Binary form.

A musical structure consisting of two mutually dependent sections of roughly equal duration. It is usually symbolized as AB, but often may be better expressed as AA'.

1. Definition.

Binary form is characterized by an articulated movement to another key followed by an articulated return to the tonic. A conclusive arrival on the principal contrasting key (normally the dominant) marks the end of the first section, and is matched by the final return to the tonic at the end of the second half. Each section is usually marked to be repeated. Binary form is generally understood to imply a continuous form in which the harmonically incomplete first half demands continuation. It may also be sectional or composite, however, and contain harmonically complete and thematically distinct first and second halves. In its most characteristic manifestations binary form is associated with Baroque instrumental music, in particular the dance movements of the suite; but so obvious a form was in use long before the Baroque period.

2. To 1700.

The medieval Bar form can be classed as a sectional binary form in which only the first part is repeated, giving an AAB structure. Even in the early rondeau and other formes fixes, in which a complex system of phrase repetition was required by the verse structures, the music itself was often made up of two periods or phrases. With the disappearance of the formes fixes, and the development of instrumental music whose shaping owed a good deal to the symmetries of phrases required for dancing, binary movements became more and more frequent.

Some of the keyboard settings from a Venetian collection of about 1520 (I-Vnm Ital.iv.1227) illustrate this. De che le morta la mia signora has two strains closely corresponding in rhythm, the first in G minor, the second beginning in B and moving back to G minor. No repeats are indicated but they would make good sense. Elsewhere in the collection double bars suggest that repeats should be made (O Dio, ch’a fatto il ciel con la fortuna), or such repeats are actually written out (Margaritum). Attaingnant’s publications of the 1530s contain branles in binary form; an allemande by Claude Gervais (HAM no.137) and Ammerbach’s Wer das Töchterlein haben wil from the Leipzig Orgel order Instrument Tablatur of 1571 are similarly constructed, and partsongs like Anerio’s Al suon (HAM no.160) and Hassler’s Ach Schatz (HAM no.165) provide vocal examples. In balletts such as Morley’s My bonny lass or Weelkes’s Hark, all ye lovely saints, fa-las provide a textual identity for the close of each section: a comparable musical identity was to become a usual feature of instrumental dances later in the development of the form.

Many dances of the late Renaissance were written in three strains, however, and such pieces are preponderant in a collection like the Fitzwilliam Virginal Book, though galliards by Bull and Philips (nos.17 and 87 respectively) and Muscadin (no.19) show the new tendency towards binary form. But the pavan in three strains persisted almost to the end of the 17th century and sarabands and minuets were also occasionally constructed in this way. By the close of the century, however, binary form was usual in the majority of dances.

3. After 1700.

In the 18th century sectional binary form continued to appear in folk music and in chorales (for example in Bach’s chorale no.38, Straf mich nicht in deinem Zorn). It is most commonly found in arias, and may be understood retrospectively as a da capo form that unexpectedly fails to complete itself. This almost always occurs for dramatic reasons, as in Jonathan’s ‘No, no, cruel father, no!’ from Handel’s Saul, where a lamenting first section in B minor is succeeded by a G major Allegro. Both sections are harmonically closed, leaving the larger structure open; AB is clearly a more appropriate designation here. A more complex example is Iole’s aria ‘My father! ah! methinks I see’ from Handel’s Hercules. In the first section, beginning and ending in C minor, Iole relives the killing of her father by Hercules. The relative major is held in reserve for the second section, in which Iole bids her father rest in peace. Rather than finishing in E major, though, the music clouds over into E minor, implying that Iole’s remembrance of the violent death has invaded her thoughts. The close thus reverts to the mode of the first section and creates some sense of rounded shaping to the whole, if in the first instance for dramatic reasons; there are also some subtle thematic recollections from A. Handel therefore manages to give both an informal hint of a da capo in terms of mode and material and a sense of coherence to an unusual sectional binary structure.

