I noticed that there are a lot of words in Standard Japanese which have more than one accepted pitch accent pronunciation; is generally one always preferred?

In the last year or so of studying I noticed that some words are listed with more than one acceptable pitch patterns.

Now what I always wondered is: are most of these words still *supposed* to be pronounced in the first listed way and are uncommonly or no longer generally pronounced in the other patterns or are they generally totally interchangeable?

If the latter is true, what determines what pronunciation is chosen, generally speaking?

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I understand this is quite a broad question and that it probably is a matter of “specific” words being more commonly pronounced one way and other words commonly pronounced two or more ways so if you want you can give specific examples of words and how and why they are pronounced that way