In 1964, Cordero held his first concert at the
Ponce Museum of Art located in the city of
Ponce. He also worked as the producer of the television show
La guitarra y sus temas (The guitar and its themes) on WIPR-TV. After the series went off the air, Cordero traveled to
Madrid, Spain where he continued to take guitar and composition lessons. While in Spain he composed
Pavana Jibara and
Danza Puertorriqueña the first
danza written for a guitar. In 1970, he made his debut outside of Puerto Rico when he held a concert in
Aruba. He formed a group called "Quinteto de Federico A. Cordero" with Italian
cellist Enrico Orazi, the
violins of Roberto Alvarez and
Francisco Morla and the
viola of
Jaime Medina. In 1971,
Guitar Player magazine published an article about Cordero, and Great Britain's
Guitar News, the official publication of the International Classic Guitar Association, featured Cordero on its cover. That year he also held concerts in various cities of Switzerland. In 1974, he was invited to the
White House by President
Gerald Ford to give a concert. He performed with his group which also included the
pianist Vanessa Vassallo and the
tenor Edgardo Hierbolini. In 1975, Cordero was invited to participate in a forum by the president of the Guitar Committee of American String Teachers Association to help create a system to teach guitar playing. That year he went on tour to Germany, Italy, Spain and
New Orleans, United States. In 1983,
Soundboard magazine published his articles "The Interaction Between Manuel Ponce and
Andrés Segovia: 1923-1928". In 1987 he became the first Puerto Rican to be named to the board of directors of the Guitar Foundation of America. ==Recordings==