Simple binary form was the most common type of continuous binary form used in the Baroque period. It is characterized by a broad continuity of manner, with much freedom of detail, and the second section is often at first only loosely thematically related to the first. In the second half of the Courante from Handel’s Suite no.6 in G minor, for example, references to the material of the A section are sporadic and unsystematic, and although much of the material is new, it is not distinctively so and is similar to the manner of the first part. The two halves are roughly equal in length, creating a large-scale temporal balance that helps secure the coherence of the whole. (This simple continuous binary form is rarely found after the mid-18th century, and it is perhaps for that reason that Schoenberg omitted it from his Fundamentals of Musical Composition, implying that it was no longer of use to the student of tonal music.)

Both these aspects of design were subject to alteration. It became increasingly common during the Baroque era for the second half to relate more precisely to the first. In particular, the listener’s comprehension of the form was aided by a ‘rhyming’ of the outer parts of each half. Thus the second half would often begin with a dominant version of the first half’s opening unit or phrase, either briefly acknowledged or quoted extensively. An inversion of the material was also common, particularly in gigue movements (see, for instance, the Gigue from Bach’s English Suite no.4 in F). In the Allemande from the same work, not only does the material appear in retrograde, but also the hands swap roles, the left hand now taking the melodic lead. This dominant version of material was often used as a springboard to regaining the tonic, albeit often only briefly before the harmony moved further afield.

The dominant equivalent of the first-half opening was retained as if by force of habit for some time in sonata-form movements, remaining common until the 1780s. In the first movement of Haydn’s Sonata no.46 in E, for example, the account of the theme in the dominant is followed immediately by one in the tonic. This acts rather like a false reprise, although it is quickly deflected by a turn towards V of VI. The two features may be seen in conjunction in a simple binary context in the Presto of Benedetto Marcello’s Sonata no.2 in G. Occasionally the return to the tonic is still more direct, such as in the Sonata no.21 in A by Seixas (ed. in PM, ser.A, xxxiv, 1980), where the first two bars of the second half are almost identical with the first two bars of the first. With the first half ending unusually in the relative minor, though, the tonic and its initial material are a necessary reference point before further ambitious harmonic journeys can be undertaken. This exposes the underlying premise of this harmonic habit.

Such rhyming could also be found at the ends as well as the beginnings of the respective halves. At first it may have amounted to little more than a correspondence between the respective cadences, as in the Allemande of Froberger’s Suite in E minor, but the explicit thematic matching became more extensive, as often the entire final strain of the first half in the dominant was repeated in the tonic at the end of A'. This procedure yields the so-called balanced binary form. It is perhaps associated above all with the sonatas of Domenico Scarlatti, where a significant amount of end-rhyme is common. Many binary-form pieces of the period are ‘balanced’ at both the beginning and the end of the second half.

The end-rhyming form has perhaps received more emphasis (to the extent of earning its own label) because of its apparent anticipation of one of the governing principles of sonata form. That is, it restores to the tonic prominent material originally exposed in another key, making thematically explicit the harmonic structure that underpins the form. Sonata form in fact exemplifies the other principal binary type, rounded binary form. Here the double return creates a discontinuity of design that leads to the perception of three sections in thematic terms, yet the harmonic process remains the same as that found in simple binary form. This conflict between melodic and cadential design leads to a designation of ABA' for this binary form. Sonata form does not have to coincide with rounded binary form, however. Chopin’s sonata-form movements are closer to the principles of balanced binary form, avoiding as they do the return of the opening material in the tonic but transposing all the important non-tonic material in the last section. On the other hand, there are also many rounded binary movements that are not in sonata form, particularly minuets and scherzos. A representative example is the Minuetto from Clementi’s Sonata in A op.10 no.1. Where the first section ends in the tonic, though, the form should be thought of as a sectional rounded binary form: in spite of the firm tonic cadence at the end of A, the thematic continuity between first and second sections makes the description ‘ternary’ misleading (see Ternary form). The Minuet of Haydn’s String Quartet in E op.20 no.1 provides an instance of this.

