From the PREFACE. THE advantages accruing from a knowledge of Harmony are not sufficiently understood, except by those who are ambitious to compose. Every singer, performer, teacher, and critic is benefited in knowing the principles of chord succession, harmonization, etc. Pianists who possess this information have an immense advantage in the knowledge that modulatory tones, suspensions and appoggiaturas are accented; that dissonances are to be connected with the consonances to which they resolve; that passing tones are unaccented; that anticipations are slightly marked, and that different kinds of cadences require different kinds of punctuation. As an aid to sight-reading (that most necessary accomplishment) a knowledge of Harmony is indispensable, for it enables one to anticipate a considerable portion of music by being familiar with the notation, resolution and progression of chords in general. Our present system of music has been gradually evolved during centuries of artistic and scientific progress. Some of the world's greatest geniuses laid the foundation, built up the structure and added the ornamentation. The theorist has, therefore, but little to do beyond that of presenting the material of composition and showing how this has been employed. Certain principles and theories may be deduced from the music of a Beethoven, and these are to be systemized and explained. But while the creative impulse in music continues to manifest itself it must be unfettered by arbitrary rules and prohibitions. Recent composers, in their use of harmony, have gone far beyond the formulas and precepts of textbooks. It is no longer possible, according to existing systems of theory, or of acoustics, to explain the harmonic structure of such works as Saint-Saens' Danse Macabre, Grieg's Norwegian Dances, Tchaikovsky's Francesca da Rimini, or the later music-dramas of Wagner. These creators of music followed a higher law than didactic theorem, and the theorist should act only intermediately, explaining to the student the artistic phenomena of cause and effect. During the past twenty-four years since this system was commenced the author has confined himself principally to this task: 1. To present the material and technic of composition in systematic and graded order. 2. To explain this analytically and clearly. 3. To illustrate the application of this material in the construction of music. 4. To show the esthetic effect (and, consequently, the object) of certain chords and progressions. These are the main features of the present system, which is based upon the actual results of composition rather than upon existing theoretical works; and whatever merits this book may possess are thus ascribed to the influence of Scarlatti, Couperin, Bach, Mozart, Beethoven, Schubert, Schumann, Chopin, Mendelssohn, Wagner, Rubinstein, Dvorak, Gounod, Saint-Saens, Jensen, Lassen, Goldmark, Tchaikovsky, Grieg, and Mascagni, not to Zarlino, Rameau, Kirnberger, Gottfried Weber, Marx, Weitzmann, Richter, nor Riemann.