Theme and variations in Western art music is a musical form in which after the first statement of a theme, modifications or elaborations of it occur with each subsequent statement of that theme. In those subsequent statements, certain elements of the theme are retained, while others are altered. Ordinarily, enough are retained in order for the listener to be able to perceive the relationship of the modified statements to the original.
Historically, when the theme occurred in the bass, the length of the theme was seldom more than eight measures. This type of variation form is called either basso ostinato (obstinate bass) or ground bass variation. An excellent example in the literature is Johann Sebastian Bach’s Passacaglia from the Passacaglia and Fugue in C minor. A passacaglia — prounounced with a silent “g” — is a series of variations over a relatively short triple-meter (three beats to the measure) basso ostinato pattern.
In contrast to the passacaglia, another type of variation form is one based on a chord progression instead of on a melodic theme. This chord-progression type of variation form is known as a chaconne. A fine example of this in the literature is J.S. Bach’s Goldberg Variations. In jazz, a good equivalent of a chaconne is 12-bar blues chord progression.
As stated earlier, in theme and variations, every variation is characterized by retention of certain elements of the theme while others are replaced. This can be accomplished in various ways: through decoration or ornamentation (although the melody ostensibly still remains recognizable), or through using substitute chords (re-harmonization), or through changing the chords of cadences (resting points in music), or through changing the rhythms and/or meter (time signature), or through changing the tonality (from major to minor, for example), among other possibilities.
Ludwig Van Beethoven’s Eroica Symphony, 4th Movement
The fourth and final movement of Beethoven’s Symphony No. 3 in Eb Major (The “Eroica”) employs variation form in an extremely novel and clever manner, in that the composer utilizes two themes rather than just one, and moreover plays a trick on the listener in Variation III (see below).
The first theme, in Eb Major, is played in unison:
Two variations in contrapuntal treatment ensue.
In this variation Beethoven tricks the listener by transforming the first theme from its role as the principle melody, into a bass line for a second theme.
The key shifts to C minor, the relative minor of Eb major, and a somewhat fugal treatment occurs in this variation.
There are a total of ten variations in this movement, in which various permutations of both themes are presented prior to the arrival of the coda, the concluding section of the movement.
I will now illustrate several variation techniques as employed by Wolgang Amadeus Mozart in his Twinkle, Twinkle, Little Star Variations, known by its real name as Ah! Vous dirai-je, Maman (K. 265). Here is the original Mozart theme:
And now here are the first few measures of each of the variations of this utterly charming Mozart work:
In conclusion, various manifestations of variation form have been widely employed by composers of many different historical musical eras, serving as both a unifying element in their music and as a marvelous vehicle for giving free rein to their creative imagination. In fact, when I teach composition, I often assign the composition of a series of variations on a given theme as an easy and effective way to teach the principle and importance of unity in music and as a tool for stimulating students’ creative juices.