The present essay is the sequel of an article on Greek music which the author contributed to the new edition of Smiz'h's Dictionary of Greek and Roman Antiquiz'ies (london, 1890 — 91, art. Musica). In that article the long-standing controversy regarding the nature of the ancient musical Modes was brieﬂy noticed, and some reasons were given for dissenting from the views maintained by Westphal, and now Very generally accepted. A full discussion of the subject would have taken up more space than was then at the author's disposal, and he accordingly pro posed to the Delegates of the Clarendon Press to treat the question in a separate form. He has now to thank them for undertaking the publication of a work which is necessarily addressed to a very limited circle.