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I've been coming across these three lately in a visual novel that I've been using to try to learn to read Japanese, and it seems their usage is not that interchangeable.
I'd like to confirm/deny if my intuition is correct.
解る seems to be quite dry, esp. when used to address the speaker in a "you get it?", patronizing manner. 分かる seems mostly neutral, worldly and interchangeable with わかる. As for 判る, I'm not really sure. Is it to just ascertain already suspected facts, e.g. time/weather? This post helped to get the general gist about 分かる. This was useful in a way but I feel like it's only scratching the surface.
For example, 話がわかる seems like an expression without any imbedded negative connotation, i.e. a type that 'gets it', much worldly wisdom and such. However, here, 話の解る seems to be more like 'you get it' in a dry, patronizing manner - is that down to the choice of Kanji in わかる, or simply context?
NB: A is B's master [マスタ] (it's a novel about magi and their hero-like familiars).
It's obvious from A's follow-up that she's frustrated with B's cheekiness. Would replacing 解る with say わかる make B's phrase it a lot more mild on A (as in, I'm relieved I got a down to earth マスタ, buddy buddy way)?
I would be grateful if someone could confirm/deny my intuition about 解る and clarify the essential usage of 判る. Resorting to Japanese sources isn't very helpful as they seem to refer back and forth to ideas that are already assumed to be intuitive to the speaker (and probably differ in the ways an English language-speaking person would interpret that idea, as is the case with any foreign language).