1 7,6 Experiments and Inquiries refpeSiing Sound and LigJii, 



cartilages and the epiglottis, feems to fucceed to tiie office of the ligaments of the glottis, 

 and to produce a retrogade falfetto, which is capable of a very great degree of acutenefs. 

 The fame difference probably takes place between the natural voice and the common 

 falfetto : the rimula glottidis being too long to admit of a fufBcient degree of tenfion for 

 very acute founds, the upper orifice of the larynx fupplies its place ; henge, taking a note 

 within the compafs of either voice, it may be held, with the Hime expanfe of air, two or 

 three times as long in a falfetto as in a natural voice ; hence, too, the difficulty of paffing 

 fmoothly from the one voice to the other. It has been remarked, that the larynx is always 

 elevated when the found is acute : but this elevation is only necefTary in rapid tranliticns, 

 as in a fliake ; and then probably becaufe, by the contra£lion of the capacity of the trachea, 

 an increafe of the preflure of the breath can be more rapidly effefted this way, than by the 

 a(Siion of the abdominal mufcles alone. The refleftion of the found thus produced from 

 the various parts of the cavity of the mouth and noftrils, mixing at various intervals with 

 the portions of the vibrations dire£lly proceeding from the larynx, mufl, according to the 

 temporary form of the parts, varioufly affeft the laws of the motion of the air in each 

 vibration, or according to Euler's expreffion, the equation of the curve conceived to cor- 

 refpond with this motion, and thus produce the various charadlers of the vowels and femi- 

 vowels. The principal founding board feems to be the bony palate : the nofe, except in 

 rafal letters, affords but little refonance ; for the nafal paffage may be clofed, by applying 

 the finger to the foft palate, without much altering the found of vowels not nafal. A good 

 ear may diftindlly obferve, efpecially in a loudbafs voice, befides the fundamental note, at 

 leaft four harmonic founds, in the order of the natural numbers; and, the more reedy the 

 tone of the voice, the more eafily they are heard. Faint as they are, their origin is by no 

 means eafy to be explained. This obfervation is precifely confirmed, in a late differtation 

 of M. Knecht, publifhed in the mufical newfpaper of Leipfic. Perhaps, by a clofe attention 

 to the harmonics entering into the conftitutions of various founds, more may be done in 

 their analyfis than could otherwife be cxpeded. 



XVI. Of the Temperament of Muftcal Intervals. 



It would have been extremely convenient for praftical muficians, and would have faved 

 many warm controverfies among theoretical ones, if three times the ratio of 4 to 5, or four 

 times that of 5 to 6, had been equal to the ratio of i to 2. As it happens to be otherwife, 

 it has been much difputed in what intervals the imperfedlion (hould be placed. The 

 Ariftoxenians and Pythagoreans were in fome fenfe the beginners of the controverfy. 

 Sauveur has given very comprehenfive tables of a great number of fyftems of temperament ; 

 and his own now ranks among the many that are rejected. Dr. Smith has written a large 

 and obfcure volume, which, for every purpofe but for the ufe of an impracticable inftru- 

 mcnt, leaves the whole fubjedl precifely where it found it Kirnberger, Marpurg, and other 

 German writers, have difputed with great bitternefs, almoft every one for a particular 

 method of tuning. It is not with any confidence of fuccefs, that one more attempt is 

 4 made. 



