Edward T. Cone, Musical Form and Musical Performance, 76-77:
The formnal design that is ideal for the Classical style, as the fugal or ritornello design was for the Baroque, is of course the sonata-allegro. One can trace how, during this period, other patterns, from compact song forms to extended rondos, aspire to the sonata -- how dominant cadences tend to return in the tonic, how central episodes expand into developments, and so on . . . But more important than the form as a patern is the unifying principle behind it, which, I believe, is not to be found in its bithematicism, or its developmental aspect, or its binary or ternary (take your choice!) structure. Let us recall for a moment that the principle underlying both the fugue and the concerto was the recurrence of the theme at every important point of harmonic arrival. The corresponding principle for the Classical style -- let us call it the sonata principle for want of a better term -- is somewhat more complex. It requires that important statements made in a key other than the tonic must either be re-stated in the tonic, or brought into a closer relation with the tonic, before the movement ends.
Charles Rosen, Sonata Forms, 100:
In the first of the two sections of first-movement form (the exposition), there are three "events": the last event and one or both of the first two must be set in relief. They are:
a) the movement away from the tonic;
b) the establishment of the dominant (e.g. emphatic half-cadence on V of V);
c) confirmation of the modulation by a full cadence on V.
In early eighteenth-century works, the first two events are rarely emphasized by the texture, and the last is held back as far as possible until the end of the section: in the sonata, however, the half-cadence on V of V is succeeded by a theme, new or old, and a change in rhythmic movement.
The exposition may be thought of as consisting of only two large sections:
(1) First Group and Transition -- consisting of one or more tonic-key themes and ending with a transition that leads to a cadence off the tonic.
(2) Second Group -- consisting of one or more non-tonic themes (in Classical works, usually all in the secondary key, i.e. V in most major-mode movements, III in most minor-mode movements, but in the Romantic period each theme can appear in a different non-tonic key) and ending with a non-tonic closing theme. The exposition is often repeated, reflecting the origins of sonata form in a binary form.
The development leads to a retransition on V, followed by a recapitulation that restates the First and Second Groups from the exposition. The First Group most often returns in the tonic, but may appear in the subdominant or in some other closely related key instead. The Second Group will either be re-stated in the tonic, or brought into a closer relation with the tonic (to quote Cone). The transition must be recomposed so as not to lead to the non-tonic key that started the Second Group in the exposition. A coda may round out the movement.
Sonata form originated historically as an elaboration of continuous (rounded or balanced) binary; Rosen (Sonata Forms, Chs. 3,4, 5) also sees the early 18th century aria, concerto and other forms and genres as precursors.
Rosen (p. 98) states that the purpose of the exposition is to polarize, or set in clear opposition, the two key areas and the themes associated with them.
1. Main Theme (or group) in tonic.
2. Transition from tonic to key of Secondary Theme, sometimes consisting of (or beginning with) a
2(a) Counterstatement of the Main Theme.
3. Secondary Theme (or group) in new key (usually V if movement is major, III if movement is in minor).
4. The last theme in the second group is called the Closing Theme.
Here other non-tonic keys are explored and motivic relationships latent in the exposition are developed. Then, as Cone states, "important statements made in a key other than the tonic during the exposition must either be re-stated in the tonic, or brought into a closer relation with the tonic."
5. Development -- Area of harmonic flux ("free fantasy") which usually develops motives from Part I. Leads to V, often culminating in a
5(a) Retransition (expansion of V7 or V8-7) leading to
6. Recapitulation of Main Theme (or group)
7. Recap of Transition -- unlike (2), stays in opening key, and thus must be extensively recomposed.
8. Recap of Second Theme (or group), this time in opening key.
9. Recap of Closing Theme in opening key: may be followed by a
10. Coda, a separate section occurring after the end of the Closing Theme; often based on Main Theme and often inflected with subdominant harmonies.
A main theme or themes (1) establishe(s) the principal tonality. A transition, or bridge (2), leads to a new key --typically V if the movement is in a major key, III if the movement is in a minor key. The bridge may begin with a counterstatement of the main theme, i.e. a passage that starts like a repeat of (1), but soon veers off towards the second key area of the movement. A second theme or themes (3) signal(s) the arrival of the second key area. A closing theme (4) in the second key area signals the end of the first half of the movement, called the exposition. In more expansive sonata form movements, more than one theme may occur in the two key areas; in such cases, analysts speak of a first group and second group, rather than a main and a second theme. The second group may include tonicizations of two or more non-tonic keys. A repeat sign at the end of the exposition is usual. Rosen (p. 98) states that the purpose of the exposition is to polarize, or set in clear opposition, the two key areas and the themes associated with them.
