This link will help you with the most common adverbs:
Generally and usually mean about the same thing.
Often by itself is a little less frequent than usually.
Most often - adding the superlative (most) - makes it a comparison with other times, and would probably mean almost the same as usually.
However, I get up at six most often sounds a little awkward to me. I would say either:
- I most often get up at six; or
- Most of the time, I get up at six. (This might be a particularly American way of saying it... )
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