Theme and variations presents a theme and then transforms it through a series of variations, each preserving the harmonic skeleton while altering the surface. It is the formal manifestation of how music can be simultaneously familiar and endlessly surprising.
THE VARIATION PRINCIPLE
Theme and variations is a formal principle rather than a rigid form: present a theme, then vary it in a series of versions (variations), each transforming some aspect of the theme while preserving others. The preserved element is typically the harmonic structure — the chord progression underlying the theme — while the varied elements are melody, rhythm, texture, tempo, mode, register, and character. The listener's pleasure comes from simultaneously recognising the original and discovering something new. Variation form, more than any other, demonstrates the inexhaustibility of musical material: a simple 8-bar theme can sustain an entire half-hour movement when imagination is applied to its transformation.
Variation form appears in every musical era and genre. Baroque passacaglia (a continuous bass line or harmonic pattern over which variations accumulate), Classical theme-and-variations movements, Romantic character variations (Brahms's Variations on a Theme by Handel), 20th-century jazz standards (a lead sheet melody as theme, improvised variations as the solos), and popular music (the instrumental break as a variation on the verse) — all are manifestations of the variation principle.
TYPES OF VARIATION
Theorists distinguish several variation techniques, each preserving and altering different aspects of the theme:
- Ornamentation variation: the melodic line of the theme is preserved but ornamented with additional passing tones, turns, trills, and flourishes. Classical in character.
- Figuration variation: a new accompanimental figure (broken chords, running passages, dotted rhythms) is introduced while the melody moves more slowly or is implied by the figuration.
- Harmonic variation: the harmonic structure of the theme is altered (changing mode from major to minor, substituting related chords, adding chromatic harmony).
- Character variation: the tempo, meter, or expressive character changes (a slow lyrical theme becomes a march, a scherzo, or a funeral march).
- Contrapuntal variation: a countermelody or canon is added to the original theme, or the theme itself is treated fugally.
- Fantasy variation: the original theme is more freely transformed, going further from the source material while retaining essential harmonic or motivic connections.
- Constant-melody variation: the theme remains in one voice while other voices change around it.
- Constant-harmony variation: the harmonic skeleton remains fixed while melody and texture are continuously reinvented (the passacaglia principle).
BACH'S PASSACAGLIA AND GROUND BASS
A passacaglia is a type of continuous variation in which a repeating bass line (or chord progression) is stated over and over while variations accumulate above. Bach's Passacaglia and Fugue in C minor, BWV 582, is the supreme example: a solemn 8-measure bass line is stated 21 times, with each repetition building increasingly complex variations above it, culminating in a fugue that uses the passacaglia theme as its subject. The form creates a sense of inevitable accumulation — the bass is a fate motif that every variation must accommodate.
Henry Purcell's opera Dido and Aeneas ends with Dido's lament ('When I am laid in earth'), a passacaglia over a chromatically descending bass. The fixed, inescapable bass line embodies the fatalistic resignation of the text — a perfect union of form and expression. Purcell's chromatic descending fourth (the lament bass) became one of the most powerful affective topoi in Baroque music, used by Bach in the Crucifixus of the B minor Mass and countless other works.
CLASSICAL VARIATIONS: MOZART AND HAYDN
The Classical theme-and-variations movement is typically the slow movement (second movement) or the finale of a multi-movement work. Mozart's Piano Sonata K. 331 famously opens with a theme-and-variations movement (rather than a sonata-form opener) — six variations on a graceful 18-bar theme, each exploring a different figuration technique while preserving the theme's harmonic and phrase structure. Haydn's late symphonies often include variation slow movements; the "Surprise" Symphony (No. 94) is the most famous, its second movement built on a simple theme that Haydn deliberately disrupts with a sudden fortissimo chord.
BEETHOVEN'S TRANSFIGURING VARIATIONS
Beethoven transformed the variation principle in his late style. The Diabelli Variations Op. 120 (1819–23) takes a trivial waltz by Anton Diabelli and produces 33 variations of staggering expressive range, from grotesque parody to spiritual elevation. The finale of the Ninth Symphony is a variation set on the "Ode to Joy" theme, with each variation introducing new orchestral and choral textures. The Arietta of the Piano Sonata Op. 111 (Beethoven's last piano sonata) is one of the most sublime variation movements in the repertoire, beginning with a simple theme and progressing through variations that grow rhythmically more complex (sixteenths, then triplet sixteenths, then thirty-seconds) until the music seems to dissolve into pure rhythmic energy.
ROMANTIC AND 20th-CENTURY VARIATIONS
Brahms's Variations on a Theme by Handel Op. 24 and Variations on a Theme by Paganini Op. 35 are among the most demanding variation sets in the piano repertoire. Brahms's Variations on a Theme by Haydn Op. 56 (the "St. Anthony Variations," for orchestra; the theme is probably not by Haydn) ends with a passacaglia finale — a variation set within a variation set. In the 20th century, Schoenberg's Variations for Orchestra Op. 31 applies serial technique to the variation principle: the theme is a 12-tone row, and each variation transforms the row through transposition, inversion, and retrograde. Britten's Young Person's Guide to the Orchestra is a variation set on a theme by Purcell, using each variation to feature a different instrumental family.
JAZZ VARIATION
Jazz improvisation is essentially variation form: the "theme" is the lead sheet melody and chord progression; each chorus is a variation on that fixed harmonic skeleton. A 12-bar blues might be performed as fifteen or twenty choruses, each a fresh variation. Charlie Parker, John Coltrane, Bill Evans, and Sonny Rollins are supreme variation composers in this sense; the entire history of jazz improvisation is the history of the variation principle applied to a relatively small set of standard forms.
SOURCES & FURTHER READING
- Caplin. Classical Form. Oxford University Press. Chapter on Variation.
- Rosen. The Classical Style. Norton. Chapter on Mozart and Haydn variations.
- Open Music Theory — Variation Form (openmusictheory.net, CC BY-SA 4.0).
- IMSLP — Bach Passacaglia BWV 582, Beethoven Op. 111 (imslp.org).
- Sisman, Elaine. Haydn and the Classical Variation. Harvard University Press, 1993.
- Ratner. Classic Music. Schirmer.