There are some tried and true methods for varying a melody, which have been handed down through time. Much of this comes from the practice of imitative counterpoint. In its simplest form, counterpoint is the use of two or more complementary melodic lines. These lines or “voices” are played simultaneously and they may imitate one another since they share the same motivic material (Think: Row, row, row your boat). Such is the case with rounds, canons, and the granddaddy of them all: the fugue.

The fugue is a highly sophisticated composition that uses complex imitative counterpoint and several independent voices. In this form, the primary thematic material is called the subject. When multiple subjects are employed, a double, triple, or quadruple fugue is formed.

Structurally, a fugue is designed around the subject (theme), an answer (restated theme in a different voice part), with episodes (connecting passages), and further entries. With each successive entry, the composer develops and varies the initial subject(s), often by introducing countersubject(s). The result is a “subject and answer” musical dialog. New entries typically cycle through keys using the circle of fifths. Fugues then close with a coda, which reverts back to the original key. J.S. Bach is best known for his fugal masterpieces especially The Well Tempered Clavier (Books 1 and 2) and late uncompleted work, The Art of Fugue.

Contrapuntal voices are connected harmonically. However, they maintain melodic independence. Sometimes lines move in parallel motion (up and down together). However, composers generally prefer to write voices moving in contrary motion (away from one another). This means that one line will ascend while another descends. During the Renaissance and baroque periods, five devices evolved to vary a melody or line. When set against the primary theme or motive, all of these variances encourage contrary motion and line independence. These devices are:

• Melodic inversion

• Retrograde

• Retrograde inversion

• Augmentation

• Diminution

With melodic inversion, the melody is turned upside down. For example, if the original melody jumps up a major third, in the inversion, it will now jump down a major third. If it raises a perfect fifth, it will now drop a perfect fifth, etc. Often, however, the contour of the melody is simply flipped upside down but the diatonic quality is maintained (see Figure 7-17).

Figure 7-17: Using melodic inversion, retrograde, retrograde inversion, augmentation, and diminution

When the motive is played backward it's called retrograde. For example, if you have the notes C, E, A, D, a retrograde treatment would mean that the notes appear as D, A, E, C. In counterpoint, retrograde is typically used in the imitative voice (often the second voice that enters in a round). Retrograde inversion means that the melodic line is turned backward and upside down. It's really a combination of retrograde and melodic inversion.

Augmentation means that the melody is stretched out rhythmically. In other words, the rhythms—not the tempo—are slowed down or lengthened in some way. For example, you might have quarter notes shifting to half notes or eighth notes shifting to quarter notes. You may also use ties to expand the duration of each note.

Diminution is the reverse of augmentation. Here, the notes are sped up. Typically, quarter notes become eighth notes, eighth notes becomes sixteenth notes, etc. In all cases, you must first introduce the melody plainly or unadorned then build variations from this. The ultimate goal with melodic variation in any form—round, canon, fugue, or modern usage—is to show juxtaposition, development, and contrast. Figure 7-17 shows the original motive used in Figure 7-13. However, now it is varied using melodic inversion, retrograde, retrograde inversion, augmentation, and diminution, respectively.