Relating to or characteristic of a rooster; having qualities associated with roosters such as arrogance or crowing.
From Middle English and Old English 'cock' (rooster) plus the suffix '-al' meaning 'of or pertaining to.' The word evolved from Proto-Germanic roots referring to the male fowl.
This word shows how we attach '-al' to almost any noun to make adjectives—it's such a productive pattern in English that many of these 'cockal-' words exist, even if they're rarely used today. Language is full of these ghost words that follow perfect rules but nobody says anymore!
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