Quartal Harmony
(continued)

B. Quartal Harmony Fugue

In the following example, I have adopted another form familiar to us from the previous lesson on the fugue.

1. Exposition. Although not necessary, we have molded our subject here to incorporate many of the significant intervals of the quartal system, namely the perfect fourth, fifth, and major second. However, unlike the Common Practice fugue, the transposition of our answer is not restricted to the dominant key region. As well, the final entrance of the subject in the exposition is introduced in a key to our taste.

2. Counter-Exposition. In bar 22 a second exposition begins, this time with the subject inverted.

3. Key/Modal Regions and Cadence Points. As we have seen in the ternary example, and distinctly evident in this piece, the use of the quartal system allows for easily accomplished modulations, more so than in the tertian. A notational obstacle can occur, however, and the composer may sometimes have to jump from sharps to flats (or vice versa) to keep the diatonic relationships readable (see bars 17-18 below). As well, the composer can choose not to observe the tertian (Common Practice) necessity to return to the original key, especially since in the quartal system the key can be somewhat ambivalent from the outset. In our piece, for example, there are three cadence points: the first in Bb, the second in F, and the third in F#.

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