The question, "What is music?" is not new, not recent, not even modern; it is as old as history itself. In the remotest antiquity it has occupied the minds of thinkers, and elicited curious, ingenious, and interesting fundamental theories. I have, therefore, thought it advisable, before setting forth my own views, to give a résumé of the various theories current in ancient times, as well as during the Middle Ages, together with a not lengthy discussion on the theories of Euler, Herbert Spencer, and Helmholtz. The question being in my estimation a cosmical one, I believe that, on the whole, the ancients, in considering so, understood it better than most of the moderns, who treat it too much from a sentimental, subjective point of view. Of course, we must make allowance for the method of expression of the ancients; their language was to a great extent symbolical, and abounded even in what may be termed compound symbols; that is to say, an originally symbolical expression came to be so commonly understood, that it was used to serve as the basis for still deeper symbols: this is particularly the case with the number symbolism, which at the outset was simple enough-as may be learned from the interpretations given to it in Dacier's "Life of Pythagoras," but which later came to be so complicated that it is to us but little more than a number mysticism. There are no commentaries incorporated in this little work, and for two reasons: first, because they have no practical value; secondly, because the great aim of the ancient fundamental theories of music is easily perceived even without having a key to the mysterious expressions. This aim is, to show that music is a great part of the cosmos, and not a human contrivance. The ethical and psychological speculations of antiquity on the subject of music are, by-the-way, also deserving of our attention: and, in fact, the sooner we follow the precepts of Plato and Aristotle, deduced from those speculations, the better will it be for our civilization.In the mathematical and physical branches of the science we have, of course, completely overshadowed the ancients; for, since the publication of Newton's "Principia," there has hardly been a name of distinction among physicists and mathematicians, but it is intimately connected with progress in acoustics; and this is not strange, for, to use the language of Prof. Leslie, "the doctrine of sound is unquestionably the most subtle and abstruse in the whole range of physical science." It occurs to me that the reader might here ask me, "Why, then, do you hold our conception of music to be less true than that of the ancients? If we are superior to them in knowledge, why should we be inferior to them in comprehension?" These questions, I think, can be easily answered. To paraphrase a sentence of Boetius, we have numbers of instrumentalists and vocalists, but musicians are rare; in other words, the art and the science of music have become distinct studies, and in consequence our conception of music has become confined and imperfect.In this little work, then, I have attempted to give the outlines of a cosmical theory of music, based on the knowledge of our times, and, whether it be correct or not will be for an intelligent public to judge. For my part, if I have but succeeded in freeing the matter from the subjectivity by which it is now so enthralled, and shown that it can and ought to be treated from a purely objective point of view, I shall consider myself amply rewarded