Modern Harmony in Its Theory And Practice

g other well-grounded points of view, e. g. the chords of the llth and 13th. The chord of the 6th has been treated with more detail than usual, an attempt having been made to analyze and classify the features that make this chord so difficult for the student. While the old strict rules as to secondary 7ths are given fully, the modern theory and use of these chords have received just consideration. The chord of the 9th has been discussed as a largely independent chord it was also obvious that the growing feeling about chords of the llth and 13th ought to be recognized, although the opinion of the authors, as ex plained in the chapter on that subject, is that these latter can seldom be classified as independent chords. It is believed that the treatment of chromatic alterations in chords, and of the augmented 6th, 6-5 and 6-4-3 chords is in accordance with present thought, and that this is also the case as regards suspension. The chapter on the old modes is necessarily brief, but it is hoped that it may lead the student to further investigation of an important and inter esting question. It is often the case that exercises with figured basses are written, correctly, but only mathematically, by simply reckoning each chord as-a kind of puzzle, without reflecting that the whole thing means music after all. The most difficult thing, for one not used to it, is the having a mental conception of the real sounds of the symbols written down in other words, hearing with the eye. Education now is directed to the thing, not to the symbol. As the practical way of working in that direction, in this book from the very beginning the harmonizing of melodies goes step by step with the writing from figured basses. It is hoped that the illustra tions quoted from many composers will be of help by showing what has actually been done with our harmonic material. For matters connected with acoustics 5, 13, the student is referred to Helmholtzs book On the Sensations of Tone, and to the essay on Partial Tones in Groves Dictionary of Music BOSTON, August, 1905. Contents include: I INTERVALS 1 Consonance and dissonance, 7 Inversion, 9. II THE SCALES 11 Circles of 5ths, 13 Relative minor, 15 Chromatic, 16 Tonic, etc., 17. in TRIADS 18 Chord defined, 18 Doubling of intervals, 19 Open and close position, 20 Similar motion, etc., 22 Consecutive 8ves and 5ths, 24 Voice-leading, 27 Leading-tone, 28 Rules for triads, 29. IV EXERCISES WITH TRIADS IN MAJOR KEYS 31 Directions as to figured basses, etc., 31 Exercises, 34. V EXERCISES IN HARMONIZING SOPRANO MELODIES ....... 36 Triad successions in major keys, 36 Exercises, 37. VI TRIADS IN MINOR KEYS 38 Additional rules, 39 Tierce de Picardie, 42 Triad successions in minor keys, 43 Three-voice writing, 43...