Motifs: Molecules of Music

Motif: A short musical unit, usually just few notes, used again and again.  

A recurrent short phrase that is developed in the course of a composition.

A motif in music is a small group of notes encapsulating an idea or theme. It often contains the essence of the composition. For example, the opening four notes of Beethoven’s Fifth Symphony express a musical idea that is repeated throughout the symphony. 

Motif-LvanB-5

The motif, comprising just four notes, is instantly recognizable, and evokes all the developments and dynamics that occur in the piece.

Beethoven’s motif is simplicity itself: just three short notes followed by one long one; but he uses this motif in a masterly manner. It recurs throughout the work in numerous variations and is an icon of the symphony.

Transformations and Manipulations

A motif is the minimum unit that conveys the character of a musical piece, the smallest independent particle with a definite identity. Thus, we may call a motif a molecule of music. It is most often thought of in melodic terms, but may be a harmonic chord sequence without an explicit melody, or even simply a rhythmic pattern.

The composer can develop a piece of music by using variations based on the motif. Essentially, the motif is subjected to a series of mathematical transformations. These transformations are organized into (algebraic|) groups. The motif may be transposed (raised or lowered in pitch), inverted, reversed, etc. These transformations are especially important in twelve-tone music.

The Klein 4-Group

Take a book, place it on the table and draw a rectangle around it. How many ways can the book fit into the rectangle? There are four ways that this can be done. They are shown — for a randomly chosen book — in the figure below. The four orientations can be described in terms of simple rotations, starting from the upright configuration on the left:

RRI-Cover-Four-3D

    1. Place the book upright with front cover up (that is, do not move it).

    2. Rotate through 180º about X-axis (horizontal line through centre).

    3. Rotate through 180º about Y-axis (vertical line through centre).

    4. Rotate through 180º about Z-axis (line through centre perpendicular to book).

Klein-4-CayleyTable

We use the four symbols {I, X, Y, Z} for these geometric operations. They combine according to the multiplication table shown here. They form a group called the Klein 4-Group, and the figure below shows how the transformations are applied to a tone row.

Twelve-Tone-Transformations

Rhythmic Motifs

A motif usually carries the seed of a melody, or a crucial chord sequence. However, it may simply be a rhythmic structure, like the motif of the One Note Samba, shown here.

Motif-OneNoteSamba

The B-A-C-H Motif.

Motif-BACHThe B-A-C-H motif is the four-note motif, B-flat, A, C, B natural. In German musical notation, in which the note B natural is named H and B-flat is named B, it spells out Bach’s name. It is an example of a musical cryptogram. The B-A-C-H motif has been borrowed and re-used by many composers. Bach himself used the motif in a number of works; indeed it appears so frequently in the bass lines of his fugues that its use had to be intentional.

A motif reminiscent of Bach’s motif is used in the song It’s Impossible, popularised by Perry Como.

Motif-ItsImpossible

Rachmaninov Modifies a Molecule to Make Magical Music.

Niccolò Paganini’s Violin Caprice 24, composed in 1817, was the basis for Rachmaninov’s Rhapsody on a Theme of Paganini. The motif in the opening bars is shown below (left). Rachmaninov performed his magic, converting this molecule into a new and wonderful form by a few simple transformations. For his 18th variation, he inverted it (a flip about the horizontal) and changed from minor to major. He also modulated to another key, D-flat major (not shown). This composition is described by Stephen Hough in a video (link below).

Motif-Rachmaninov

Sources

Proms, 2013: Stephen Hough on Rachmaninov’s Rhapsody on a Theme of Paganini. Video


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