Invertible Counterpoint

Most of Bach’s 2-part inventions display a technique called “invertible counterpoint.” The inventions that we’ve studied so far in labs, and in class, have given you an intuitive sense of how this works, so we’re ready to think about it as a method of composing.

Invertible counterpoint is any counterpoint that works well with the parts “inverted”: i.e., treble and bass parts trading places. It sounds complicated, but it’s not. Most counterpoint already favors imperfect consonances in its basic structure, and those intervals, when inverted, are still imperfect consonances. Most dissonance-resolutions work just as well when the moving voices trade places. So if you’ve applied the guidelines of 2-part writing in your previous assignments, and mastered them, there are only a few new problems that have to be considered in order to make counterpoint “invertible.” In invertible counterpoint, the only interval that is generally problematic is the 5th, because it inverts to a 4th.

Two invertible 5ths:

When composing invertible counterpoint, all P5 have to fit one of these two criteria:

  1. From a P5 on a strong beat, the bass moves down by step (forming a 6th) while the treble note holds steady. (This will invert to resemble a 4-3 suspension.)
  2. A fifth formed on a weak beat, passing by step or clear arpeggio between two imperfect consonances (or dissonances resolving to imperfect consonances).

In any other case, for example, P5 on strong beat in an arpeggio, or P5 on a weak beat with the bass descending to a sixth, the inversion of the counterpoint will produce an improper P4, creating a dissonance without a proper resolution.