C 75 ° 3 
menon to hypate mefonj fo that the diagram and 
the tables agree in every refpedt, except the generic 
differences, which I had no occafion to confider. In 
the fecond fet, indeed, the numbers are applied to 
the diapafon, from mefe to proflambanomenos > and 
there being no explanation in this chapter of the 
diftindt ufe of this fecond fet, nor any reafon affigned 
for giving it, but the convenience of having the op- 
tion, to begin the tuning from nete or mefe (26), this 
may feem to furnifh an objection to the proof pro- 
pofed to be gained from thefe tables : but if we look 
forward to the fecond chapter of his third book, we 
fhall there fee his meaning j which I fhall proceed 
to explain. 
Having, in the fixteenth chapter, fhewn how the 
numbers, given in the two fets of tables, are to be 
applied to an odtachord canon, he propofes, in the 
firff chapter of the third book, to fhew, how the di- 
vifions for the fifteen founds of the whole difdiapafon 
fyffem might, if required, be found, according to 
the fame ratios he had already affigned for the 
extent of a diapafon. Now, for the doing this, two 
inconveniences were to be obviated. Firff, If the in- 
ftrument, on which this experiment was to be tried, 
was to receive an addition of feven firings, to com- 
plete the difdiapafon, and thefe additional firings 
were all to be in unifon with the eight before applied, 
it would happen, that, in fhifting the moveable ma- 
gas, or bridge, to the fedtions required, thofe firings, 
which were to exhibit the acute fedtions of the tetra- 
(26) r 'lv' dp' o'ZoTi^i av T apX*’!' 'Tffycuptjy.idcL 7 toi£<S cu ras 
«f [JLoyelf. Ptol. Harm. p. 174. v. ult. 
chord 
