Music is, I suppose, one of the most natural and intuitive art forms in the world -- at its most primitive, you don't need any sort of tool or equipment to produce, since your own body is all you effectively need. And bad or good, ANYONE can do it. Probably that's why music is one of the art forms that "speak" the most to people, since not only the sounds are something very easy to connect to, but it gives you a pretty clear interface to the artist producing them; those "emotional" singers emote like that exactly to make the listener "see" or "feel" it.
That's not ALL that music is about, though, and I think that's a common misconception. "Feeling" the music is good, but it's not sufficient, really. Ever since I reached a certain maturity in listening to music, I've been naturally leaning towards trying to understand my music makes me feel the way I do. And I say that not in terms of "oh, the artist puts so much emotion in this!", but in terms of "why does that arrangement fit the melody so well?". It's pretty crazy, but sometimes it's tough to realise that, in a music recording, every little detail and little sound has most likely been painstakingly and carefully PUT there. It just didn't appear by magic, or because it was "meant" to be there - somebody decided it sounded good there, and put it there. How did THAT happen? How do those ideas appear? It's a process that definitely fascinates me, and I like analysing music in those terms, searching and discovering the little combinations that make music work, sometimes without us truly noticing.
And I don't think it's a "cold" or "boring" way to listening to music, really. Sometimes people think that "overthinking" music takes the fun away from it. In my case, it's the opposite! It's a somewhat "scientific" way of listening to music, and I honestly think science is absolutely beautiful and fascinating. So, why not using that approach on art? You don't need to give up entirely your feelings in order to study music. Sometimes they seem like mutually exclusive things, but honestly, I think some people just like to show off. I certainly don't. But yes, I do believe that the emotional response to music is not something you can measure and describe, because it's FAR too personal and subjective. But the sounds themselves have objective properties, and they can lead to interesting observations. Emotions aren't to be observed, and they come from within us. I don't deny they exist and affect us, but they don't reach us through the air, like the soundwaves do. Emotions can be, at best, expressed -- which is fun too, of course.