On the Fnperiles ef Wini hiflrumtuts. ' 217 



By the afliftance of thefc pipes it is very eafy to perform a chromatic fcale, or at pleafure 

 to tranfpofe the key of an air half a tone. The truth of the intervals in the key thus 

 aflumed depends very much upon the width of the pipes. Thofe of the flute, delineated in 

 Fig. 5 and 6, would be pretty true ; but one or two oftave notes of its original fcale are too 

 fliarp, and this imperfedtion is tranfmitted to the tranfpofed fcale. 



To determine whether the original founds of the fecond o£lave could be raifed by dofing 

 the interior ends of thefe pipes, or (which would anfwer the fame purpofe in diminifliing 

 the internal capaqity of the inftruraent) by filling them with water, I made the following 

 experiment: 



The three pipes were inferted into that fide of the flute oppofite the holes for the fingers, 

 and nearly at right angles with the tube. The lower end of each was then jufl: immerfed 

 in water contained in a fmall vefl"el, and_ while the flute was held in a pofition nearly 

 horizontal, founding each of the notes C, D, E, F, G, A, B, of the fecond o£tave, and 

 C, D, E, of the third, the veflels were raifed fo high, that the water would very nearly fill 

 to the higher end of each pipe. No variation in any of thefe founds C, D, E, F, G, was 

 perceptible: but the pitch of the five higher. A, B, C, D, E. rofe a little with the afcent 

 of the water. The variation, however, was fo flight as to be no objeftion to the ufe of 

 the pipes. 



When an air is tranfpofed out of D into D fharp by opening thefe dufts, the key note of 

 the original mode D muft be ufed for the fliarp feventh of that which is adopted, inftead of 

 C fharp, which, when fingered in the ufual manner, is too flat ; for the fame reafon it 

 is alfo preferable in the fcale of D fliarp, to ufe the common C inft;ead of B fharp for the 

 major fixth major; and when an air is tranfpofed out of middle C into C fliarp, to ufe the 

 common C ftiarp for the key note. 



Thefe, and fome other defers, induce me to think -that the following method of tranf- 

 pofition by one pipe will be moft eligible, as the fingering of the fcale in any common key 

 need not be altered. 



Infert one end of a round pipe, three-tenths of an inch in diameter, and one inch long, 

 into the infide of a German flute, fo much nearer the holes for the fingers than the found 

 hole, tliat a line which encircles the flute, and pafles through the middle of this lafl: hole, 

 may be feven-tenths of an inch from the centre of the interior orifice of the pipe, and all 

 the founds of the flute will be raifed about half a tone when the ends of the pipe are open. 

 Turn this pipe by the Cde of the flute, and let its exterior orifice be clofcd by a valve or 

 key, which may be opened by the thumb of the left hand. 



In the model with which I made the experiment, the pipe was inferted into the contrary 

 fide of the flute to that into which it fliould be inferted, when the infl;rument is intended for 

 praftice : it is delineated in this pofition by the two dotted lines in Fig. 6. I have not 

 had an inllrument conflirudted upon this plan, but I think it much preferable to the method 

 propofed before. The flute may have all the common keys, and the fingering of no fcale 



Vol. V. — September 1801. F f will 



