'nonmusical' is formed in Modern English from the prefix 'non-' (from Latin 'non', meaning 'not') + 'musical' (from 'music').

'music' comes from Greek 'mousikē' → Latin 'musica' → Old French 'musique' → Middle English 'musike', from which 'musical' developed; the negative prefix 'non-' was later attached in Modern English to form 'nonmusical'.

Initially, the elements meant 'not' + 'related to music'; the overall meaning has remained 'not musical' but now covers both absence of musical quality and lack of relation to music.