So long ago as 1828, the American public was told by Philip Trajetta,[A] that 'if counterpoint be not a science, neither is astronomy.' For want of proper expounders, this truth has made but little impression, and, while the Art of Music has advanced considerably among us, the Science has remained nearly stationary. In Europe, erudition, research, and collections of rules have not been wanting. Much has been accomplished, but an exhaustive work, based upon the simple laws of nature, has (so far as the writer can learn) never yet appeared. The profoundly learned and truly great Bohemian musician, W. J. Tomaschek, who died in 1849, taught a system of musical science founded upon a series of beautiful and easily comprehended natural laws. His logical training and wide general cultivation gave him advantages enjoyed by few of his profession. The result of his researches has unfortunately never been published, and his system of harmony is _thoroughly_ known only by his more earnest and studious pupils. [Footnote A: 'An Introduction to the Art and Science of Music,' written for the American Conservatory of Philadelphia, by Philip Trajetta. Philadelphia: Printed by I. Ashmead & Co., 1828. Trajetta was the son of a well-known Italian composer of the same name. He was a pupil of the celebrated Conservatorio of Naples, and, as I have been informed, was about to obtain a professorship in the Conservatorio of Paris, when political circumstances diverted his course to America. He was the friend of General Moreau and President Madison. Of noble appearance, fine manners, and sensitive temperament, he for some time received the consideration due to his talents and acquirements, but, in after years, was sadly neglected, and finally died in Philadelphia, almost literally of want. His musical knowledge perished with him; his manuscripts (operas, oratorios, etc.) were, I believe, all burned by him before his death. A sad history, and, in a land where there has been so little opportunity for the beet musical instruction, a strange one!] To define the provinces of _science_ and _art_, we may briefly say, that science is concerned with the discovery of demonstrable principles, and the deduction of undeniable corollaries; while art is occupied with expression, performance, and the creative faculty with which man has been endowed. Music and astronomy are both sciences, that is, founded upon certain fixed and ascertainable laws; but astronomy is no art, because man has not the power to create, or even remodel worlds, and send them rolling through space; while he can produce sounds, and arrange them in such a way as to result in significant meaning and in beauty, two of the chief ends of art.