"How music filled the air!" (with an exclamation point) is a more exciting and expressive way to express the idea of music filling the air. It conveys a sense of wonder and awe, emphasizing how the air is filled with music.
On the other hand, "How music filled the air." (with a period) is a simple statement describing how music fills the air. It is a more matter-of-fact way of expressing the same idea without any additional emotional emphasis.
Therefore, the exclamation point is more appropriate in this context.