Alternierte

Alternierte refers to a concept found in various fields, most notably in mathematics and music theory. In mathematics, "alternierte" can describe a series or a sum where the signs of the terms alternate, such as + - + - ... or - + - + ... . This alternating pattern is a characteristic feature of certain mathematical sequences and series, influencing their convergence properties and behavior. For example, the alternating harmonic series is a well-known example.

In music, the term "alternierte" is often used in the context of organ music, particularly in Baroque and Classical periods. It refers to a practice where a chorale melody is presented in two alternating forms: a plain, unadorned version and a more elaborate, ornamented version. This technique allows for a richer and more varied performance of a single melody. The organist would typically play the plain version with the pedals and the ornamented version with the manuals, or vice versa, creating a dialogue between the different voices. This interplay between simplicity and complexity is a hallmark of this musical style. The concept of alternation, in general, signifies a change or succession between two distinct states or elements.