Relating to or of the nature of an antiphon; characterized by antiphonal singing or alternating responses.
From antiphonic + -al (relating to). This is a longer form of the adjective antiphonic, with both forms used in music and liturgical contexts.
The fact that English has both 'antiphonic' and 'antiphonical' shows how musical terminology evolved—sometimes multiple forms survive just because different scholars preferred different endings.
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