How would I find 1000 participants to sing and play in an orchestra on Zoom?

1. Linkedin
2. Facebook.
3. Music forums
4. Instagram.
5. Bands / Orchestras.
Ask others on the above platforms to help. People enjoy sharing and participating in such things.
Sounds fun. Good luck
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Contact multiple orchestra's.
I know one in southern Ontario has already taken their performances online;
if your proposed vision is enticing and benefits them you might be able to collaborate with several orchestra's for a performance.
Why do you want 1000 participants?

This is a great question! Reminds me of a time when I was tasked with trying to find a marching band, choir, a cheerleading group, and a youth step dance team all in a specific city... What I thought, at the time, was an impossible task became way easier when I unexpectedly became quite the expert in these various fields. I would recommend reaching out to various schools, as they are all at home and most likely looking for projects to work on. In my experience, schools also had lots of great information. They informed me, at the time of my hodgepodge performance, that there was something called the Patriot Brass Ensemble, which is a national marching band association that is a non-profit, supporting veterans. They had talent all across the country. I then brought in a musical director, composer, and worked closely with all of the different groups to create a cohesive performance for the brand. Now, doing this all virtually, definitely changes the game. There are many tips and tricks on how to produce this for a virtual event or a zoom meeting. If you'd like more detail on this process or sourcing talent, I am happy to help!