'even-metered' originates from English, specifically a compound of 'even' and 'meter(ed)'. 'even' ultimately comes from Old English 'efen' where 'efen' meant 'level, equal', and 'meter(ed)' is built from 'meter' which derives from Greek 'metron' via Latin 'metrum' meaning 'measure'.

'even' changed from Old English 'efen' to Middle English 'even' and retained the sense 'level, equal'; 'meter' came from Greek 'metron' → Latin 'metrum' → Old French/Latin-influenced Middle English 'metre' and then modern English 'meter/metro-' with the adjectival suffix '-ed' forming 'metered'. These elements were combined in modern English to form the compound 'even-metered'.

Initially, 'even' meant 'level/equal' and 'meter(ed)' meant 'measured/with measure'; over time the compound came to mean specifically 'having a regular, consistent metrical pattern' (i.e., a steady rhythmic measure).