Bach wrote a set of fifteen two-part Inventions to serve two purposes. They were intended to provide keyboard exercises of intermediate difficulty, and to demonstrate compositional techniques in counterpoint. Bach also wrote fifteen three-part Sinfonias for the same purposes, with additional complexity.
The inventions are basically monothematic, and do not adhere to any specific formal structure. They employ a countertheme that is used to accompany the theme, which is presented in closely related keys interspersed with episodes in which fragments of the theme are often sequenced.
Analysis of an invention involves identifying appearances of the theme (T) and countertheme (CT) as well as the tonal areas in which they are presented. When episodes occur, the material that is used can be traced back to the theme or countertheme and identified along with the compositional devices Bach uses to spin out his music. There is rarely any new material introduced after the exposition, which leads to a very unified piece of music. It may take some practice at realizing the harmonic implications of two moving parts. Included in the Materials is Invention No. 4 in D minor. It is a good piece to analyze harmonically, placing a Roman Numeral under each measure, noting modulations, and marking each appearance of the theme and countertheme.
Procedures to follow in writing a two-part invention in the style of Bach are clearly defined in the assignment below, along with examples that demonstrate the technique.
Invention Assignment: Write the first 8-12 measures of a two-part Invention
The Sinfonia are much more complex, may have several themes, and demonstrate triple counterpoint. This is a reordering of the parts vertically. Most of them are highly chromatic, and all parts are treated with equal contrapuntal importance. To alleviate the density of three rapidly moving parts, Bach uses contrary motion and plenty of rests.
Analysis of these three-part inventions involves identifying themes, tonal areas, and compositional devices.