C 743 ] 
octachord lyre, where it was natural to expedt them; 
for when the lyre had but eight firings, the fpecies 
could be taken no where elfe ; and it cannot be 
thought, but that, after the extenfion of the inftru- 
ment, they were taken at the fame pitch as before, 
unlefs we fhould fuppofe, that the new firings 
brought with them an immediate change, both of 
the theory and practice of the fcie.nce, which is moft 
improbable. We fee our modern harpfichords have 
more keys given to them than thofe of the lafl cen- 
tury ; and yet neither the portions of the cliffs, nor 
any other circumfiances attending our theories of the 
fcience, have been altered by them. But that this 
point may not reft wholly on the circumfiances of 
the diagram, I fhall produce four paffages, that plainly 
fbew the relation between the two dodtrines. The 
firffc from Arifioxenus. 
“ Now, as fome of thofe [fyfiems] which we employ- 
in mufic, are fimple, and others mutable, we muft treat 
of mutation ; and firft of this, what mutation is, and 
how it is accomplifhed ; now, I fay, there happens, 
as it were, a pathos in the melody ; afterwards, how 
many mutations there are in ail, and according to 
what intervals (21).” 
In this paffage, the author is fpeaking of the fixth 
divifion of harmonic, which was mutation 5 and 
more particularly of mutation with refpedl: to tone, 
which, in this divifion, was always treated upon the 
(21) ’Egth S'i 7 y.zAoS'ay.iVav \717a, p. ’i aztXa, 7 A q duzTctCoAa, 
[corrige, zyyZ 7 aCo A«] 'Gft yilaCoAn? a.v tin hZKTitr 'vparov pc' dura, 
71 TtOl' Z 71 V >1 y-ilaCoAp, KUl TTobf yivoywov . Aiycj W-Jsf 7/Vc( 
<ruy.6cum']& zv ra f yzhuS'iits *E ■zreijci. kovai itch cu wi- 
<?ai ixijcibohaiy K*t kata 7707 a i ctr {] [xa'Ja. Ariftox. p. 38. v. 7. 
principle 
3 
