The lawsuit said Sirius in particular reduced by 10 percent to 15 percent the gross revenues it reports to calculate the royalties because that corresponded with performances of pre-1972 recordings.
The royalty rate that would be charged against those gross revenues ranged from 6 percent in 2007 to 8 percent in 2012, according to SoundExchange, which was established by the Recording Industry Association of America.
"We cannot sit by and watch this multi-billion dollar company reap record profits from the creative contributions of artists and labels without paying them everything they deserve," SoundExchange Chief Executive Michael Huppe said in a statement.
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Representatives for Sirius XM did not immediately respond to a request for comment.
But in the complaint, SoundExchange said Sirius had taken the position that the statutory license established under federal law does not cover pre-1972 recordings.
Sound recordings were not given federal copyright protection until 1972 and instead relied on state law for protection.
The lawsuit also accuses Sirius of, among other things, excluding from its revenue calculations money it earned from customers subscribing to its Sirius XM Premier package and of failing to make timely royalty payments.
The lawsuit seeks $50 million to $100 million or more, along with appropriate late fees and interest.
The case is SoundExchange Inc. v. Sirius XM Radio Inc., U.S. District Court, District of Columbia, No. 13-01290.