Unfortunately the only way to have your music continuously play would be to create several iframes (essentially a page within a page). Please take a look at this post: creating an iframe.
It will take some time, but essentially your homepage is just going to be your logo, maybe a header image, and then the music file (not text, images, etc..). All your other pages will want to be your site, but without the logo and header image. On your home page you will then add step 3 code on the attached thread, changing the iframe.html to whatever you have your home page content on (ex. index1). That code will then open up your homepages content and because it is in an iframe, any link they click on will open within the iframe and not reload your actually index page.
Hopefully that makes sense. If not please let me know and I can further clarify.