The second half of the movement begins with a development (5), which serves to delay the final resolution of the oppositions set forth in the exposition as well as to explore the component motives, rhythmic and harmonic implications of the exposition's themes, and may recombine them so as to create new melodic ideas. Often, a completely new theme is introduced during the second half of the movement as well. Typically, a development begins in the key that concludes the exposition and moves through a number of other key areas before returning to the dominant, which is then transformed from a second, opposing tonic into a signal that the original tonic is about to return. The order of themes is also a variable (some development sections develop main theme, bridge materials, and second theme in turn; others develop only one or two of the themes from the exposition; others develop all three themes or groups, but out of order). Harmonic sequence and motivic fragmentation are frequent features of development sections, as is a false reprise, i.e. a statement of the main theme in the "wrong key".
A retransition, generally featuring a dominant pedal, may lead from the development into the recapitulation, which serves to resolve the polarization of keys and themes established in the exposition. The recapitulation features a restatement of the main theme(s) (6), a new transition (7), restatement of the secondary theme(s) (8) and closing theme, and optionally a coda (10), which draws the work to a close. The most important event in the recapitulation is the transposition of the second theme(s) and closing themes to the tonic. The transition must be recomposed to remain within the tonic key area. Although the entire recapitulation functions as an assertion of the supremacy of the tonic, often strong hints of subdominant harmonies occur there to balance the tonic-dominant polarity of the exposition.
1. A slow introduction may precede (1).
2. Additional development may take place during either of the transitions and in the coda as well.
3. In (3), the first theme of the first group may appear transposed to new key in lieu of a second-group theme ("monothematic" sonata form movement.)
4. The transition may temporarily stabilize a separate key area (e.g. vi), and / or may assume the character of a separate theme -- often called the bridge theme.
5. The second group may contain themes in two or more different non-tonic keys. This is a favored device of Schubert and composers who come after him.
6. Sonata form historians have posited a "rule" whereby one new theme may be introduced in either the devlopment or the recapitulation. More accurately, perhaps, we might observe that as long as the tonal requirements of the sonata principle are observed, composers may do whatever they wish in terms of introducing new themes after the exposition.
It is customary (following James Webster) to label themes in the first group with the letter "a" followed by a subscript denoting their order of presentation; the transition is labeled "tr," and themes in the second group are labeled with the letter "b" followed by a subscript denoting their order of presentation. If desired, an additional label that describes each second-group theme's function within the group may be added in parentheses, e.g. b2 (cl) for "second theme of the second group, closing theme," or b3 (coda) for "third theme of the second group, coda."
See Bass line sketches, below.
A sonata form movement, or any of its component parts, may be described by making a bass line sketch. This may be either a summary sketch or a detailed sketch. Both make use of analytical stem and slur notation.
A summary sketch shows only principal tonal areas and structurally important dominants and lines them up with thematic events. This is useful for expositions and recapitulations. Here is a summary sketch of the exposition and development of Mozart's Piano Sonata in B-flat K. 281:
The sketch shows that the first group consists of a single theme followed by a transition that leads to V in m. 16. The second group consists of a main theme (mm. 17-38) and a very brief closing theme (mm. 39-41).
A detailed sketch is useful for tracing the harmonic and thematic path of development sections. It uses analytical notation to show the relative structural weight of the various tonicizations and linear progressions that underlie the developmental process. Here is a detailed sketch of the development section of Mozart's Piano Sonata in B-flat K. 281:
Thematically, the sketch shows that after the introduction of a new melodic idea in m. 41, the two important themes from the exposition are developed in turn. Harmonically, the sketch indicates that the development section follows an overall trajectory from a tonicized V in m. 41 back in m. 68 to a V7 that is properly subordinated to (and prepares) the return of I. On the way, a vi-ii-IV progression is composed out. This is a "tour" of the three most common diatonic predominant scale degrees, and thus logically prepares m. 68's V7.