In an earlier comment, I said "clarity and tonality". It just occurred to me that there’s an overlap of the two together which I could call harmonic completeness.
Subtle overtones can’t be heard without clarity, and these make music seem lively and realistic. An imbalanced tonality will also affect the ability to hear them. Without refined tonality, sound reproduction will be less full or pleasant to me. The way I am using tonality, I mean the totality of the degree of the presence of all potential tones across the audible range in relationship to each other.