The 60-year-old, who was killed in the explosion on the Piccadilly line train at Russell Square on 7 July 2005, was born in Grenada.
As a young man, he moved to the neighbouring island of Montserrat, a British overseas territory, where he made his home and established his career as a police officer.
His son Astrid Wade, a firefighter in Montserrat, said: "He was well-respected in the Montserrat community, known for his dedicated service to the island as a police officer, as well as recording the calypso hit Signs of Christmas."
In 1997, Mr Frederick retired after 31 years in the Royal Montserrat Police, and moved to London.
He settled in Seven Sisters, north London, and took work as a museum security guard.
Mr Wade said it was the eruption of the Soufriere Hills volcano in the late 1990s that had made his father first think about leaving Montserrat.
"He was scared of the volcano so packed up and left.
"London became his second home but his mind and his heart were in Grenada, and his mum and dad are still there."
Shortly before his death, he had returned to his country of origin for several weeks to help his elderly parents rebuild their home, which had been severely damaged by Hurricane Ivan.
Mr Frederick had a couple of hits on the island and he recorded a CD when he moved to London. His musical talents earned him the nicknames Soul, Vision, Napo and Otis.
At the inquest into his death, Mr Wade said in a statement: "I knew my father as a friendly person who got along with everyone.
"A man who loved his music and participated in the local calypso competition every December (in Montserrat).
"I still hear his songs on the radio and it brings back his memory to me. I do miss him.
"Although we had our ups and downs, he was my father and I have a lot of feelings for him."
Mr Frederick also left behind a brother, Albert, who lives in the US.
Shortly after his death, Montserrat police commissioner John Douglas paid tribute to Mr Frederick, who he first met in 1967.
"He was a very committed and devoted police officer who took his job very seriously and he served his country well," he said.
Arthur Frederick's first love was music, and fittingly his songs can still be heard on the airwaves of his Caribbean island home.