Introduction
Binary form is a way of structuring a piece of music in two related sections, both of which are usually repeated. Ternary form refers to a three-part A–B–A structure in a piece of music.

Binary form was popular in the Baroque period: most dance movements of the suite are binary forms. The Menuet en trio in the suite is an example of a ternary form.
Binary and Ternary form
Binary form
We can distinguish two types of binary forms
  1. Simple binary form
    The simple binary form consists of two sections, AB. Section A starts on I in the orginal key and ends with a 'open', inconclusive cadence on V (half cadence in original major key or tonic in the dominant key or -if the original key is minor- in the relative major). Section B returns to the original key and ends with a 'close', conclusive cadence, i.e. on I in the original key (sometimes a short coda follows).

    With respect to the numbers of bars, symmetrical and asymmetrical binary forms can be found. Example: the Allemande of Bach's E flat French suite is symmetrical (10 + 10 bars) and the Courante from the same suite is asymmetrical (16 + 20 bars).

  2. Rounded binary form
    The Sarabande of Bach's E flat French suite shows at the end of section B some kind of 'recapitulation': the last seven bars are in the orignal key repeating melodic material from the beginning of section A (Section A has 8 bars and section B has 9 + 7 bars). This is referred to as rounded binary, and is labeled as ABA'.


Ternary form
  1. Simple ternary form
    Ternary form is a three-part A-B-C structure in a piece of music (as the theme of the slow movement of Haydn's op. 76 nr. 3) or A-A-B as in the old Bar form (such as the Dutch national anthem).
    However, ternary form is usually understood as an A–B–A structure in a piece of music. The first and third parts (A) are musically identical, or very nearly so, while the second part (B) contrasts sharply with it.

    The first section of a piece in ternary form does not usually change key. The middle section will generally be in a different key. It usually also has a contrasting character, e.g. by means of different key and orchestration. Around Lully's time, it became a common practice to score this section for a trio (such as two oboes and a bassoon, as is common in Lully). As a result, this middle section came to be called trio, even when no trace of such an orchestration remains.
    Commonly, the third section will feature more ornamentation than the first section (e.g. da capo arias).

    Ternary form is often found in baroque opera arias (the da capo aria; 'Buss und Reu' and 'Blute nur' from Bach's Matthew passion) and in suite movements as menuet and bourrée.

  2. Compound ternary form
    A distinction is sometimes made between compound ternary form—in which each large part of the form is itself divided in a way to suggest ternary or binary form (giving, for example, an overall scheme of A–B–A–C–D–C–A–B–A)—and simple ternary form, in which each large part of the form has no particular structure itself. Minuets and trios are normally compound. Another name for the latter is 'composite ternary form.'
Binary and ternary forms in classical and romantic period
The (asymmetrical) binary form begins to be more common than the symmetrical type from about the time of Beethoven onwards, and is almost routine in the main sections of Minuet and Trio or Scherzo and Trio movements. However less popular in seperate pieces, some striking examples can be given: Beethoven (slow movements piano sonatas as in the Appassionata; German Dances), Schubert (Ecossaises)
The ternary form can be found in the menuet's and scherzo's from sonatas, symphonies en quartets of Haydn, Mozart en Beethoven. In the 19th century especially composers of small works (Schumann, Schubert, Grieg) used often the ternary form. Although most of Chopin's nocturnes are in an overall ternary form, quite often the individual sections (either the A, the B, or both) are in binary form.
Notes
Rounded binary is not to be confused with ternary form, also labeled ABA—the difference being that
  1. in ternary form, the B section contrasts completely with the A material as in, for example, a minuet and trio.
  2. in rounded binary, when the 'A' section returns, it will typically contain some references to the 'A', whereas ternary form will end with the full 'A' section.