Variation is a fundamental principle of musical composition, and a musical form based on that principle. To vary a musical idea means to change parts of it while keeping other parts constant—as in a folk song in which the second phrase has a new tune but has the same rhythm as that of the first.
Variations have been among the staples of the keyboard literature. There are four basic types where the piano repertoire is concerned:
Melodic Variation. In this form, the original tune varies in style and texture (ornamental turns, decorative scale passages, rhythmic, textural and tempo alterations, among many others) while the chief outline of the melody, the original harmonies and the overall form of the theme are preserved, although the mode (major/minor) may be altered. Almost all variation sets of the Classical Period are melodic variations, with Mozart’s perhaps the best known.
Harmonious Alliances. In this form, harmonic pattern of the theme is preserved while its melody, tempo, rhythm, texture (chords or intertwining melodic lines) and mode (major/minor) may change beyond recognition.
The most famous, and perhaps the greatest, example of this type is the Goldberg Variation by Johann Sebastian Bach. Lasting more than half an hour, the work is said to be a miracle of beauty, ingenuity, refined complexity and technical brilliance.
Passacaglia or Chaconne. This type consists of continuous variations on an ostinato (a phrase constantly repeated in any voice). The theme is not self-sufficient melody but either a constantly reiterated bass line, above which the upper parts may change, or a series of chords, whose harmonic sequence and unvarying rhythm is reiterated and unchanged throughout the composition. The most famous passacaglia for the piano is the set of 32 Variations in C Minor by Beethoven.
Fantasia Variation. In this type, only a part of the original theme (a single melodic phrase, a motto rhythm, or a structural form) is retained as a basis for variation, all other aspects and parts being subject to a very considerable transformation. It will often have recurring theme or fragment that serves as an agent of unity. It reached the peak of its development in the 19th century, particularly in the piano works of Schumann and Liszt.
Free forms are pieces developed by composers in improvisatory styles for keyboard instruments. These pieces are called preludes, fantasias, toccatas and fugue.
Prelude and Fantasia. The terms prelude and fantasy are basically interchangeable. A prelude is a movement which serves as a kind of introduction to another movement, generally a fugue. Formal preludes may also precede several movements, as in the suite or the partita. There are also self-contained preludes that precede nothing but each other such as in the preludes of Bach’s, Hummel, Chopin, Alkan, Rachmanimov, Debussy, Szymanowski and Scriabin.
Preludes originated with the tuning of instruments prior to a performance, and developed into an improvisatory preamble. Where the piano is concerned, it survived in an elaborate form in the fantasy or fantasia. Fantasia emphasize the rhapsodic, colourful and imaginative, subjective element, and the movement often ranges freely through a number of keys, and draws on different elements of style: aria, virtuoso keyboard writing, operatic-style recitative, etc.
Among the most notable examples of 19th century fantasia are Beethoven’s Fantasy in G minor, Op. 77, Fantasia in C minor and the two Sonatas alla Fantasia, Op. 27 (No. 2 being the famous Moonlight Sonata); Schubert’s four movement Wanderer Fantasy and Fantasy in F minor for piano duet, and Schumann’s Fantasia in C, Op. 17. The most common forms of 19th century fantasy, however, are the highly virtuosic reworking and elaborations of popular and operatic tunes, such as those of Liszt, Thalberg and Kalkbrenner.
Toccata is a musical composition for a keyboard instrument dating from the 16th century. It is closely related to the basic concept of prelude and fantasia. Its definitive characteristic is a degree of keyboard virtuosity; a display piece exploiting the skill of the keyboard player. It originally allowed for much improvisation. Generally it begins with full chords that give way to fast virtuoso or rhapsodic passages among which small fugato (fuguelike) sections are interspersed.
Important composers of toccatas include the Italian Girolamo Frescobaldi and the Germans Dietrich Buxtehude and Johann Sebastian Bach. Bach’s best-known toccata is the Toccata in D minor for organ. A 20th-century example is the Toccata, op. 2 (1912), by the Russian composer Sergey Prokofiev.
Fugue is a musical composition in which a melodic theme is systematically subjected to melodic imitation. The musical texture of a fugue, therefore, is contrapuntal, that is, based on interwoven melodies. Its most important stylistic feature is its treatment of thematic material by means of imitation. The fugue, however, does not necessarily conform in every detail to a fixed form. In the hands of its masters, the fugue depends on the rigorous contrapuntal exploitation of a single idea; thus, any given fugue will adhere essentially to the abstract formula but will deviate from it to some degree.
