What are the key features of sonata form and why is this form significant in the Western Classical tradition?

Sonata form is an important large-scale formal type in instrumental music of the classical period; in this medium, composers reveal their greatest technical skill and expressive potential. It is, arguably, the period’s most highly developed and complex compositional design and almost every multi-movement work (except the concerto) contains at least one movement written in this form. The form is composed of three significant sections, the exposition, development and the recapitulation. In addition to these components there may also be an introduction and/or a coda. The large-scale tonal and form-functional organization of sonata form is analogous to the small ternary form. Sonata form resembles the rounded binary version, because the exposition is normally repeated and the development and recapitulation are sometimes repeated together. The portioning of sonata form into bipartite and tripartite sections has been debated. Different modes of organisation generate characteristics of both in sonata form. The constituent parts of the musical material conventionally include a main theme, transition and a subordinate theme. These elements are introduced in the exposition and form the bedrock of the thematic material, which will be developed and transformed throughout the course of the work. The primary role of the exposition is to fulfil a series of cadential goals, with the aim to establish two primary key areas: tonic (I) and dominant (V). The main theme is in the tonic key and the subordinate theme is usually in the dominant in a major key (or the relative major in a minor key). The transition provides the modulatory link between the tonic and dominant key areas.The degree to which these cadential goals are achieved determines the course of the other two structural sections, the development and recapitulation. Tonal polarity is thus a vital part of the sonata design. The second region in the exposition creates a structural dissonance in relation to the first home key. This is intensified throughout the development, most notably through the use of rapid modulation to more distant key areas and is eventually resolved to the tonic in the recapitulation. Indeed, it is possible to argue that the entire trajectory of the sonata form is set up to ensure the resolution of the harmonic tension first outlined in the exposition.