There are two main patterns: unless the first syllable is accented, in which case it is H followed by all L, syllables between the second and the accented one are all H. There is always an upstep on the second one, unless there's actually a downstep. So in a three syllable word like that, you can have HLL, LHL, or LHH (you cannot have LLH), and you can also have one without an accent, in which case when you add an extra syllable like a particle you would get LHHH instead of LHHL like in the case of baai above.
Anyway except for a few two-syllable minimal pairs (hashi and hashi, or whatever), it's not a very prominent feature of Japanese phonology in my opinion.
(I may be failing to answer your actual question though, sorry)
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