Back in the Zoo during the mid 18th century, Saya is taught to play the cello and she is really good at it. When Hagi is brought over there and after Saya befriends him, she teaches him to play cello and violin. Years later, when Hagi has grown up, he excels his teacher and Saya hands him over her cello.
On Joel's birthday, Diva's freedome costs plenty of lives and Saya vows to repay her. Until she fulfils that objective, she sees it befitting for herself to handle swords only. She puts aside cello forever. Even after Hagi offers her to play when they are taking shelter in a church, Saya refuses.
Hagi, on the other hand, has the cello as a partner of lonely times. When Saya sleeps in hibernation period, he travels with the cello and plays it. Not only is the music a pastime, it also helps to bring flashbacks when Saya couldn't recall her memories. The cello music played by Hagi is also soothing during times of distress. Riku is interested and once urges Hagi to teach him to play which he does.