If elven women were aware of the day of conception, as burrahobbit's quote indicates, they must have had some kind of active control over their reproductive capability. In that case, I'm not sure that menstruation would have happened, since it only occurs when conception does not take place.
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'Mercy!' cried Gandalf. 'If the giving of information is to be the cure of your inquisitiveness, I shall spend all the rest of my days in answering you. What more do you want to know?' 'The whole history of Middle-earth.. .'
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