SOUND. 



becaufe the air is the only medium of which we are certain, 

 between the founding body and the organ of hearing : that 

 we mud not multiply bodies unneceflarily, as the air is fuf- 

 ficient th explain the formation of found ; and it is found by 

 an exhaufted receiver, that found cannot be produced with- 

 out air. 



The continuance or permanence of found can only be oc- 

 cafioned by the agitation of the air. As long as this agi- 

 tation continues, the tremulous motion of the air is com- 

 municated to the ear, and hkewife prolongs the fenfation of 

 found. And there is no way more fimple of accounting for 

 the duration of found, than in fuppofmg that the fucceflion 

 of vibrations continues to renew the impreflion. Further, 

 this agitation of the air, of whatever kind it may be, can 

 only be produced by a fimilar agitation in the feveral parts 

 of the founding body ; and it is a certain faft, that thefe 

 feveral parts of a founding body are in conftant vibration as 

 long as it continues to found. If we touch the body of a 

 violoncello, or any inflrument, while it is founding, we feel 

 it tremble under the hand, and we may even fee the llring 

 tremble as long as it founds. It is the fame with a bell 

 caufed to found by a blow of the clapper, we may feel and 

 fee it tremble ; and grains of fand, if fprinlcled on its fur- 

 face, will be feen to jump and i\<.\p. If a llring is relaxed, 

 or a bell cracked, there is no longer either found or vibration. 

 If, therefore, neither the bell nor the itring can communicate 

 to the air no motion but Inch as they have themfelves, there 

 can be no doubt but that found is produced by the vibra- 

 tions of the founding body, and is propagated by fimilar 

 vibrations, which this tremulous body communicates to 

 the air. 



This being fuppofed, let us firll examine what conltitutes 

 the ratio of found, with refpecl to grave and acute. 



RouiTeau, in his article Son, found, repeats all the ex- 

 periments for meafuring and comparing found with found, 

 which we have given, and (liall give, under the different 

 heads of tuning glafles by water, fee Armonica ; firings 

 by weight ; by moveable bridges, fee Monochord ; by 

 the number of vibrations, fee Ratio ; by the relative 

 length, thicknef^, and tenfion of njlring, whicli fee ; by the 

 beats of organ-pipes, fee Beat ; by the holes in flutes and 

 hautbois, which ferve to fhorten the tube ; by the different 

 columns of air, which form the different tones of horns 

 and trumpets : thefe are all upon the fame principle as 

 the fons harmouiques of the violin and violoncello. See 

 Harmonics. 



The fecond point to be confidered in analyfing found, is 

 its force, which depends on the vibrations of the founding 

 body : the more powerful and Itrong thefe vibrations are 

 made, the more vigorous and audible is the found. A cer- 

 tain limited degree of force can only be given to a pipe or 

 firing, beyond which all its proportions are broken, and its 

 tone rendered falfe and difagreeable to the ear. The velo- 

 city of found has been confidered by the moll eminent phi- 

 lofophers and mathematicians ; but the refult of their en- 

 quiries and experiments have materially varied. Halley and 

 Flamftecd make found move, in England, 1070 Fr. feet in 

 a fecond ; and La Condamine 1 74 loifes in Peru ; while 

 Merfcnnus and Gaffendi alTure us that the wind being fa- 

 vourable or contrary, neither accelerates nor retards the 

 motion of found. But fince the experiments of Derham 

 ( Phil. Tranf . ) , and the Academy of Sciences at Paris, former 

 calculations are regarded as erroneous. 



Without flackening its pace, found becomes weaker by 

 extent from the place of its produftion ; but if not 

 checked by any obltacle, nor repreffed by the wind, it gene- 

 cally moves in the ratio of the fquares of The diitance. 



12 



Thirdly, as to the difference of found in the quality of tone, it 

 certainly does not arife from its elevation in the fcale, nor 

 from its force. The tone of a flute and a hautbois, though 

 perfectly in tune together, can never referable each other. 

 There will always be a foftnefs and fmoothnefs in the flute, 

 and a fpirit and agreeable vibration of the reed in the haut- 

 bois, which muft ever prevent fimilarity ; without mention- 

 ing the different tones of voices, by which individuals are as 

 well recognized as by their features. See Voice. 



Rouffeau fays, a compofer does not confider merely whe- 

 ther the founds he ufes are high or low, but whether they 

 fhould be loud or foft, rough or fmooth, dull or brilliant ; 

 and he diilributes them to different inllruments and voices 

 accordingly ; fometimes in folo parts, and fometimes in 

 tutii, or full chorus ; at the extremities or medium of in- 

 llruments or voices in piano or forte, as the compofition 

 fhall require. 



For the appreciable extent of the mufical fcale or com- 

 pafs, it depends on our power of perception, though in 

 nature it is infinite. Lengthen or fhorten a mufical Itring 

 to a certain degree, and it produces no found. We can 

 neither augment nor diminiffi the compafs of the flute at 

 our pleafure, or the length or fliortnefs of an organ-pipe ; 

 both have their limits. All appreciable founds are com- 

 prifed, according to Euler, within the numbers 30 and 7552. 

 So that by the experiments of this great geometrician, the 

 lowed found of which we can afcertain the tone, makes 30 

 vibrations in a fecond, and the higheft 7552 vibrations in 

 the fame time ; an interval of nearly eight oftaves. See 

 Euler, and Compass. 



In our prefent fyftem of mufic, we have but one oftave of 

 twelve founds, the rell are all replicates, recurrencies, or 

 repetitions of thefe twelve femitones in the odlaves above 

 and below ; and if we could ufe all thefe oftaves or recur- 

 rencies of found in the firll oilave, they amount in all to 

 96, which is the greateft number of prafticable founds in 

 mufic, generated by one fundamental. 



It is impolTible to calculate, with fimilar precifion, the 

 number of praAicable founds in the mufic of the ancients. 

 For the Greeks may be faid to have formed as many fyllems 

 of mufic, as they had different ways of tuning their tetra- 

 chords. It appears, in reading their treatiles of mufic, that 

 thefe different tunings amounted to an indefinite number, 

 including all the changes of genus and mode which a new 

 found or key would introduce. See Tetrachord, and 

 System of lie ancient Greeks. 



With regard to the twelve founds of the modern fyllera, 

 the tuning never changes, and they are always immoveable. 

 Broll'ard pretends that they are moveable, founding his opi- 

 nion of their being often altered by flats and fliarps ; but 

 the changing the qhord or ftring, or its found, are different 

 things. 



Sounds, Harmonical. See Harmonics. 



The harmonical founds, wc. t!ie twelfth and feventeenth 

 above the principal (as well as fome others), have been 

 long known to accompany every fundamental found ; and 

 may naturally, and in general, be fuppofed to be produced 

 by the partial or feparate vibrations of the ftring or fonorous 

 body, fpontaneoufly dividing itfelf, according to a deter- 

 minate law, into three, five, or other ahquot parts of the 

 whole, confidered as unity. The theory of M. Rameau, 

 which has been fo excellently illuftrated by M. d'Alembert, 

 in his Elemens de Mufique, is founded on thefe harmonical 

 founds. See Fundamental Bafe, Harmony, and System. 



Sounds, Harmonic, denote alfo a fingular kind of founds, 

 which are produced in certain inftruments, fuch as the violin 

 and violoncello, by a particular motion of the bow, and by 



placing 



