Instead, councillors are considering proposals to spread the specialist resources across four sites in the Scottish capital, which they say will reach more children.
Former pupils at the school – housed in Broughton High and Flora Stevenson Primary – include Shirley Manson of rock band Garbage and the late Martyn Bennett, a pioneer of modern Celtic fusion.
Mary Campbell, education spokeswoman of the Green party, said the council was “jumping the gun” in putting a Scottish government grant at risk – and might not save a planned £363,000 after all.
She said: “I want children and young people across the city to benefit from music, but the provision at Broughton and Flora’s has given an extra focus for those children with a real talent, and allowed them to flourish. It is important that there is a provision, open to all, within the public sector, rather than only for those who can afford private tuition.”
Education convenor Ian Perry said the plans were open to consultation. Current bands, orchestras and access to instruments would remain unaffected.
He explained: “The school would be delivered in several sites across the city, so fulfilling our commitment for developing our gifted and talented pupils. In addition, we would explore ways of strengthening our partnerships with professional music organisations and we have committed to protecting free school music.”
Parents have started a campaign against the proposals, amid fears that national funding will be cut and standards slip.
The centre combines musical excellence and mainstream education, with many students going on to study at conservatoires around the world.
The school’s director, Tudor Morris, writes on the school’s website: “Nowhere else in Europe is there a school in the maintained sector which offers a complete specialist music programme from primary to secondary level in two neighbouring centres.
“The happy association with Flora Stevenson Primary ensures the musical development of our students from an early age within a caring and sensitive framework.”