WordNet records no synonym and no antonym for rhapsody. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
an enthusiastic expression of emotion
“rhapsodies of joy”
(music) a free instrumental composition in one extended movement; typically emotional or exuberant in character
(in ancient Greece) an epic poem adapted for recitation
Synonyms, antonyms and the broader and narrower relations for rhapsody come from Princeton University’s WordNet. Full sources and licences.