What is the source and reason for saying Tehilim 47 - 7 times before the blowing of the Shofar?
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Rivevos Ephraim 6:309:1 notes that the Arizal instituted the seven times; he also cites the Imrei Emes ( קרח שנת תרע"ו ) who cites the Arizal and gives a reason; see there. See also Likutei Maharich 3:70.
In addition: The Tamei Minhagim 717 brings that there are 587 letters n the psalm; 587 is the gematria of the word Shofar with itself (im hakollel).