This is just my personal accounting of the greatest composers of piano
concertos in order of preference:
1. Mozart - Not only did he write so many, but they are all gems. Nos.
17 through 24 are masterpieces. The best by a wide margin.
2. Beethoven - Five masterful works plus the Choral Fantasia.
3. Rachmaninoff - Close to Beethoven. His third is one of my favorites.
4. Brahms - A distant fourth.
5. Chopin - I know of the so-called orchestral weaknesses. But, I
greatly enjoy both his concertos.
6. Schumann - Similar to Chopin.
7. Prokofiev - A distant 7th.
8. Ravel - Very close to Prokofiev.
9. Gershwin - The one American.
10. Grieg - Somewhat overrated.
My honorable mentions are Saint-Saens, Bartok, and Hummel.
The two notable no-shows are Liszt and Tchaikovsky. For me, their
concertos are romantically "over the top."
Don Satz
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