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"Her legacy will live on, through them and the countless others she inspired," he said.
Hughes offered condolences to Vallely's husband and children and all "those who had the pleasure of playing music with her, or learning from her".
SDLP Councillor Thomas O'Hanlon described the news as "devastating".
He said that while Vallely was originally from Donegal, "she made Armagh her home".
"What an extraordinary contribution she made to the cultural and musical life of our city, this island and far beyond over many decades,"he said.
O'Hanlon said that in recent years, he worked with Vallely, and witnessed the "patience, care and encouragement she gave to young people".
"She was a gifted teacher, an experienced administrator and Director of Music, but above all she was someone who gave so generously of herself to others," he said.
