Harmony (Exercises 21–40)

This chapter focuses on sounds that occur simultaneously. The concept of harmony here is broad and has a far-reaching scope; it includes functional and non-functional harmonies, color, and any other approach to simultaneous sonorities. Exercise 21 suggests the implementation of voice leading as a constructive principle through stylistic imitation. Number 22, in which “melody becomes harmony,” proposes the harmonization of a melody using exclusively its pitch content. Exercise 23 incorporates symmetrical harmonies; 24 and 25 use the harmonic series to create harmonies. In 26 the harmonies are built around major and minor triads with pitches in common. Exercise 27 incorporates the use of integer notation; 28 uses scale degrees but not triads. The base of exercise 29 is the 12-tone row; 30 uses the concept of “circle” progression or harmonies that move around the circle of fifths; 31 and 32 incorporate harmonies that move in major and minor thirds; 33 and 34 discuss overlapping triads and polytonality; 35 provides an opportunity to work with pedal tones; 36 incorporates the church modes and 37 the use of clusters (i.e., harmonies based exclusively on minor a major seconds). Exercise 38 is based on harmonic sequences; 39 and 40 discuss implied harmonies and writing “contrafacts.”