retrograde inversion
English era
Definition
A transformation technique in which a melody is both reversed (retrograde: played backwards) and inverted (all intervals flipped up/down). The relationship between the Praeludium and Postludium of Ludus Tonalis is one of the most famous applications in the piano repertoire: the Postludium is the Praeludium played backwards and upside down, yet it sounds like a natural continuation, not a mathematical curiosity.
Interpretive Guidance
In the Postludium, do not perform the retrograde-inversion as a puzzle demonstration — let it be music. The notes may derive from transformation, but the phrasing and voice-leading should be as natural as any other Hindemith page.