What word describes something lacking in harmony, incompatible, or not in agreement?

The word that describes something lacking in harmony, being incompatible, or not in agreement is “incongruous.” This term refers to situations, elements, or ideas that do not fit together well or are out of sync with one another. For example, if two people have fundamentally different values and beliefs, their views could be described as incongruous because they clash and do not create a cohesive understanding or agreement.

In contrast, "inane" means lacking sense or meaningfulness, which does not directly relate to harmony or agreement. "Impermeable" refers to something that does not allow passage, especially of fluids, and does not pertain to compatibility. "Incremental" describes something that occurs in small steps or increments, which also does not relate to the idea of harmony or agreement.

Therefore, "incongruous" is the most appropriate and precise term for describing the lack of harmony or incompatibility among elements or ideas.