In The Twilight Saga, 'la tua cantante' seems very little explained, and, personally, I'm not going to wait for SMeyer to answer the question herself and dilute the whole phenomenon with her signature 'SMeyer Science'.
Disclaimer:
This theory is the speculation of an untrained, inexpert child; I may be incorrect, I may not be. The purpose of this article is to broaden the field for speculation, intelligent discussion, or correction on the blood that sings.

Here Goes:

This doesn't require very much knowledge of the basic anatomy of blood; all you need to know is that it carries important stuff throughout the body, like nutrients, oxygen, hormones, etc. I'm pretty sure Bella's blood smells all wonderful to Edward based upon two factors: genetics and nutrients (or diet).

I'm not covering genetics here under the belief that SMeyer is a follower of Mormonism, which holds the same basic belief of creation as plenty of other faiths, now without getting into to much detail, this belief is that everyone is distantly related because there were only two people originally.
As for diet, it seems impossible to tell from the books how each individual nutrient smells to Eddie, or other vamps, for that matter. So allow us now to look at Meypires for a moment.

It is known that drinking human blood makes a Meypire its strongest, and also known that during a Meypire's first year or so it is stronger and faster because of the human blood still in the system. Putting those thoughts together: A vampire's own blood makes it the strongest.

Which, of course, leads to my very simple theory: A vampire will be attracted to whatever blood will make it the strongest, fastest, best vamp out there, in a word, the blood most like its own. Therefore, la tua cantante happens when a vampire happens across blood most like its own.

That's basically it. :) All comments and constructive criticism is greatly appreciated. :)