Question

We make a blessing before eating food (taste), when inhaling a fragrant aroma (smell), and upon seeing something wondrous such as a rainbow (sight). So why is there no blessing for beautiful music (hearing)?

Answer

There are several classes of blessings, each with its own set of parameters.

Natural Wonder

There are blessings we make in response to the awesomeness of G‑d’s natural world, which is the closest we can get to even an inkling of just how magnificent G‑d Himself is.

This includes seeing natural wonders such as mountain ranges and oceans, or experiencing the magnitude of an earthquake or lightning strike, as well as the sound of crashing thunder.

So there is a blessing to be said over sounds, but it is limited to natural sounds (like thunder) and excludes man-made sounds (like music).

Experiencing Pleasure

Then there is another class of blessings, which we say before a pleasurable experience. This includes the blessings over foods and aromas, both of which enter our bodies and sustain us.1 This does not, however, include that which we experience through sight (a bright light), sound (music) or feel (a refreshing swim or a cool breeze), all of which are “external.”2

Milestones

There are also blessings said to praise G‑d for the pleasure of reaching milestones or experiences (such as the birth of a child or purchasing a new home). Listening to fine music would not fall under this category either, since it is not tied to a specific event.

If you read through Maimonides in Hilchot Berachot, Chapters 9 and 10, you will see these categories explained quite neatly, and in general accordance with what I've written above.