From the PREFACE TO THE FIRST EDITION: THE chief motive for the publication of this system of Harmony is given on the title-page. It was to furnish pupils through their course of study in musical theory with some aid in illustrating and reviewing the principles brought before them. The essential qualities of such a book the author believed to be these: that it contain the substance and fundamental features of musical theory in as condensed and complete form as possible; that it present these outlines together with practical directions and hints, to prepare the way for later attempts in composition. The book comprises, scientifically speaking, no theoretical treatise upon Harmonics, but although, like every system of Harmony it rests upon a firm foundation, it is devoted only to practical ends, which with the scanty means now accessible it might be difficult to reach upon abstractly scientific principles. There has indeed been hitherto an eager inquiry for mathematical precision in musical rules, especially among the young, who, naturally opposed to an authoritative creed, would fain have everything so clear as to be beyond a doubt; while on the other hand they are ever fearful of learning to know and comprehend the blooming life of art by the anatomical knife; nor is it to be denied," that in this regard there is a gap in musical literature, which no one has yet been able completely to fill. All attempts of this kind have thus far failed to produce a really tenable scientifically musical system, in accordance with which all phenomena within the domain of music shall be constantly regarded as necessary deductions from a single fundamental principle; and all that the philosophers, mathematicians and physicists have achieved in the matter is indeed worthy of notice, but has been on the one hand too disjointed to form a complete whole, and on the other too abstract, less serviceable for music than for other purposes, and whatever comprehension of musical matters it may have displayed, having but little reference 'to the essentially musical, which for the musician is the chief point in 'question. But all that has been laid down in musical manuals as a scientific basis has thus far failed to hold good, partly because as the result of individual and learned research it was also unable to form a complete system with infallible deductions, and partly because as a fanciful structure it was wholly wanting in scientific support. (It may be permitted here to call attention to a work which may be able to fill an evident gap; The Nature of Harmonic and Metrical Laws, by M. Hauptmann.) Yet rightly considered, this want is felt only by the riper and cultivated musician, who loves to busy himself with theory; but for the less advanced scholar is not so detrimental as to affect his immediate progress; and the skepticism above alluded to is to a certain extent no more to be heeded, than that childish disposition, which from overweening curiosity would fain come at the primal cause of everything by questions that can seldom be answered intelligibly enough to conform to the precise stage of his progress. In his early course the musician has to direct all his energies to his technical formation, as it will cost him time and trouble enough to reach the point whence he may with greater ease meet his peculiar position as artist. It concerns not here to ask Why, but more nearly How; to learn from experience and from the best models the necessity of certain principles, not to calculate it; afterwards, when culture, knowledge, capacity and calling demand, it will be time to search out the why, and all the knowledge acquired by experience will be an assistance not to be despised in discovering the musical laws of nature.