I think the latter is about frequency. But then, does it mean that the former is not used to describe the frequency of an event?
What exactly is the difference between 'hardly/scarcely' and 'rarely/seldom'?
I think the latter is about frequency. Yes.
But then, does it mean that the former is not used to describe the frequency of an event? Yes, I certainly wouldn't associate it with frequency. I think you may be thinking of how these words relate to the sequencing of events.
eg I had scarcely/hardly sat down when the phone rang.
The two events were almost simultaneous. The act of ringing came just after the act of sitting down.
There are also some other ways of using these words,
eg I scarcely/hardly know Tom.
meaning I have very little knowledge about him.
Best wishes, Clive
1. Hardly, barely, scarcely imply a narrow margin by which performance was, is, or will be achieved. Hardly, though often interchangeable with scarcely and barely, usually emphasizes the idea of the difficulty involved: We could hardly endure the winter. Barely emphasizes the narrowness of the margin of safety, “only just and no more”: We barely succeeded.Scarcely implies a very narrow margin, below satisfactory performance: He can scarcely read.
—Usage note 1, 3. Hardly, barely, and scarcely all have a negative connotation, and the use of any of them with a negative like can't or couldn't is often condemned as a double negative and thus considered nonstandard: I can't hardly wait. Such constructions do occur occasionally in the speech of educated persons, often with jocular intent (You can't hardly get that kind any more) but are not found in formal speech or writing. Whenhardly in the sense “only just, almost not” is followed by a clause, the usual word to introduce the clause is when: The telephone had hardly stopped ringing when (not than) the doorbell rang.
And the next clip is also from the same site. Thee is no discussion of the differences between rarely and seldom. They mean the same in terms of frequency in time.
Rarely: Usage Note: Strictly speaking, the use of ever after rarelyand seldom is redundant; She rarely ever watches televisionadds nothing to She rarely watches television. In an earlier survey a large majority of the Usage Panel found this construction unacceptable in formal writing. But ever has been used as an intensive with rarely for several hundred years, and the construction is common in informal contexts. By contrast, the constructions rarely (or seldom) if ever and rarely (orseldom) or never are perfectly acceptable: She rarely if ever watches television. She rarely or never watches television.
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