I used the phrase "we'll mull it over" in an e-mail. My intent was to let the readers know that we (the team) needed to give it due consideration and come up with a considered response to their obviously important question. To my mind, we clearly needed to think things over, but for how long? I meant overnight (though didn't say so), but my audience assumed we would take a week.
What period of time (if any) does the use of the word mull convey?
Mulling takes an indeterminate time. If you're mulling wine, you heat gently, and add spices; it might take twenty minutes. If you're mulling over a life-changing decision, you might take several weeks, possibly longer. Anywhere in between might be counted as mulling.
I don't believe that the word mulling in your context has any period of time associated with it. It refers to the act of thinking something over or considering something in one's own mind or as a group. Your audience may have assumed a week for a response simply because they estimated it would take that long. If their question was indeed important you may have been better off giving them an explicit timing for your response: "...we'll mull it over and give you an answer tomorrow."
Mulling something over is vague time-wise; you can safely assume a week, and probably longer.
The phrase is troublesome not just because it is vague, but also doesn't convey a sense of serious consideration; it sounds half-hearted. It's best to avoid it in a business e-mail.
To mull, in the context given from the question, means think about (a fact, proposal, or request) deeply and at length. The word is a little vague on how much time thinking will take.
Instead of mull you can use ponder, consider, think over, think about, reflect on, or give some thought to.
In this particular case, it could very well have meant "We have no intention of getting back to you EVER, but we're not going to come out and say that, we're going to leave you hanging."
It is the fact that it is so vague that allows it to be used this way. In business or other negotiation/communication, being anything less than definitive frequently means either saying "No" or revealing your own lack of understanding.
If you meant "a week" it would have been courteous, more informative, and an indication of sincerity to have said "we'll mull it over and get back to you in a week".
To expect your mail recipient to consult a dictionary for the literal meaning of to mull would be stretching it a bit too far. The impression it gives is one of casual dismissal, which is not appropriate in business communications.
I always thought the word mull was associated with the Old English word fortnight (two weeks).
