Search Block - Search Current Page Only

Hello! I see in the documentation that we can limit a search block to a specific blog or collection, but I'd really like it to search the current page only. I am open to other solutions as well. 

The use case: I am listing about 100 songs and artists for sheet music. We are using an accordion block differentiated by genre to make the list a little more user friendly. Screenshots attached. This works fine for browsing. Alphabetizing will help too, but I'd love to have a search function for situations where students are trying to straight to a particular sheet music without having to click through the accordion. 

Very open to ideas! 

I don't think there's a simple way to have a search block that just works on a single page, sorry about that!