Your question piqued my curiousity. As I am not yet motivated on this cold, wet Sunday morning to get off the sofa and make breakfast, I researched. Here's what I discovered and, although I make no claim to be a language scholar, it might answer your question.
Apparently there is a language process called "transliteration." Which, according to the Online Dictionary means to represent (letters or words) of one language into the corresponding characters of another alphabet. So the "words" remain the same, they aren't translated
like you'd translate French into English, but changed from one alphabet system into another.
So, when the Hebrew script is transliterated into romanized characters, the direction in which the text is read is reversed. That would answer your question. And it makes my head hurt to think about reading backwards and forwards!
I wonder, though, if the music had been composed by an ancient Hebrew-speaking composer and was actually written down somewhere, if there was some special music notation at that time that did read right to left?