There is no clear definition for invention. The name has been used by composers for different types of compositions. Here we will refer to Johann Sebastian Bach's inventions that are an excellent example of simple - yet complex - compositions using contrapuntal techniques.
Originally Bach called preambulum the two part inventions and fantasia and later sinfonia the three part inventions. Today we normally refer to both as two and three part inventions. Some of the two part inventions follow a structure similar to fugues, detailed here using fugue terminology:
|Exposition||The subject or theme is presented. It is usually very short and is imitated by the second voice.|
|First episode||After the exposition a transition - called episode in fugue terminology - using material from the subject leads to the key of the dominant or in the case of minor key invention to the relative major.|
|Second subject presentation||Once in the new key, the subject is presented often changing the roles of the voices.|
|Second episode||Another episode leads to a new closely related key. Relative minor in the case of major keys inventions or the dominant in the minor keys inventions.|
|Third subject presentation||This presentation is not as clear as the previous one and often seems more like an episode.|
|Third episode||This episode brings us back to the main key.|
|Last subject presentation||Finally the subject or a variation is presented in the main key to conclude the invention.|
An example of an invention using this structure is the C Major Invention BWV 772. You can read here a detailed analysis. Other inventions like the C minor and F major use extensive use of the canon. The E major and A major have longer themes that make use of the invertible counterpoint technique.