Chapter 1

Figure 1.1.1. Small movements sound melodic (a), while large registral leaps create the impression of multiple melodies (b).

Figure 1.1.3. Major and minor triads belonging to the same diatonic scale.

Figure 1.1.4. A single melody will sound different in different harmonic contexts.

Figure 1.2.1. Four randomly generated sequences. Sequence (a) is completely random; (b) exhibits efficient voice leading; (c) exhibits harmonic consistency and efficient voice leading; (d) exhibits harmonic consistency, efficient voice leading, and diatonic macroharmony.

Figure 1.2.2. Randomly generated twelve-tone music.

Figure 1.3.1. (a) Confining a melody to the notes of the C major chord produces large leaps, so it is necessary to add “passing tones” (b).

Figure 1.3.2. Confining a melody to the notes of the cluster {B, C, Df} produces conjunct melodic motion, but changing octaves requires a large number of passing tones.

Figure 1.3.3. (a) Every note of the C major triad is near some note of the F major triad. (b) It is possible to use a series of C and F major triads to construct three simultaneous melodies.

Figure 1.3.4. Any two major triads can be linked by stepwise voice leading; in the case of the tritone, this requires four voices.

Figure 1.3.5. Chromatic clusters cannot always be linked by efficient voice leading.

Figure 1.3.6. Chromatic clusters allow conjunct melodic motion to be combined with harmonic stasis.

Figure 1.3.7. Scale steps provide a means of measuring musical distance. The intervals C-E and E-G are two steps large relative to the diatonic scale (a), two and one steps large relative to the pentatonic scale (b), and four and three steps large relative to the chromatic scale (c).

Figure 1.3.8. The music makes use of two scales to create a chromatic macroharmony.

Figure 1.3.9. (a) In earlier music, composers emphasized different centers within a single fixed diatonic collection. (b) In classical music, composers restricted the available modes to two, creating long-term harmonic change by emphasizing different major or minor scales. (c) Only in the twentieth-century were these two techniques systematically combined, creating a much wider range of tonal areas to choose from.

Figure 1.3.10. Two levels of voice leading in Clementi’s Op. 25, No. 6.

Figure 1.3.11. Voice leading between macroharmonies in Debussy’s “Le vent dans la plaine”.

Figure 1.3.12. Voice leading between diatonic triads.

Figure 1.3.13. Single-step voice-leading between diatonic triads can be modeled with a circle.

Figure 1.3.14. (a) One-semitone voice leading and (b) two-semitone voice leading among triads.

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