'harmonious' and 'combine' are older English words joined together: 'harmonious' (from Late Latin 'harmoniosus' via French and ultimately from Greek 'harmonia' meaning 'agreement, concord') and 'combine' (from Latin 'combinare', where 'com-' meant 'together' and the root was used for 'join').

The compound phrase 'harmoniously-combined' is a modern adjectival formation combining the adverb 'harmoniously' (from 'harmonious' + English adverbial suffix '-ly') with the past participle 'combined' (from 'combine'). Individually, 'harmonious' and 'combine' entered English via Latin/French and evolved into current forms; they were later used together in English to describe things joined in a pleasing way.

Initially, elements like 'harmonious' emphasized musical or formal agreement and 'combine' meant 'to join together.' Over time, their combined use came to specifically describe parts joined so they produce a pleasing, well-matched whole — the current meaning.