Appendix: as précis of Variation Forms
Dr. William Renwick
Variation forms sprang up with the rise of instrumental music in the 16th century, and have continued to the present day. The principle of variations is a fundamental one: it combines and unites the opposites of repetition and contrast.
There are two basic types of Variation form, Sectional and Continuous.
Sectional Variations utilize a theme that has a definite ending and a complete musical form. Such themes are most often in binary or rounded binary form. (Ternary is seldom used. It would appear that the internal repeat structure of ternary form works against the progressive notion of the variation idea.)
Continuous variations typically use a theme that is less than a complete musical form in itself, usually a single phrase. The simplest of these is the descending-fourth bass progression, which outlines a harmonic pattern I-V. Longer examples are found in Purcell’s Dido’s Lament and Bach’s Passacaglia and Fugue in C Minor.
In most variations, the composer retains the tonality, proportions, and general harmonic content of the theme in each subsequent variation. This provides a consistent formal model.
Growth and development. Variations are frequently found in which each succeeding variation projects an intensification of what has gone before. These variations basically project a crescendo (or wedge) of activity from beginning to end. The composer must develop a strategy to provide a convincing ending to this plan. In some instances the regular increase of intensity is broken into two or more separate waves. This is seen, for example, in Bach’s Passacaglia.
Arch form. Variations are often found which contain one or more variations in the middle that project a contrasting character. This is usually accomplished through a change of mode. This strategy will suggest an arch form to the composition as a whole. An Example is Handel’s chaconne in G Major.
Connection and contrast. It is considered artistic to relate one variation to the next. This shows a kind of continuity that balances the disjunct quality of sectional variations. The connection from one variation to another may occur through any of the parameters of music, such as motive, register, texture, and so on. Schenker’s analysis of Brahm’s Op. 24 describes this technique in detail, and points to the subtlety with which a composer can link variations into a single sweep. On the other hand, contrast is an equally valid principle of organization. The freshness and diversity of musical parameters helps to engage and amuse the listener. Contrast appears to be a principle factor in the ordering of Bach’s Goldberg variations and Beethoven’s Variations on a theme of Diabelli, for example.
Rhetoric: Rhetoric can play an organizational role in variation forms, whether through a systematization of order, as proposed by Alan Street for Bach’s Goldberg Variations, or in a more straightforward manner through the affective variations of Mozart, for example. A further development of the rhetorical model would be “Character Variations”, such as Elgar’s Enigma Variations, in which the content of the variations is guided principally by extra-musical associations.
Grouping: Composers often establish groups of variations through similarities of mode, key, texture, or content within groups, and contrast between groups. This technique provides a larger sense of form and development and can lead to effective arch and recapitulatory forms.
Combination: Complex sets of variations often employ combinations of formal procedures, so that a single set of variations may comprise aspects of arch form, and development, for example. Handel’s G Major Chaconne, for example, beautifully combines “wedge” and arch forms.
Ending: Unlike ternary and sonata forms, variation has no inherent rounding or recapitulatory characteristic. Composers have invented a variety of ways to provide closure in variation form:
Coda: The breaking off of the final variation into a coda can provide a convincing ending. Typically the coda breaks away from the established proportions of the theme. This technique is familiar in the works of Mozart.
Reprise of the theme: A simple repetition of the original theme can provide a sense of closure and rounding. This occurs in Bach’s Goldberg variations, and is frequently found in the jazz literature.
Fugal finale: A concluding fugue can provide closure by (1) breaking from the established phrase patterns of the theme and variations, and (2) by treating the material in a fundamentally different way. Brahms Op. 24 is a good example. Bach’s Passacaglia is another. This can provide a sense of balance in analogy with the Prelude and Fugue pair of the baroque, for example. The fugue will normally provide an intensification of the content by allowing shifts of key and added rhythmic and textural complexity.
Simplification: Occasionally we find that a set of variations concludes with a relatively simple variation. This technique provides a kind of balance and reflection with the original theme.
Combination: The ending variation(s) may attempt to sum up the work by re-using elements from previous variations. This appears in Sweelinck’s Mein junges Leben hat ein End’, and is a governing feature of Rzewski’s The People United Will Never Be Defeated.
Hybrid forms: The variation principle can participate in more complex forms. For example, the ostinato of Purcell’s Dido’s Lament provides the harmonic foundation for an aria in strict binary form. In the opening chorale movement of Bach’s cantata Weinen, Klagen, Sorgen, Sagen, the ostinato provides the basis for a ternary form choral movement. Hybrid forms are also seen in a number of the articles in this journal. I am thnking particularly of the Bartok Rumanian Christmas Carols, and Saint Tyagaraja’s Merusamana, but they also appear in the seventeenth-century “variation-fugue”, for example. Indeed, Beethoven’s Grosse Fuge may be seen as a massive hybrid of fugue, variation, and four-movement sonata form, a unique combination and intersection of elements unified and controlled by a single theme. The notion of meta-variations can arise in even larger works, such as the Art of Fugue or the Musical Offering, for example, in which a single theme is worked out systematically through a large number of separate musical compositions.
 This précis describes some of the more salient features of variation form. Standard technical discussions are available in Douglass M. Green, Form in Tonal Music (New York : Holt, Rinehart, and Winston, 1965), and Wallace Berry, Form in Music (Englewood Cliffs, N.J. : Prentice-Hall, 1986.)
 Heinrich Schenker, “Brahms’s Variations and Fugue on a Theme by Handel, Op. 24.” Der Tonwille II (Oxford: Oxford University Press, 2005), 77-114.
 Alan Street, “The Rhetorico-Musical Structure of the `Goldberg’ Variations: Bach’s Clavierübung IV and the Institutio Oratoriaof Quintillian.” Music Analysis VI:1-2 (1987), 89-131.