Music Theory for the 21st-Century Classroom

Inversion as applied to music means an idea is exactly upside-down or “mirrored” across a horizontal plane, like mountains reflected in a lake.

First, listen to the following example.

The first seven notes in measure 1 are inverted in measure 3, shown in the following example.

Melodic inversion can be real (where every interval is exactly the same quality) or tonal (where the intervals abide by the scale or key). For the majority of this text, we will encounter tonal inversion until we discuss techniques of 20th- and 21st-century music in the final chapters of this text.

Intervallic change is less exact than inversion. With intervallic change, the rhythm is generally intact and the motive relates to a previous iteration, but some of the intervals are different.

The next example has two intervals changed, one of which includes a change in contour.

Augmentation usually refers to an exact doubling of the duration of every rhythmic value in a motive or phrase.

We will discuss extension and fragmentation of motives later in this chapter.

Diminution is the opposite of augmentation and usually refers to the exact halving of the duration of every rhythmic value in a motive or phrase. However, diminution can also refer to the use of shorter rhythmic values, as in the following example.

Similar to the inexact nature of intervallic change, label a motive as having rhythmic change when some but not all rhythmic values of the motive are varied.

Imagine the effect if there had been no rhythmic change and the first measure was merely repeated.

In the next example, from Beethoven’s “Pathétique” sonata, motive 1 has dotted rhythms during the introduction of the piece.

In the development section, Beethoven changes the rhythm of motive 1 then abbreviates it in the following measure when it is sequenced up a step.

Ornamentation means the notes in a motive can be ornamented or embellished with passing tones, neighbor tones, and the other non-chords tones we studied in the previous chapter.

Here is an example of the ornamentation of a 4-note motive.

Extension of a motive needs little explanation: additional material is added to the end of a motive upon its repetition or reoccurrence at a later point in a piece.

Refer to the “Sir Duke” example directly above and to the final measure of the J.S. Bach Invention in C Major example in the section on augmentation.

While rare in tonal music, it is worth mentioning retrograde, which is an exact reversing of the order of notes, as can be seen in the following example from popular music.

We will not consider transposition of a motive (also known as a sequence, see Definition 9.1.11) to be a motivic alteration worth labeling since it is so common.