Since its first appearance in 1938 Harmonic Relations has been in continuous use in the classrooms of the New England Conservatory of Music. Every chapter, illustration, and exercise has been subjected to the most careful scrutiny, in an effort to make each statement and explanation as simple and clear as possible, and the exercise material varied, musical, and attractive. The revised edition has benefited greatly from the combined experience of students and teaching staff. Material that proved of doubtful value has been eliminated, the order of presentation has been considerably revised, and much new material has been added, particularly in the latter part of the book. Its principal object is to provide the student with a comprehensive knowledge of the principles of harmonic writing as they may be observed in the works of the great composers of the past, and a theoretical basis for the investigation of the divergent harmonic practices of contemporary writers.From the IntroductionTABLE OF CONTENTSI ScalesII IntervalsIII Triads; TonalityIV Chord-root Progressions in ClassIV Chord-root Progressions in ClassIIVI Chord-root Progressions in ClassIIIVII Harmonization of MelodiesVIII First Inversions of TriadsIX Second Inversions of TriadsX The Minor ModeXI Harmonization of Figured BassesXII Fundamental Harmonic RelationsXIII The Dominant Seventh ChordXIV The Inversions of the DominantSeventh ChordXV Extended Dominant HarmoniesXVI The Supertonic Seventh ChordXVII Other Diatonic Seventh ChordsXVIII Modulation by Common ChordsXIX Harmonization of Chorale MelodiesXX Chromatic TriadsXXI Neighbor Dominant Seventh ChordsXXII Neighbor Diminished SeventhChordsXXIII Augmented Sixth ChordsXXIV Non-chord TonesXXV Non-chord Tones in the Bach