'asyllabical' originates from Greek and English formation: the privative prefix 'a-' (from Greek a-, meaning 'not') combined with 'syllable' (from Greek 'syllabē') plus the English adjectival suffix '-ical' (from Greek/Latin '-ikos'/'-ical').

'asyllabical' developed from 'asyllabic' (formed from a- + syllabic). 'Syllabic' itself comes from Late Latin/Greek roots related to Greek 'syllabē' and entered English via Medieval/Modern formations; the suffix '-ical' was later attached to form 'asyllabical'.

Initially it meant 'not forming syllables' (the direct negative of 'syllabic'), and this core meaning has been retained in modern linguistic usage.