I don't understand this question, please clarify.

Dear Negi, "madness", is not a scholary defined mental disorder, but it is mainly a folk-usage or even a derogatory word for definining those people who seem to have lost contact with reality etc. But if we try to link the word madness with mental problems, we would link it with "psychotic" disorders like schizophrenia. A professor, when mentioning the history of schizophrenia, stated that the word "mad" is mainly used for people who had schizophrenia throughhout history. Now we do not need this "term" for defining abnormality. Maybe you can look up the exact mental problem with distinctive characteristics.

I'm wondering: If besides the usual psychotic context, couldn't something like psychopathy not be considered a kind of madness?

Madness, is a non-scientific and thus non-operationalized term which can refer to a wide spectrum of states like ecstacy, extreme levels of courage, psychopathy, mania, euphoria, schizophrenia and mental retardation for some people, so on and so forth. I think someone who is trying to understand "madness" should choose a specific form of disorder to deal with.

I would suggest that madness is the best term to use for disturbing behavior since I don't believe terms like mental disorder or mental illness have scientific validation. I am attaching a recent article that you may find interesting that goes into a bit of detail.