Antonymy is the lexical relation of opposition. The nature of the oppositeness may differ - e.g., contradictory ('true'-'false') or gradable ('tall'-'short') - and there may be variation as to the relationship in their formal encoding, whether the antonyms are expressed as distinct lexical forms (e.g., true vs. false) or if one form is derived from the other (e.g., true vs. untrue). We investigate the relationship between the two members of 37 antonym pairs across 55 spoken languages in order to see whether there are patterns in how antonymy is expressed and which of the two antonym members is more likely to be derived from the other. We find great variation in the extent to which languages use derivation (labeled neg-constructed forms) as an antonym-formation strategy. However, when we do find a derived form, this tends to target the member of the pair that is either lower in valence (positive vs. negative) or magnitude (more vs. less), in line with our hypotheses. We also find that antonyms that belong to a core set of property concepts are more likely to encode antonyms as distinct lexical forms, whereas peripheral property concepts are relatively more likely to encode the antonyms with derived forms.