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My understanding is that clauses starting with "unless" should always be in the present tenses,
i.e. simple present, present progressive, and present perfect.
Could you please provide any examples, if any, using other tenses than the ones above?
Holding my breath.
Comments  
'I can meet you at noon tomorrow, unless you will be busy then.'
'I'll help you with your homework at noon, unless you will have finished it by then.
'Unless you will be arriving very late, please call me as soon as you disembark.'
Hontoni arigato gozaimas. (one of the few Japanese sentences I know)

What if I say or write your examples after editing them slightly as follows?
(1)'I can meet you at noon tomorrow, unless you ARE busy then.'
(2)'I'll help you with your homework at noon, unless you HAVE finished it by then.
(3)'Unless you ARE arriving very late, please call me as soon as you disembark.'

I feel (1) and (3) convey the same messages as the original sentences.
If that is the case, would the choice of tenses be just a matter of personal preference, or are there any subtleties?

In case of (2), however, I myself somehow hesitate to give a credit to my own editing. "will have finished" seems natural because of the phrase "by then."

Your further comments will be highly appreciated.
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Hi KM,

Gee, I thought your screen name was a rebus of your real surnname.

(1)'I can meet you at noon tomorrow, unless you ARE busy then.' Same practical meaning; speaker is thinking more of being there then than being here now.

(2)'I'll help you with your homework at noon, unless you HAVE finished it by then. Same practical meaning; speaker is thinking more of the process of finishing, which has already begun.

(3)'Unless you ARE arriving very late, please call me as soon as you disembark.' Same practical meaning; speaker is thinking more of the 'scheduledness' of the arrival-- that is the use of the present progressive as a future form.

Those are the subtleties, mostlly too subtle to worry about.
"unless" is not different from any other situation which requires a coordination of tenses in two or more clauses.

When I was young, every summer we used to go and live in a little cottage by a lake - that is, unless my dad had a conflict with his work. We would go swimming every day unless the weather was bad. We had a phone, but it hardly ever worked unless you shook it violently before dialing! One summer we decided to go to a nearby restaurant for my sister's birthday. We had no idea it was so popular. The place was packed! We soon found out that no one could get in unless they had made reservations at least a week in advance.

"unless" also works somewhat like "if" in terms of the three common conditional patterns.

1. We'll go swimming if the weather is good.
We'll go swimming unless the weather is bad.
2. I would take my umbrella if the weatherman predicted rain.
I wouldn't take my umbrella unless the weatherman predicted rain.
3. You would have gone to that movie if you had known in advance how funny it was.
You would have gone to that movie unless you had known in advance how awful it was.

I'm sure you can think of better examples!

CJ Emotion: smile
Thanks a lot, CJ.

Thanks to your advice, I have now gotten a much clearer picture regarding the usage of "unless." Having summed up the tips from you and Mister Micawber, I am about to scrap my apparently ill-founded understanding. Yet, I am still a bit hesitant. The dictionary
I often refer to says "unless" is rarely used in the subjunctive mood. It also offers an example
that shows "If I had not studied..." cannot be changed to "Unless I had studied..."
I'd say your example sentences 2 and 3 are the subjunctive patterns. I know dictionaries are not always right and the one I have was published a couple of decades ago. Would you rather think the rule laid down in the dictionary is archaic, failing to reflect changes in grammar rules ? As I said before, I am on your side.
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I think the truth is somewhat the reverse of what you are suggesting. The tendency is to move away from the subjunctive, so my use of it in the examples shows you just how old-fashioned I am! Suppose "rare" means one in several hundred thousand people. In that case you've just had the good fortune to run into the "one"! Emotion: smile

I would trust the dictionary unless it were published more than 75 years ago. Emotion: smile

you can't go into the reception unless you've got a ticket.