To make classical in style or character; to render something in a classical manner or to impose classical principles upon it.
From 'classical' + '-ize' (to make or cause to become). The '-ize' suffix is productive in English for creating verbs from adjectives.
Composers who 'classicalize' folk melodies transform them—think of how Brahms took peasant dances and made them symphonic; the verb captures that act of elevation and transformation according to classical rules.
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