## Section30.7Invention Expositions

J.S. Bach’s Two–Part Inventions were not only intended as instructional keyboard pieces but also as examples of how to compose. In this section we will wed our species counterpoint knowledge with our knowledge of harmony in order to write a four-measure invention exposition using Bach’s C major and E minor inventions as models. Note the I–I–V–V–I harmonic progression.

### Subsection30.7.1How to Write an Invention Exposition

In the majority of examples, you will be given an invention theme in the first measure, which you will write an octave lower in the bass part in the second measure, then a perfect fifth higher than the first measure in the third measure, the fourth measure will be the third measure transposed down one octave, and, finally, you will end on the interval of a 10th—tonic in the bass part and $\hat{3}$ in the upper part. Please see the example below.

### Subsection30.7.2Altering Themes to Fit the Harmonies

1. You may find that a theme that leads naturally from I to V needs its contour altered when progressing from V to I in measures 4 to 5 in order to emphasize the V chord and the dominant–to–tonic harmonic motion. Modify the contour to emphasize the V chord at the end of the measure, altering as few notes as possible.

2. Additionally, you may be given themes that land on $\hat{3}$ on the downbeat of the second measure, not the $\hat{5}$ that occurred in the Bach C major and E minor invention expositions. You will need to alter the theme at the end of measure 2 to emphasize the I chord as well as make the first bass note of the third measure the $\hat{5}$ scale degree.

3. Finally, when a theme in minor containing the $\hat{2}$ and $\hat{3}$ scale degrees in the first two measures is transposed up a fifth in the succeeding two measures, scale degrees $\hat{2}$ and ♭$\hat{3}$ will be transposed to ↑$\hat{6}$ and ↑$\hat{7}$ . The reasoning is that ↑$\hat{7}$ is the 3rd of the V chord, and ↑$\hat{6}$ is a step below, typically a passing tone. Another way to think of this is to use the melodic minor scale in the 3rd and 4th measures.

### Subsection30.7.3Adding Counterpoint to the Theme Statements

After copying and transposing the theme throughout this four–measure invention exposition, you will need to add counterpoint to accompany the statements of the theme in the second, third, and fourth measures. Unlike species counterpoint, your counterpoint in these invention expositions must emphasize the harmony in each measure.

You may find the need to create “microharmonies” within a measure with some themes, such as a I–IV–I or I–$\left.\text{vii}^{\circ}{}^{6}\right.$ –I progression even though the overriding harmony of the bar is the I chord. Examples are found in the first two measures of the C major invention.

Given these pieces of information, you are prepared to begin writing tonal counterpoint in two parts.