PY'rHAGORAS. 



the ad 



.,. addition of an eighth to the lyre (Phny, hb. n. cap. 2. ; 

 the harmony of th. fphercs (Plato) ; and the Greek mal.- 

 cal notation (ISotthius). His right, indeed, to fomeof thcle 

 difcoveries has bc-rn difputed by fcveral authors, who have 

 given them to others with as little reafon, perhaps, as they 

 liad been before bellowed upon him. 



But there is one difcovcry, relative to mufic, that has, at 

 all times, been unanimoufly alhgned to him, which, how- 

 ever, appears to us extremely doubtful, not only whether it 

 was made by him, but whether, in the manner it is rejated, it 

 was ever made by any one. t i-v i 



We are told by Nicomachus, Gaudentius, .Tamblichus, 

 Macrobius, and all their commentators, « that Pythagoras, 

 one day meditating on the want of fome rule to guidq the 

 ear, analogous to what had been ufed to help the other 

 fenfes, chanced to pafs bv a blackfmitli's fhop, and obfervmg 

 that the hammers, which were four in number, founded 

 very harmomoufly, he had them weighed, and found them 

 to be in the proportion of 6, 8, 9, and 12. Upon this he 

 fufpended four ftrings, of equal length and thickncfs, &c. 

 fallened weights, in the above-mentioned proportions, tocacli 

 of them reipeaively, and found that they gave the fame 

 founds that the hammers had done ; -viz. the fourth, iittli, 

 and oftave to the gi-aveft tone ; which laft interval did not 

 make part of the mufical fyftem before ; for the Greeks had 

 gone no farther than the heptachord, or fevcn ftrings, tiU 

 that time." Principles and Power of Harmony, p. 8. 



This is the fubftance of the account, as it has been lately 

 abridc^ed by Mr. Stillingfleet, who points out many incredi- 

 ble cTrcumftances with refpedt to the ftory in general, and 

 denies that the weights 6, 8, 9, 12, would give the inter- 

 vals pretended ; but feems not to have fecn the leaft difhculty 

 in the fact, relative to liferent hammers proJuchig d'ljerent 

 founds upon the fame anvil. The frontifpioce to M. Mar- 

 purg's Hiltory of Mufic, reprefents the Samian fagc 111 the 

 aft of 'weighing the hammers. 



But though both hammers and anvil have been fwallowed 

 by ancients and moderns, and have paffed through them 

 from one to another, with an ollrich-Uke digeftion, upon 

 examination and experiment it appears, that hammers of dif 

 ferent fize and weight will no more produce different tones upon 

 the fame mivi/, than bows or clappers of diiferent lizes, will 

 from the fame firing or bell. 



Indeed, both the hammers and anvils of antiquity muft 

 have been of a conftruftion very different from thofe of our 

 deirenerate days, if they produced any tones that were ftridly 

 mufical. Of the millions of well-organized mortals, who 

 have paffed by blackfmiths' lliops, fince the time of Py- 

 thagoras, we believe no one was ever detained by a fingle 

 note, much lefs by an harmonious concord, from_ thofe Vul- 

 canian inftruments. A different kind of noife, indeed, will 

 be produced by hammers of different weights and fizes ; but 

 it feems not to be in the power of the moff fubtle ear to dif- 

 cover the leait imaginable difference with refpect to gi-avity 

 or acutencfs. But though different noifes may be produced 

 'from different bodies, in proportion to their fize and fohdity, 

 and every room, chair, and table, in a houfe, has a particu- 

 lar tone, yet thefe noifes can never be afcertained Uke mufical 

 tones, which depend upon reiterated and regular vibrations 

 of the aliquot parts of a ftring, or other elaftic body ; 

 and in wind inftruments, upon the undulations of the air 

 conveyed into a tube> Noife may, indeed, he forced from a 

 mufical ftring, or inftrument, by violence ; but noife pro- 

 ceeding from bodies non-elaftic, or immulical, can never be 

 foftened into found. M. Rouffeau (Ditt. de Muf. art. Bruit) 

 has ingenioully imagined that noife is of the fame nature as 

 found, with this difference, that to produce found, the one 



tone, with its confonant harmonics only, fhould be heft-d : 

 fuch as the 8tli, I2lii, i^th, and 17th; whereas noife is 

 produced by a jarring multitude of different tones, or even 

 by one tone, when its vibrations are fo violent as to render 

 audible a confiderable number of diffonant tones, of which 

 the vibrations ftldom or never coincide ; fuch as the 7th, gtli, 

 nth, &c. 



