transpose has 6 distinct synonyms spread across 4 of its 8 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
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.
change the order or arrangement of
“Dyslexics often transpose letters in a word”
transfer from one place or period to another
“The ancient Greek story was transplanted into Modern America”
cause to change places
“interchange this screw for one of a smaller size”
transfer a quantity from one side of an equation to the other side reversing its sign, in order to maintain equality
put (a piece of music) into another key
change key
“Can you transpose this fugue into G major?”
a matrix formed by interchanging the rows and columns of a given matrix
Synonyms, antonyms and the broader and narrower relations for transpose come from Princeton University’s WordNet. Full sources and licences.