An arrangement is a musical reconceptualization of a previously existing song. In copyright law an arrangement is considered a derivative work. The holder of a copyright has the exclusive right to create derivative works, therefore the arranger must receive authorization from the owner of the original work. Co-publishing deals are often reached between the arranger and the original copyright holder. If you arrange a song that is in the public domain, that arrangement can be granted a copyright, however only the newly created parts of the work are protected.
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