'non-metrical' originates from English, specifically formed from the prefix 'non-' meaning 'not' and the adjective 'metrical,' which ultimately traces to Greek 'metrikos' from 'metron' meaning 'measure' or 'meter (poetic rhythm)'.

'metrikos' in Greek passed into Late Latin 'metricus' and then into English as 'metrical.' The compound with the English privative prefix 'non-' emerged in Modern English to denote the absence of meter.

Initially, it meant 'not having meter' in poetry, and it continues to denote absence of regular meter or beat in poetry, music, and related analyses.