Leszek H. Ward
Shakespeare wrote The Tempest for the Lord Chamberlain's Men, the acting company in which he had a financial interest. Shakespeare and his men are often associated with the famous Globe theatre, which housed the majority of their plays. The Tempest, however, "seems to have been written for and performed at no fewer than three distinct venues: the court, the Globe, and the Blackfriars."
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The Blackfriars (built inside a monastic hall of the same name) was a much smaller and more intimate setting than the Globe, and it would have attracted a much smaller and more uniform audience to performances markedly different from those at most outdoor theatres. A smaller (indoor) stage, a seated audience, a more concentrated and complicated musical performance, and the need for artificial lighting would have greatly affected the kinds of plays Shakespeare was writing for his company.
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It is not surprising that a play so reliant on visual and auditory spectacle was one of the first to be written for this new setting.