This is the 4912th most frequent Russian word.
классическую
"Classical."
The word 'классическую' is used as an adjective, in accusative singular feminine form, to describe the type of music (classical) that is being listened to.
Я слушаю классическую музыку каждый вечер.
I listen to classical music every evening.
Here, 'классической' is used as an adjective in dative singular feminine form, modifying 'школой', to describe the particular style of the ballet school.
Она занимается классической балетной школой.
She attends a classical ballet school.
In this sentence, 'классической' is an adjective in dative singular feminine form, describing 'живописи' as referring to classical painting style.