Why do composers write so few violin concertos?
Beethoven and Mozart both played the fiddle, more than adequately. Mozart is documented as somewhat lamenting having to put the violin aside if he was going to have time to be a pianist and composer. Even being fully trained in orchestration or with first-hand knowledge of the instrument, single line instruments in general are a hellish pain in the @ss to write for, that is at least successfully, making anything interesting, sustainable, etc. I’m not up to it on skill level, but would find it a real pain to have to depend upon and sit in this upper tessitura for the duration of a work of symphonic length and proportions, write the accompaniment very carefully around the lower and lower middle registers so they weren’t lost in a texture, and on and on. Prokofiev was a virtuoso pianist and composer, and wrote virtuoso music for all players. He wrote two Violin Concerti, Five Piano Concerti, more than Five symphonies. Berg, like Beethoven, only wrote one, but it is a masterpiece. Ditto St