Of the fugue written expressly for the piano, the most famous are those by Beethoven’s sonatas Opp. 27 Nos 1, 106 and 110; and Diabelli and Eroica Variations); Schubert’s final section of the great Wanderer Fantasy; Mendelssohn’s Six Preludes and Fugues; Liszt’s Prelude and Fugue on B-A-C-H; Brahms’ Variations and Fugue on a Theme of Handel; Franck’s Prelude, Chorale and Fugue; and Shostakovich’s 24 Preludes and Fugues.
Sonata is basically a musical composition for one or two instruments but it covers such a wide range of styles, techniques and forms that no single definition can possibly do it justice. During the 16th and 17th centuries the term sonata (from the Italian word, sonare, meaning, “to sound”) simply meant an instrumental “sound piece” as distinct from a vocal composition, cantata, (derived from cantare, meaning, “to sing”).
Since the mid-18th century, the term has generally been used in instrumental work in several movements, each of which follows certain standards of character and form: the first movement is usually in sonata form and in moderately fast tempo; the second movement may use one of several forms (sonata, theme or variations) and is in slow tempo; the third movement is also in one of several forms (usually a medium-paced minuet and trio or a scherzo) and in a fast tempo; and the fourth movement, often in sonata form or rondo, or a combination of both. In most three movement sonatas, the minuet or scherzo is left out.
A sonata form is divided in three sections: exposition, development and recapitulation. The first and the last are essentially the same, with one very important exception, while the second is substantially different. Few movements by great composers, however, conform to this pattern. Nevertheless, the pattern gives an idea of the general principles behind the sonata movement.
The piano sonata was not different in form and overall concept from the symphony, the concerto and the string quartet which are simply sonatas for orchestra, sonatas for soloist and orchestra and sonatas for four strings, respectively. These are all works cast in the sonata format but are composed for other combination of instruments.
The Classical period (c. 1750-1825) was the golden age of the ideal sonata in which the majority of piano works written were sonatas. Mozart has written 26 sonatas; Haydn, 62; Beethoven, 32; and Schubert, 21. During the 19th century, the classical sonata tradition was maintained by Schubert, Schumann and Brahms. Many composers, such as Chopin, however, tended to disregard large-scale musical relationships by writing short pieces with strikingly differentiated movements. Others, such as Liszt, did away with most of the traditional format; his Sonata in B Minor is a long work in one movement.
Twentieth–century composers followed a variety of paths in their sonatas. American Samuel Barber have written large virtuoso pieces in the 19th century tradition, Russian-born Igor Stravinsky have returned to the classic principles of restraint and formal clarity, but the format and character of their music have tended to be highly individualistic. The meaning of the term sonata is thus “slowly returning to its somewhat ambiguous definition as an instrumental piece that has been composed in the absence of predetermined characteristics.”
Concerto is a musical composition, typically in three movements (fast-slow-fast), for one or more solo instruments with orchestra. The basic principle in a concerto is that of contrast: of the one with the few (as in Mozart’s three concertos K. 413-415); of the few with the many, as in concerti grossi, where a smaller group of instruments is contrasted with a larger group (as in Bach’s Bradenburg Concertos); or of one kind of instrument with a band of a differing kind (any kind of wind or keyboard instrument with string orchestra). From the point of view of contrast alone, the piano concerto is ideal, since the piano differs more from all the instruments of the orchestra than any of them do from each other (with the exception of the harp and percussion). It was Mozart’s piano concertos that brought the piano concerto to a “peak of perfection.”
The concerto has straightforward structure and its scope for repetition is varied only or principally by contrasts of instrumental texture. The first movement consists of an opening by the orchestra in the home key, followed by a solo discourse on the same material, also in the home key. In the exposition, the orchestra, in an abbreviated form of the opening would then modulate to a closely related key. The central development section is dominated by the soloist, with the orchestra reduced to an accompaniment. Recapitulation consists of a slim-line version of the exposition, which then give way to a solo cadenza (traditionally improvised) before a final return to the opening material for a formal close.
The second movement often follows a similar procedure but in contrasting mood, key and tempo: not to slow; essentially lyrical, though with greater harmonic and structural freedom than in the first movement; and with the soloist still the dominant feature.
The finale, by contrast, is generally virtuosic and quick, though some composers close with a graceful dance in the style of an extended minuet.