Which term is used to describe melodies or patterns that manipulate intervals in a reversed manner?

The term "Retrograde Inversion" refers to a compositional technique that involves taking a melody or musical pattern and reversing both its pitch and its interval relationships. This approach creates a transformation of the original melody, maintaining the same intervals but presenting them in reverse order.

In this context, the term captures the essence of manipulating intervals not just by inverting them—which would typically involve transforming an upward interval to a downward one and vice versa—but also by reversing their sequence. This makes "Retrograde Inversion" the most fitting term for a process where both the order of pitches and their relationships are flipped around, resulting in a distinctive new melody that retains structural connections to the original.

Understanding this concept is crucial in advanced music theory, as it highlights sophisticated ways composers can play with musical material to create variations and iterations that build upon existing themes.