advisable for beginners, who may take up this work without any previous knowledge of the subject, to omit at least Chapters II. and III., dealing with the Harmonic Series and Key or Tonality, until some considerable progress has been made in the practical part of the volume. The exact point at which the student will do well to return to the omitted portions will depend upon his progress and his general intelligence, and must be left to the discretion of the teacher.
In the practical part of the work an attempt has been made to simplify and to codify the laws. With a view of effecting these objects, many rules now obsolete, and contravened by the daily practice of modern writers, have been altogether omitted, and others have been greatly modified; while the laws affecting the chords, especially the higher discords—the ninths, elevenths, and thirteenths—have been classified, and, it is hoped, materially simplified. It is of the utmost importance that students who wish to master the subject should proceed steadily and deliberately. For example, a proper understanding of the chords of the eleventh will be impossible until the student is quite familiar with the chords of the ninth, which in their turn must be preceded by the chords of the seventh. The learner's motto must be, " One thing at a time, and that done thoroughly."
In preparing the exercises a special endeavour has been made to render them interesting, as far as possible, from a musical point of view. With this object they are, with a few exceptions, written in the form of short musical sentences, mostly in four-bar rhythm, illustrating the various forms of cadence. To stimulate the pupil's imagination, and to encourage attempts at composition, many exercises are in the form of double chants or hymn tunes. Each bass can, of course, be harmonised in several different positions; and the student's ingenuity will be usefully exercised in trying to write as melodious an upper part as possible for these little pieces.
Not the least interesting and valuable feature of the volume will, it is believed, be found in the illustrative examples, considerably more than 300 in number. These have been selected chiefly, though not exclusively, from the works of the greatest masters, from Bach and Handel down to the present day. Earlier examples are not given, because modern harmony may be said to begin with Bach and Handel. While it has been impossible without exceeding reasonable limits to illustrate all the points mentioned, it is hoped that at least no rule of importance has been given without quoting some recognised author in its support. It may at all
