@Haimy
You are not correct.
There are copyrights on both music and lyrics and the owner is entitled to performance royalties if they are played in a for profit enterprise (simcha band that gets paid).
If you don’t want to pay royalties, play your own original music or something in the public domain (so old the copyright has expired).
Please DON”T give legal advice if you are NOT a lawyer admitted to the bar and licensed,
It doesn’t matter if it is played on a keyboard or clarinet or sung………………