NO satisfactory reason can possibly be given why harmony exercises should necessarily be (as they certainly are in most books) a mere series of dry chords, mostly in notes of uniform length. An attempt has, therefore, been made in the present work to do for harmony what the late Stephen Heller did so admirably for pianoforte studies — to invest them with musical int'erest, thus cultivating the student's feeling for melody and rhythm, while at the same time giving him an insight into the harmonic relations of the various chords employed. For this purpose, all the exercises, excepting a few of the earlier ones, are the basses of little pieces, varying in length from eight to thirty two bars, and containing considerable diversity, both of rhythm and of cadence. In dealing with the various discords, such as the ninths, elevenths, and thirteenths, it has not been thought needful, or. Even desirable, to insert them in every bar. The author's aim has been to show how they could be introduced easily and naturally, as a composer might use them in the course of a piece. The rarer discords will, therefore, be much seldomer met with in these exercises than those which in actual practice are more commonly employed.