PetrB,
I do, in fact, and have taken formal piano lessons for quite a long time! By "study music," I meant studying music in a college/university/conservatory!
But yes, I understand that "glaring gap" which you talk about. In truth, I do not listen to very much of the Baroque era. But that's what makes classical music itself so interesting. If we all had the same taste in music, there would only be one type of music, and that would be quite boring. As for 20th century music, I listen to some on occasion, but I love the Classical Era! Beethoven is excellent! I enjoy his sonatas very much.
Chopin, I enjoy immensely, especially when I need a break from heroism and passion.
His piano works are wonderful, especially his nocturnes!
And who knows? Maybe I will minor in music.... I also sing, and have a professional mentor for that. I am a soprano, though I am told that I could also sing alto. Have you done any singing/choir accompaniment? Did you ever want to?