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thefe fifteen a diftindt pitch wasaffigned; but, as 
Ptolemey has rejected eight of them, I fhall, as I 
have propofed firft, feparately confider the pofitions 
cf the mefe for the feven modes he admits. 
Concerning the relative pitch of the refpedtive 
mefes for thefe feven modes, I find no difagreement 
amongft the harmonic writers. There are not want- 
ing, indeed, who charge the antients with giving, 
in refpedt thereto, contradictory accounts. Amongft 
others, the learned Dr. Gregory afl'erts, that Ariftides 
Quintilianus inverts the order of the modes ( i ) : but 
what led the dodtor into this miftake, was his not 
diftinguifhing the double dodtrine. Ariftides, in the 
pafiage cited, is not fpeaking of the pitch of the 
fyftem for the feven modes in queftion, but of the 
feven fpecies of diapafon, as they lay in the fyftem y. 
which ^ was, indeed, in the inverted order of the 
mefes of the feven modes, as will appear, when we 
come to confider the other dodtrine. This, then, is 
no contradiction in the Greek writer, nor, if it weie, 
would it be chargeable fingly on him j fince, if the 
dodtor had but caft his eye on his own Euclid (a), 
he would have met with the very fame dodtrine he 
found in Ariftides. But his remark is, indeed, en- 
tirely without foundation ; and I make no fcruple to 
aftert, that the antients agree in their accounts of the 
relative pitch of the mefes, for thefe feven modes ; 
(1) Atque Ariftides Quintilianus (pag. *8. editionis Meibo- 
mianae) tonum Hypodorium acutiorem tacit quam Dorium, et 
Hypophrygium quam Phrygium, et Hypolydium quam Lydium. 
Vide Praefat. ad Opera Euclid. 
(2) Pag. 540. verf. 6. et feq. feu pag- 15* ver ^' J 5 * 
Meibom. 
