[ 76 ] 
the nicety of the diefis is ftealing infeiifibly into the fan- 
cy of fingers, and of fome other elegant mufical perfor- 
mers, it is not as yet adopted, or n fed as fuch, in the nota- 
tion of modern mufic. The interval between N® i . and 
2. in thefe pipes, is only of two femitones ; whereas, that 
between the N° i. and 2. of the former fyftem, was of 
three femitones. The feries N° 2. 3. 4. and 5. and the 
feries .N® 6. 7. 8. and 9. (both of which I have dillin611y 
marked within bars) have fimilar intervals in both fyf- 
tems (making allowance for what I have faid in page 
75, t and J.) Wherefore I imagine thefe to have been 
the original extent of the whole modulating 'feries, like 
the double tetrachord of the Greeks, and that The N® i . 
and N® 10. are additional at pleafure; as, in the fmal- 
ler fyftem, the interval between N° i. and 2. was a fe- 
mitone greater than that between N® i. and 2. in the 
larger fyftem; and N® 10. in the fmaller fyftem (firft 
examined) was totally omitted, though 1 have feen two 
others which had it. The founds in this larger fyftem 
are feven tones lower tlian thofe of the fmaller, which 
correfponds with the difference of their dimenfions; the 
pipe N® 4. in this fyftem meafuring nearly thirteen 
inches and a half in length, with diameter feemingly 
proportional; whereas the N® 4. in the fmaller fyftem 
meafured only feven inches and a quarter. By increaf- 
ing the velocity of the blaft, I found thefe pipes gave 
founds ftill higher, which \ngyq fourths above the upper 
minims, or oBave and Jixths above the fundamentals; 
and with a little more force, tritoneSy or fbarp fourths^ 
above 
