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442 On Ancient Greek Music. Euclid has left two musical treatises, one on Harmonics, the other on the Canom Both these are characteristic of the author of the Elements; with however this difference — that the purely mathematical nature of the Elements kept out of view any prominent marks of an individual mind, whereas in these treatises we see things subjected to the rule of system- atized opinion — concerned indeed with definitions and axioms and postulates, but from the nature of the subject, less precise and restricted than the Elements. The following passage occurs in the Harmonics : Kara he fiekoTrouav yiveTat fxeTafioXf], oTav etc ciaa- toXtlkov tjOov^ el^ crvGraXriKOVy rj rjcrvyaaTLKov^ rj e^ rjav^aaTLKov ei^ tl toov Xolttcvv yj jueTafioXrj yevtjTai* eaTi ce OLa<TTaTiKov jixeu yevo^ nxeXoiroiias ^ ci ov arijuaiueTai fxeyaXoTrpeireia Kal oiapima >|/f^i79 dvcpidoe^^ kul Trpa^ei^ f]pcoi~ /ca«, Kal iraOrj toutol^ olKe^a* y^prJTai ce tovtoi^ /udXiaTa jmev 7] Tpaycpoia^ Kal tcov Xolttwv ce ocxa tovtov eyerai tov yapaKTYipo^* avcxToXTLKov oe, di ov avvdyeTai t] ^v^rj el^ ^aweivoTijTa Kal avavcpov ciaOecnV' dp/uocrei ce to tolovtov KaTacTTrjfljia toT^ epcoriKoT^ TraOecn Kal 6pr]voi^^ /cat olktol^ Kal Tol^ TrapaTrXrjaloLs. rjavyacTTiKov ce rjOo^ ean fxeXoiroua^y w TrapeireraL 7]pejuoTr]^ ^i^X^?? ^^l KaTaarrjixa eXevOepiov re Kai eiprjvLKov. ap/motjovai ce avTto vjulvol^ 7rataF69, eyKcvfxia^ av/ufiovXal^ Kal Ta toutol^ ofxoLa* p. 21. Ed. Meibom. Now this passage, coming as it does from a book which is not speculative or fanciful but purely scientific, shews I think very plainly in what way the art of music was at that time studied, and what were the effects attributed to it by men who were not fable-makers or compilers of marvellous stories, but close and judicious reasoners. Now if any one should suspect that these effects and the like of them, were not so likely to be produced by the bare sounding of so many notes which were exactly alike and in unison, as by the interweaving of many parts, and the mazing and dazzling power of a rich system of harmonies, I can only refer him to the times when such effects have set about explaining the work of the ancients. For when with the utmost stretch of their genius they cannot comprehend them, they call them, after the modern fashion, barbarians. And if any one happens to think that the ancients were elegant and well skilled in every part of music, he is accounted by them inelegant, and a foolish enthu- siast in admiration of the Greeks.