The fishery forms part of the Common Good of the old royal burgh area.
Burgh Island, which inspired some of Agatha Christie's murder mysteries, is 250m (820 ft) from the beach.
So far Yoko Ono, Steven Gerrard, Ken Dodd, Cherie Booth and Chris De Burgh have all signed up.
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According to Australian media, van der Burgh admitted he'd broken the rule but only because "99%" of swimmers do.
The beds were originally gifted to the Royal Burgh of Tain by King James VI of Scotland in 1612.
Founded in 1897, Glen Moray is located on the banks of River Lossie, in the Royal Burgh of Elgin, the capital of Speyside.
Agatha Christie is said to have written "And Then There Were None" and "Evil Under The Sun" while staying on nearby Burgh Island.
Van der Burgh also broke a mark set at the 2009 championships in Rome, shaving Australian Brenton Rickard's old mark of 58.58 seconds.
The beach is overlooked by the Burgh Island Hotel, a favourite haunt of writer Agatha Christie, and has been a location for several films.
Highland Fresh Mussels began trading in 1998 with four directors - three Highland councillors and a representative of the local community within the Royal Burgh.
Surrey County Council is due to submit plans for a separate housing development on the former de Burgh School site in Banstead in the coming weeks.
Introduced by Paul Van der Burgh, Director Lexus Europe, the Lexus Press Conference will be held at 8.45 AM CET on September 27 (hall 4, stand 120).
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The mussel scalps belonged to the Crown up until 1612, when ownership and the right to fish for them was bequeathed to the royal burgh in perpetuity by James VI of Scotland.
South Africa's Cameron van der Burgh put in the fastest 50m breaststroke time in the world this year, a Commonwealth Games record of 27.18 seconds, to win gold and complete a 50m-100m double.
The other day, Solve Climate News provided in-depth coverage of a small regional business story with global ramifications: a battery maker called Axion Power in the Rust Belt burgh of New Castle, Penn.
After learning that Australia's coach had complained about his kicks, van der Burgh told reporters he thought the situation was "pretty funny" and noted that the video also shows an Australian doing the very same thing.
Swimming's micro-scandal came last week after South African swimmer Cameron van der Burgh was asked by reporters about an underwater video that showed him using three underwater "dolphin" kicks at the start of a breaststroke race.
"I just have to pay tribute to Alexander Dale Oen tonight, I know he has been with me this year, I think he helped me finish the race in such a strong manner, " van der Burgh said.
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