The development of rounded binary form is indicative of a trend found also in simple binary form: the tendency for the second half to become longer than the first. A succinct example is the Sarabande of Bach’s French Suite in D minor. The first half, a single eight-bar strain moving to a half-cadence on the dominant, is answered by a second half of precisely twice the length. Although there is no rounding of the form as such nor any end-rhyme beyond the rhythmic resemblance of the two final cadential bars, similar impulses are at work. Bach begins A' by transferring the melody of the first five bars to the left hand, untransposed, and reharmonizing it with new upper parts; this is part of an eight-bar phrase that cadences on the subdominant. The final eight-bar phrase restores the first five melodic bars to the soprano, but transposes them with slight adaptations up a 5th. The whole of the second section, while obviously maintaining continuity of material with the first part, has the more expansive and somewhat exploratory character typical of this lengthened version of simple binary form.

There was no simple progression from simple to balanced to rounded binary form, however. For a considerable time in the earlier 18th century these types were merely alternative means of structuring an instrumental movement. Bach’s Partita no.4 in D, for example, exploits all the resources and nuances of binary construction. A simple binary form can be found in the Minuet, but the minimal end-rhyme found between the left-hand parts of the respective final bars of each half is not enough to constitute a truly balanced form. The second half begins with fresh material, and, although there are two references to the opening melodic unit, neither would justify the description ‘rounded’ binary form. The second half is much expanded, having 20 bars as opposed to the eight of the A section. The Allemande, on the other hand, has nearly equal halves, the first having 24 bars and the second 32, and it is balanced at both ends. The start of the second half provides an equivalent of only the first bar of the piece, with the characteristic flattening of the fourth scale-degree and consequent touching on the tonic, but the end-rhyme is extensive, the final six bars of the first half being transposed at the end of the second. Bach inserts some derived material near the end to create a grander sense of climax. Apart from this, almost every event of A is accounted for in A', but is reordered to yield a still larger, if complex, sense of rhyme. The Sarabande, too, is balanced at both ends of the second half, but it also exemplifies rounded binary form, the opening two bars being straightforwardly recapitulated at bars 29–30. After this, though, the music seems to revert to the processes and material of the central section, so that any sense of recapitulation in a later, sonata-form sense is denied. Thus, although seemingly more ‘progressive’ in its formal essentials, the Sarabande is considerably less concerned with establishing a large-scale equilibrium than the Allemande.

The example of Domenico Scarlatti also reminds us that balanced binary form should not be considered less well developed or less versatile than the rounded form. Scholars have been much preoccupied with the composer’s consistency in this formal regard and have failed to do justice to the variety of its realizations. Indeed, Scarlatti can hardly have been aware of the fact that he was using what we would now define as the subspecies of one historical form. After all, that many subsequent composers consistently employed sonata form in certain movements is hardly a matter for comment. In any case, Scarlatti’s sonatas often begin with material that is relatively indeterminate thematically (but certainly not in the force of its expression) and do not arrive at something more clearly shaped, and more ‘thematic’ in its behaviour (in other words, reiterated as a unit), until the end of the first half. By ensuring, like Chopin later, that this material is accounted for in the tonic at the end, the composer is in fact articulating the same principles of harmonic argument that are evident in rounded binary and sonata forms.

BIBLIOGRAPHY

NewmanSBE

E.J. Dent: ‘Binary and Ternary Form’, ML, xvii (1936), 309–21

R. Kirkpatrick: ‘The Anatomy of the Scarlatti Sonata’, Domenico Scarlatti (Princeton, NJ, 1953/R), 251–79

C. Thorpe Davie: Musical Structure and Design (London, 1953)

D.S. Green: Form in Tonal Music (New York, 1965)

I. Spink: An Historical Approach to Musical Form (London, 1967)

W. DEAN SUTCLIFFE (1, 3), MICHAEL TILMOUTH (2)