Sentimentally I am disposed to harmony; but organically I am incapable of a tune.

Lamb contrasts inward inclination with bodily limitation: he feels drawn to “harmony” in the emotional or imaginative sense, yet claims his physical constitution (“organically”) prevents him from producing or perhaps even properly carrying a musical “tune.” The wit lies in the mock-scientific precision of “organically,” which turns a simple confession of being unmusical into a comic diagnosis. More broadly, the line reflects a recurring Lamb theme: the gap between sensibility and capacity—wanting to participate in an art or social grace, but being thwarted by temperament, nerves, or sheer inability. It’s self-deprecation used to humanize the speaker and to defend taste and feeling even when technical skill is absent.