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Circle Records was founded in January 1946 by Rudi Blesh and Harriet Janis. They heard great jazz drummer Warren "Baby" Dodds playing inventive solos while in New York City with Bunk Johnson's band. Blesh said that he previously hated drum solos, but was mesmerized by what Dodds played. He and Janis said that there ought to be recordings of this, but regretted that it was probably far too esoteric for any record label to issue—then decided to start their own label. The name "Circle" was suggested by fellow audience member Marcel Duchamp, who said "Records are circles, and besides, no one can call you squares."
Blesh and Janis continued the label until late 1952, after which it was inactive for a number of years until the mid-1960s when it was bought out by GHB/Jazzology Records owner George H. Buck, who reissued Circle material on LP and later compact disc.
In San Francisco, there was an unrelated record pressing plant called "Circle Record Company." When the owners of the pressing plant decided to start a record label, they couldn't use the Circle name because this label had the name already. So the label was called Fantasy Records.