea- 

 fure which it affords us ; he developed this principle, and 

 (hewed whence the phenomena of mufjc were derived," 

 &c. 



And RoufTeau, Dift. de Muf. art. Harmonic, fays, that 

 *' Pere Merfcnne and M. Sauveur having found that every 

 found, though fecmingly a limple unifon, was always accom- 

 panied by other founds lefs diftinguilliable, which formed 

 with it the common chord major ; and M. Rameau, fetting 

 off from this experiment, made it the bafis of his harmonical 

 fyftem, which M. D'Alembert at length took the trouble of 

 explaining to the public." 



Rameau himfelf, in bis Nouveau Syfteme de Mufique, 

 publiihed 1726, fays "we have in our nature the germ of 

 harmony, witliout knowing it. It is however eafy to per- 

 ceive it in the found of a ftring, a pipe, S<c. in the tone of 

 which there are three different founds at once." In a note he 

 adds, «' this experiment is cited by different authors." But 

 he does not feem to know their names. Rameau's accoiuit 

 feems to have been taken from our Phil. Tranf. quoted 

 above, where it was fuppofed to be an Englifh difcovtr)-. 

 But in p. 17 of his treatife, he refers to ^lerfenne's Harm. 

 Univerlelle, chap, des luftrumens, p. 209. for the invention; 

 but Merfenne, in the very title of the chapter alluded to, rclin- 

 quifhes all claim to the dilcovcry, by merely promiHng his 

 readers " to explain many circumftances and properties of 

 motion, natural or forcei, oblique or perpendicular, where 

 the ideas and experiments of Gahlco are examined." 



This puts it out of all doubt who was the firft difcoverer 

 of this raufical phenomenon. But the name of the true 

 claimant does not feem to have been mentioned by any 

 writer in England before the year 1748, when Dr. Smith 

 firft publiihed his Harmonics ; who begins the firft fcftion 

 of that fcientific work in the following manner. " Sound 

 is caufed by the vibrations of elaftic bodies, whicli communi- 

 cate the like vibrations to the air, and thefe the like again to 

 our organs of heaiing. 



" Philofop'.iers are agreed in this, bccaiifc founding bodies 

 communicate tremors to dillant bodies. For inftance, the 

 vibrating motion of a mufical ftring puts others in motion, 

 whofe tenfion and quantity of matter difpofe their vibrations 

 to keep time with the pulfes of air propagated from the 

 firing which was ftruck. Gahlco explains this phenomenon 

 by obferving, that a heavy pendulum mav be put in motion 

 by the leaft breath of the mouth, provided the blafts be 

 frequently repeated, and keep time exactly with the vibra- 

 tions of the pendulum ; and alfo by the like art in raifing a 

 large bell ; and probably he was the fii ft that rightly ex- 

 plained that phenomenon." 



And now, having traced this curious difcovery to the 

 fountain-head, we fliall draw all furlhtr information f;om 

 that fource. 



B A S 



The admirable Galileo, perhaps the moft aci-.te and ufcful 

 experimental philofophcr of any age or countiy, in his firft 

 dialogue (Opera del Galileo, vol. ii. Bologna 1655.), after 

 difcufling the vibrations of pendulums, which he firft ap- 

 plied to the meafuring of time, proceeds with his friends 

 Sagredo, an intelligent enquirer into mechanical powers, 

 who a(]<s queftions of difficult folution ; and SimpUcius, a 

 5-oung philofopher, curious concerning the caufes of comm.on 

 effects. Galileo, under the name of Salviati, after difcufling 

 the doctrine of motion, and the range of cannon-balls, fays ; 

 " vengo ora da i quefiti di V. S. dirvi qualche mio penfiero 

 fopra alcuni problemi Lttcnenti alia mufica ; and now, at 

 your requeft, gentlemen, I fiiall give you my thoughts on 

 ibme mufical problems, a noble fubjert, on which fo many 

 great men have written, and, among the reft, Ariftotlc 

 himfelf; concerning which he has left us many curious 

 problems ; fo that if by fnch eafy and intelligible experi- 

 ments I (hall be able to account for the wonderful pheno- 

 mena of found, I may perhaps hope that my reflection* 

 would amufe you. 



" Sagredo. They will not only amufe me, but are what I 

 moft particularly wifli for, being extremely delighted with 

 all mufical inftruments ; and though I beftowed much medi- 

 tation on harmonical confonances, I have always remained 

 perplexed and unable to account for one of thefe intervals 

 pl.afing me more than another. For fomc not only give me 

 no pleafure, but are extremely offtnfive to my ear; and 

 that cotnmon problem of two firings tuned in unifon, when 

 one. of them is caufed to found, the other not only vibrates 

 but aftually founds, I ttill am unable to folve ; nor do I 

 clearly underftand the forms of confonances, or many other 

 particulars concernmg them." 



" Salviati. Let us try whether from our doftrine of pen- 

 dulums we cannot acquire fome information concerning thefe 

 difBculties. And as to the firft doubt, which is, whether 

 it bt true that the fame pendidum performs all its ofcillations, 

 whether its fwing be the greateft, the mean, or tlie leaft, 

 exactly in equal times ? I ftiall depend on what our pro- 

 feffor told us, who has clearly demonftrated that a pendulum 

 fubtending any arcs whatever, paffes them all in equal times, 

 i.e. whether of 180^, or 60, 10, 2, | a degree, or of four ■ 

 minutes, fuppofing them all to terminate in the loweft point, 

 which touches the horizontal plane — all is pei-formed in . 

 equal times." This accounts for the tone of a ftring not 

 finking or changing as the vibrations become more feeble. 

 Here too he gives the ratio of vibrations ; and afterwards 

 the hiftory of his difcovering in a church, from the fwing of a 

 lamp, the laws of a pendulum, and that all its ofcillations %vere 

 ifochror/ous; This doCbine he applied to the vibrations of 

 mufical ftrings, upon the nunr^ber of which the gravity ard 

 acutcnefs of founds more depend than on their length, ten- 

 fion, or thicknefs. It feen s as if few difcoveries had been 

 made in the philofophy of found fince this dialogue was : 

 written. Galileo has demonftrated that if a ftring founding 

 C, for exan.ple, be divided by a moveable bridge into h.alt, 

 each half would be an octave to the whole ; if divided into 

 three parts, each would be a fifth to the oitave ; divided into 

 four parts, each v.ould be a fifteenth or double odlave to the 

 whole ; if into five parts, each would be a major fcventfenth 

 (commonly called a tierce or (harp third) to the fifteenth or 

 double oftave. 



Though thefe divifions arc the fame as the ratios afcribed to 

 Pythagoras, and thofe of Euclid in the fedtion of the canon ; 

 and though long before Gahleo's time, the chorus of a 

 full organ had been conftrufted on the principle of the har- 

 monics to a fundamental bafe, there can be no dovtbt but 

 that this great philofopher firil carght nature in the fact of 



producing 



