It is a well-known fact that Bach could take a simple chorale melody [henceforth referred to as 'CM'] and embellish it in various ways as he does in his chorale preludes for organ. In such cases, and also in certain cantata mvts. the CM is presented in its entirety. However, there are quite a number of instances where the CM is only hinted at with only the notes for the CM incipit or the Stollen at most being present. This is a CM allusion which may not have served quite the same purpose as the inclusion of an untexted CM as played by an instrument with long notes in the manner of a normal cantus firmus presentation. In the latter case, the audience is expected to make a meaningful text connection with simply the notes that are being played. In the following examples, however, the CM is so completely integrated with another subject or melody that it could easily go unnoticed by both performers and listeners. Another way to look at these examples is to consider them as being inspired by the CM. As Bach evolves a new musical subject or theme for a cantata mvt., a CM is always in the back of his mind. It provides a melodic structure upon which Bach can devise new and original ideas without entirely losing sight of the CM.
For each example, the CM (usually only the incipit or Stollen) is given first to establish the base from which Bach worked. After that examples from the cantatas follow. In each example, Alfred Dürr and Friedrich Smend, noted Bach scholars. both of whom have published commentaries on the cantatas from which these examples are derived, point out (the red notes identify the CM) where and how the CM is found embedded in the new material Bach has created from them.