Now feeling slightly upset that I've only been taught about English adverbial order and not about adjective order.
Things native English speakers know, but don't know we know:
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Reverse for me. I was taught the adjective order once (and promptly forgot, at least consciously). What’s adverbial order?
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The manner-place-time part of subject-predicate-object-manner-place-time. As in "I ate breakfast quickly at home today."
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I think "at home quickly" and "quickly at home" are both valid, with connotation that the second one is unusual.

Sep 4, 2016 · 7:03 AM UTC

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But I agree that "today" should either be the last adverb, or before the subject.
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Quick Googling suggests that the rule is less strict and maybe more affiliated with en-GB than I was lead to believe
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I quickly ate breakfast at home today. Today I quickly ate breakfast at home. Contextual?
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The rule doesn't even pretend to cover the order of adverbials at the beginning of a sentence.