You don't absolutely have to learn to read and write sheet music but it opens up whole new worlds of musical opportunity for you if you can.
Think of how different your life would be if you had never learned to read and write English (or any other language). You wouldn't be able to ask questions here on this forum. Your knowledge would be limited to the size of what you could memorize. And it would be difficult to obtain new information to memorize from people in different cities or different countries because you wouldn't be able to research who you should ask about information you were interested in. You would always have to talk to a person directly, and take up their time to get them to repeat information over and over and over, until you were sure you had it memorized correctly.
Being able to read and write music is very similar. It allows you to share your musical ideas with any other person in the world who can read music, talk about musical ideas in specific detail so you can improve your music, and learn any piece of music you want, without having to have someone sit down and teach it to you, or find you a recording. I generally perform maybe 1,000 pages of music every single year. And I'm not even a full-time musician. I wouldn't be able to learn anywhere near that much music if I had to memorize every note. But I don't have to memorize, I just read it. The same way I can sit down and read a novel. And I can share the music I write with people all over the world. No one would ever perform the music I write if all the performers had to memorize all their notes from a recording I made. But since they can all read sheet music, like I can, one person can find a copy of a piece I wrote, decide it looks interesting, and send a copy to everyone else in the group to read over and practice on their own. And at the concert, they don't have to have my piece memorized, they can still be performing by reading.
The one quality that all the professional working musicians I know have in common, is that they can sight read sheet music, accurately, and at the proper tempo, the first time someone hands them a piece of music. The conductor of an orchestra doesn't have time to sit down with each player and teach them their part. There are too many players and too many parts and too many hours of music to learn. They all have to be able to read it on their own. That way rehearsal time is spent deciding how loud the loud bit should be, or how a tempo change will be handled... all the things that make music feel musical, instead of just teaching notes.
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