Here is a list of The Harper Hall of Pern Books in Order.
#1 – Dragonsong (1976)
From the blurb:
A young woman allies with magnificent dragons in the first book in the Harper Hall trilogy, set within science fiction legend Anne McCaffrey’s beloved and bestselling Dragonriders of Pern series.
Every two hundred years or so, on the planet colony of Pern, shimmering Threads fall from space, raining death. Yet the great dragons of Pern, mounted by the stalwart dragonriders, scour the skies with fire to destroy the deadly Threads and save the planet.
But it was not Threadfall that made young Menolly unhappy. It was her father who betrayed her ambition to be a harper, who thwarted her love of music, because she was a woman. Menolly had no choice but to run away. When she came upon a group of fire lizards—wild and smaller relatives of the fire-breathing dragons—she let her music swirl around them. She taught nine of them to sing. And suddenly Menolly was no longer alone—she was Mistress of Music, and Ward of the dazzling fire dragons.