The long belief of this ftory proves that pliilofopliers 

 themfelves have fometimes taken facts upon truft, without 

 verifying them by experiment. And as the tone of the 

 hammers was afterted without proof, fo was the effeft of 

 their different weights faftened to ftrings : this Galileo 

 difcovered. The numbers 6, 8, y, 12, applied to dif- 

 ferent lengths of ftringf, would, indeed, givetlie intervals 

 mentioned. But it is proved, that to produce thofe inter- 

 vals by the ten/ion of different weights, the weights mult be 

 the fqu ares of thofe numbers ; that is, 36, 64, 81, 144. It 

 is allonifliing how the blunder had been echoed from author 

 to author, without experiment, till the time of Galileo. 

 And Bontempi, in trying the power of weights upon ftrings 

 in the Pythagoric proportions of 6, 8, 9, 12, found, that 

 inftead of giving the 4tli, 5th, and 8th of the graveft tone, 

 they produced only the minor 3d, major 3d, and tritonus ; 

 fo that tlie whole account falls to the ground. But though 

 modern incredulity and experiment have robbed Pythagoras 

 of the glory of' difcovering mufical ratios by accident, he has 

 been allowed the fuperior merit of arriving at them by medi- 

 tation and defign. At leaft the invention of the harmonical 

 canon, or monochord, has been afcribed to him both by ancient 

 and modern writers. (See Monochord.) See Ariftid. 

 Quint, p. 116. Prin. and Power of Harm. Hift. des 

 Mathem. par. Montucla. Euler, Teutamen novae Theor. 

 Muf. and all the writers upon harmonics and tempera- 

 ment. 



We {hall enter no deeper into this fubjeft here, than is ab- 

 folutely neceflary to explain the nature of tjie difcovery at- 

 tributed to Pythagoras, to which mufic is indebted for the 

 honourable appellation of fcicnce. 



Pythagoras fuppofed the air to be the •vehicle of found, and 

 the agitation of that element occafioned by a fimilar agita- 

 tion in the parts of the founding body, to be the caufe of it. 

 The vibrations of a ftring, or any other fonorous body, 

 being communicated to the air, affefted the auditory nerves 

 w ith the fenfation of found ; and this found, accordino- to 

 him, was acute or grave, in proportion as the vibrations 

 were quick or flow. It was alfo known, by experiment, 

 that of two ftrings equal in every thing but length, the 

 ftiorter made the quickeft vibrations, and gave the acuter 

 found ; in other words, that the number of vibrations made 

 in the fame time by two ftrings of different lengths, were in- 

 verfely as thofe lengths ; that is, the greater the length, the 

 fmaller the number of vibrations in any given time. By tliefe 

 difcovcries it was that found, conCdered in the vibrations that 

 caufe it, and the diraenfions of the vibrating or fonorous body, 

 was reduced to quantity, and as fuch, became fubjeft to cal- 

 culation, and expreflible by numbers. Thus, for inftance, the 

 two founds that form an oclave are expreffed by the numbers 

 I and 2 ; which reprefent either the number of vibrations in 

 a given time, or the length of the ftrings ; and mean nothing 

 more myfterious than that the acuter found vibrates twice, 

 while the graver vibrates once ; or, that the ftring pro- 

 ducing the Jower found is twice the length of that which 

 gives the upper. If we confider the vibrations, the higher 

 found is as 2, the lower as i ; the reverfe, if we coiitider 

 only the lengths. In the fame maiTncr, and in the fame 

 fenfe, the 5th is expreffed by the ratio of 2 to 3, and the 

 4th by that of 3 to 4. 



Such 



