Superlative form of gladsome; most happy, joyful, or filled with gladness.
From gladsome plus -est, the superlative suffix. This is the highest degree of the archaic adjective gladsome.
The 'gladsomest' celebration would be the happiest one possible—but you'd never hear anyone actually say this! It's a grammatically correct 'fossil word,' something that follows all the rules but has been replaced by more modern expressions like 'the happiest' or 'the most joyful.'
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