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This study explores the evolution of musical improvisation and variation across European musical history, analyzing stylistic, aesthetic, and methodological dimensions from Antiquity to the 20th century. Improvisation, as an integral aspect of musical creation, has its origins in the Hellenic modal system and Pythagorean numerical theories, which influenced liturgical music in both the Eastern and Western traditions. The research examines developments during the Medieval period, including the emergence of polyphon...