Melodic manipulation

All music has some material that unifies it: a large-scale melody, or a small gesture linking the parts of a work. Organising a composition so that its parts share related material, in pitch, melodic shape or rhythm, is the essence of composition, and composers do it, consciously or by instinct, with a handful of techniques that are easy to understand (Blatter 2007, part 5, art. 3).

This topic puts one short melody through those techniques. Here is the original idea:

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It rises by two thirds, falls by step, and settles on the tonic. Everything that follows is this same melody.

Retrograde

The simplest technique is to reverse the order: the last note, with its duration, comes first, the next-to-last second, and so on. That is the retrograde (Blatter 2007, part 5, art. 3):

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Since the melody has both pitches and durations, you can reverse just one of them (Blatter 2007, part 5, art. 3). In pitch retrograde the rhythm stays as it was and only the order of the notes is reversed:

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In rhythmic retrograde the notes keep their original order and the rhythm runs backwards:

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Inversion

In inversion the melody is turned upside down: where it rose it falls, and where it fell it rises, by the same distance (Blatter 2007, part 5, art. 3). But "the same distance" has two meanings.

In tonal inversion each interval is mirrored within the scale. A third that went up becomes a third that goes down, and the melody stays in the key:

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The price is that some intervals change quality. The original's first interval is a major third going up, C to E; in the tonal inversion it is a minor third going down, C to A. So it is not an exact mirror: it gives up exactness to keep the key (Blatter 2007, part 5, art. 3).

In real inversion every interval keeps its exact size. The major third that went up becomes a major third going down:

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Now the mirror is perfect, but the melody has left C major: its notes are those of F minor (Blatter 2007, part 5, art. 3). The term mirror is sometimes used for both kinds, and some theorists keep it for real inversion only.

The techniques combine. With three retrogrades and two inversions there are six retrogrades of inversions, all of them new material drawn from the same idea (Blatter 2007, part 5, art. 3).

Transposition within the key, and sequence

Transposing, in the ordinary sense, means changing pitch while keeping every interval exact. But there is another, very common kind: shifting the idea up or down within the same key, starting on another scale degree. Then some intervals change by a semitone, and each version has its own colour (Blatter 2007, part 5, art. 3).

This process has no established name. Blatter records tonal transposition, transmutation and also modal transposition, and notes that none of these terms is widely used (Blatter 2007, part 5, art. 3). Beware the last one: on this site, modal transposition means something else, writing a church mode starting on another note.

When the idea is shifted like this several times in a row, going up or down, it forms a sequence (Blatter 2007, part 5, art. 3). The opening of the melody, rising by step:

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Major third and minor third, then minor third and major third, then minor and major again. The shape is the same; the intervals adapt to the scale.

Shifting chords in blocks

A chord can also be shifted up or down, in two ways. Within the key, the chords' structure changes with the degree; keeping the structure fixed, the chords leave the key (Blatter 2007, part 5, art. 3). Triads rising through the C major scale:

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The same major triad, shifted without changing shape:

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Shifting in blocks, inside or outside the key, is called planing (Blatter 2007, part 5, art. 3). It is a hallmark of Debussy, and of popular guitar playing too, when one chord shape slides along the neck.

Augmentation and diminution

Augmentation lengthens the idea's durations. Doubling them all:

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Diminution does the opposite and shortens the durations. By half:

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Neither has to be proportional: durations can grow or shrink by different amounts. And the same effect can be had by changing the tempo instead of the note values (Blatter 2007, part 5, art. 3). A melody in augmentation in the bass, under the same melody in its original rhythm, is an old device of counterpoint.

Twentieth-century techniques

In the twentieth century composers took these ideas further (Blatter 2007, part 5, art. 3).

• Pitch augmentation and diminution. Instead of the durations, the intervals grow or shrink: each interval gains, or loses, a semitone.
• Chords from the melody. The melody's notes are grouped in threes or fours to make chords related to it. The reverse process draws a melody from a series of chords.
• Permutations. The order of an element is rearranged. In cyclical permutations the order stays and only the starting element changes: 1 2 3 4 5, then 2 3 4 5 1, then 3 4 5 1 2.
• Extraction. Some of the melody's notes are taken out to form a second voice, and the two lines then sound in counterpoint.
• Numerical proportions. The golden section and the Fibonacci series help some composers decide, for instance, in which bar a piece's climax falls.

Schoenberg's twelve-tone row, a fixed ordering of the twelve chromatic notes, is the natural ground for these techniques.

Choosing is the art

Combining these techniques, a single idea yields an enormous number of variations, and the composer is never short of material. But Blatter warns that not every variation is musically useful or attractive just because it grows from a good idea. The challenge has always been to select and combine the variants that make the most effective art (Blatter 2007, part 5, art. 3).

What comes next

Manipulation techniques work on short ideas. The smallest, the one that repeats and changes throughout a work, is the motive, and the most important is the theme.