B A S 



prodiicintr in\nr.b!y, and without humnn a'd, tlie fweeteft 

 chord in the whole fydem of harmony 



Here all the phenonn.cn:i are rcprefented and explained, of 

 kindred ilrings beinrr caiifeJ to tremble and found merely 

 by the tremors occafioned in the medium by the tone of a 

 neipthbouring llring or founding body. 



Here too the theory of tuning Ilrings, not only by ten- 

 fion but by weiglUs,' is explained ; from which propor- 

 tions, doubtlcfs, the lyrichord of Plenius was tuned by 

 weights inftcad of ttnfion, fome fifty years ajo. 



Having juftly reftorcd to Galileo the difcovery of the 

 harmonic proportions into which every fingle rtring and 

 founding body divides itfelf when caufed to found, it lecms 

 unnectfiar)' further to explain this phenomenon here. V^ e 

 (hall therefore proceed to the fyftem built on this foundation 

 by Rameau, under the title of Basse Fondamentnk ; con- 

 cerning which, not only the author, but the Fr;nch nation, 

 have gloried as much as if he had difcovered and conquered 

 a new world in the celeflial regions of harmony. 



Basse Fondamentak, or Fundamental Bafe, was firft 

 formed into a fyftem by Rameau, and though the Italians 

 meant the fame thing by baffo principale, fo early as the 

 time of Zarlino, it was not fo clearly explained ; nor were 



B A S 



its derivation or derivatives, from a phyfical experiment, then 

 generally kno-.vn in Italy. 



The natural harmony or cornmon chord to every bafe, 

 confids of the third, fifth, and eighth above the bafe ; or 

 their oftaves, which the Germans call the triad : or rather 

 the iinifon, or any given found, with its third and fifth, con- 

 ftiuitc their triad, without the oftavc. If inftead of the 

 fundamental or loweft found (which Rameau calls tlie 

 generator) the bafe takes the third or fifth of that chord in- 

 ttead of the loweft found or principal bafe, the harmony is 

 fald to he inverted ; and the loweft part, carrying the chord 

 of the fixth, or J, is callt-d the fuppofedbafe, and fometimes 

 the bafib continue. (See SupposED5^;/c,andBAsso Ccnt'inuD.) 

 If any fou.id is added to tlis common chord, except the 

 feventh, the bafe is no longe- fundamental. 



The fundamental bafe fhould move by confonant intervals ; 

 as 3d, 4th, 5th, or 6th : never rifing 'or falhng one note or 

 degree with perfeA and fimilar harmony to both ; as it 

 would occafion a violation of the rule againll Jths and Sths 

 in fucceflion, and preclude all relation and connettion of 

 chord to chord. Common chords may be given to the fol- 

 lowing fundamental bafes in fucceflion. 



bafes : the chords of the 6th and fth are given to the reft. 



In a regular afcent or defcent of the fcale in modern har- uaics ; me i-nuiua ui unc uui anu jui aic wucu lu m 



mony, the rule for accompanying the odave (fee Regle de Rameau (Traite de I'Harmonie, p. 190.) has made all the 



L'Octate) allows only common chords to the key note following bafes fundamental, by accompanying them with 



and the 5th of the key ; which are confequently fundamental common chords. 



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By contrary motion, however, the principal bafe may 

 have, and often has had, common chords with good effedt, 

 when afcending diatonically. 



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And if the feventh were added to many of thefe chord?, 

 they would he ftill more interefting, without divcfting the 

 bafe of the title of fundamental. 



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iior modes, or keys with flat jds. From whatever grave 

 found the harmonies have beeu obferved to arife, they are all 

 component parts of major chords, or keys with fliarp 3ds. 

 In Rameau's Generation harmonique, chap. xii. origine du 

 mode mineur, where we expefted all would be cleared up, 

 we found his derivation of this mode more perplexed and 

 perplexing than any part of his book. He tells us that we 

 arc to find indications given by nature of the minor mode 

 below the principal found, which caufes the 12th and major 

 17th below it to vibrate though not to found. And M. 

 D'Alembert in the firft edition of his " Elements" feems fa- 

 tibfied with this folution. When, after telling us that the 

 I2lh and 17th major are produced by every found imme- 

 diately after it has been heard in its totality : that is, the tone 

 of the whole firing or founding body. That the 12th and 

 17th arifing from this ftring or principal found, are calkd 

 its harmonics, and form, when approximated for the conve- 

 nience of the hand, the common chord major or triad of 

 unifon 3d and ■jth. But to acquire a natura"l origin of the 

 minor mode, if we tune the iztli and major 17th below any 

 found, below C for example, which will be an oftave below 

 the 5th and a double oflave btlow the inferior major 3d, to 

 C, we fliall find when C is ftruck, that its lower 12th and 



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7 7' 7 77 



Of all the experiments that have been made in phyfical 

 haru,ony, there has been no fatisfaAory origin found of mi- 



major 17th will vibrate but not found 



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