Read is a homophone of reed. To read means to comprehend the meaning of something by interpreting the characters seen. A reed is a part of the plant of grass. In order to produce sound in a clarinet, it needs a reed in the mouthpiece. "Couldn't reed music" sounds like "couldn't read music" meaning they couldn't understand the music they were looking at. "Read" was replaced with "reed" to reference the clarinet reed used in the mouthpiece. This joke is playing on the word "reed" becauase it sounds like "read".
I wanted to be a clarinettist but I couldn ' t reed music .