IN the following pages I shall endeavor to give, in the simplest possible form, an outline of the principles of Harmony. I shall make no attempt to give details or to deal with the subject exhaustively, but I shall present all the tone combinations found in music, and give sufficient explanations of their use to enable the student to recognize them in the works of others and use them correctly in his own. The rules given are derived entirely from the analysis of the works of the great composers, and are followed by them in the great majority of cases. It must be remembered that the canons of art are not moral laws, but simply state what is expedient in general. Violations of the rules which occur frequently in the best compositions do not concern us. Irregularities and exceptions do not come within the scope of this work. It will therefore be necessary to leave untouched many interesting and instructive points, but it is hoped that by omitting all detail the student will gain a clearer insight into the essentials of musical composition. A sufficient knowledge of piano playing to enable the student to play an ordinary hymn tune is presupposed. This work, in its inception, appeared in 1895 in serial form in one of the musical periodicals. The demand for it was so great, that it became necessary to gather the chapters into a book form, and the great success of the latter, together with the desirability of amplification made clear by its use in the hands of teachers, led to the present revised and enlarged edition.